Metrics for expax (section 3.5)

analyze27.0ms (0.8%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	6.3%	0%	0%	0%	6
75.9%	68.7%	21.9%	9.5%	0%	0%	0%	7
80%	68.7%	17.2%	14.1%	0%	0%	0%	8
86%	71.8%	11.7%	16.5%	0%	0%	0%	9
88.9%	71.8%	9%	19.2%	0%	0%	0%	10
92.4%	73.4%	6%	20.6%	0%	0%	0%	11
94.1%	73.4%	4.6%	22%	0%	0%	0%	12

Compiler

Compiled 13 to 8 computations (38.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-exp: 4.0ms (34.2% of total)

ival-mult: 3.0ms (25.7% of total)

ival-sub: 2.0ms (17.1% of total)

ival->: 2.0ms (17.1% of total)

const: 0.0ms (0% of total)

sample1.9s (59.1%)

Results

1.0s	5283×	1	valid
534.0ms	2973×	0	valid
18.0ms	323×	0	precondition

Precisions

Click to see histograms. Total time spent on operations: 794.0ms

ival-exp: 298.0ms (37.5% of total)

ival-mult: 204.0ms (25.7% of total)

backward-pass: 97.0ms (12.2% of total)

ival-sub: 92.0ms (11.6% of total)

ival->: 82.0ms (10.3% of total)

const: 21.0ms (2.6% of total)

Bogosity

preprocess50.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

48×	`fma-define`
22×	`sub-neg`
20×	`exp-sum`
19×	`fma-neg`
12×	`exp-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	143
1	58	143
2	88	143
3	126	143
4	169	143
5	203	143
6	248	143
7	298	143
8	315	143
9	331	143
10	335	143

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 (neg.f64 a) x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a (neg.f64 x))) #s(literal 1 binary64))
(neg.f64 (-.f64 (exp.f64 (*.f64 (neg.f64 a) x)) #s(literal 1 binary64)))
(neg.f64 (-.f64 (exp.f64 (*.f64 a (neg.f64 x))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (*.f64 x a)) #s(literal 1 binary64))

Outputs
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 (neg.f64 a) x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 x (neg.f64 a)))
(-.f64 (exp.f64 (*.f64 a (neg.f64 x))) #s(literal 1 binary64))
(expm1.f64 (*.f64 x (neg.f64 a)))
(neg.f64 (-.f64 (exp.f64 (*.f64 (neg.f64 a) x)) #s(literal 1 binary64)))
(neg.f64 (expm1.f64 (*.f64 x (neg.f64 a))))
(neg.f64 (-.f64 (exp.f64 (*.f64 a (neg.f64 x))) #s(literal 1 binary64)))
(neg.f64 (expm1.f64 (*.f64 x (neg.f64 a))))
(-.f64 (exp.f64 (*.f64 x a)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))

Symmetry

(sort a x)

explain187.0ms (5.8%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
132	1	(-7.546010639254621e-109 1.2526781628679343e+105)	-	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
0	0	-	-	`x`
0	0	-	-	`(*.f64 a x)`
0	0	-	-	`(exp.f64 (*.f64 a x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`a`

Results

76.0ms	218×	256	valid
27.0ms	110×	1024	valid
18.0ms	98×	512	valid
36.0ms	86×	2048	valid

Compiler

Compiled 46 to 22 computations (52.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-exp: 31.0ms (62.9% of total)

ival-mult: 9.0ms (18.2% of total)

ival-sub: 8.0ms (16.2% of total)

const: 2.0ms (4.1% of total)

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(expm1.f64 (*.f64 a x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize82.0ms (2.5%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(expm1.f64 (*.f64 a x))

Results

10.0ms	109×	256	valid
37.0ms	55×	1024	valid
7.0ms	49×	512	valid
19.0ms	43×	2048	valid

Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

composed: 45.0ms (47.8% of total)

ival-exp: 40.0ms (42.5% of total)

ival-mult: 4.0ms (4.2% of total)

ival-sub: 3.0ms (3.2% of total)

const: 1.0ms (1.1% of total)

series3.0ms (0.1%)

Counts

1 → 24

Calls

Call 1

Inputs
#<alt (expm1.f64 (*.f64 a x))>

Outputs
#<alt (*.f64 a x)>
#<alt (.f64 a (+.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 a (pow.f64 x #s(literal 2 binary64))))))>
#<alt (.f64 a (+.f64 x (.f64 a (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 a (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))))>
#<alt (.f64 a (+.f64 x (.f64 a (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64))) (.f64 a (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 a (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)))))))))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (*.f64 a x)>
#<alt (.f64 x (+.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 a #s(literal 2 binary64)) x))))>
#<alt (.f64 x (+.f64 a (.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 a #s(literal 3 binary64)) x)) (*.f64 #s(literal 1/2 binary64) (pow.f64 a #s(literal 2 binary64)))))))>
#<alt (.f64 x (+.f64 a (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 a #s(literal 2 binary64))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 (pow.f64 a #s(literal 4 binary64)) x)) (*.f64 #s(literal 1/6 binary64) (pow.f64 a #s(literal 3 binary64)))))))))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a	@	0	(- (exp (* a x)) 1)
1.0ms	x	@	0	(- (exp (* a x)) 1)
0.0ms	a	@	-inf	(- (exp (* a x)) 1)
0.0ms	x	@	-inf	(- (exp (* a x)) 1)
0.0ms	a	@	inf	(- (exp (* a x)) 1)

rewrite342.0ms (10.7%)

Algorithm

1×	batch-egg-rewrite

Rules

319×	`log1p-expm1-u`
318×	`expm1-log1p-u`
311×	`unpow-prod-down`
305×	`add-exp-log`
293×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	82	17
2	894	17

Stop Event

1×	node limit

Counts

1 → 48

Calls

Call 1

Inputs
(expm1.f64 (*.f64 a x))

Outputs
(+.f64 (pow.f64 (exp.f64 a) x) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))))
(-.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))
(-.f64 (pow.f64 (exp.f64 a) x) (log.f64 (E.f64)))
(-.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))))
(-.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))
(.f64 (expm1.f64 (.f64 a x)) #s(literal 1 binary64))
(.f64 (expm1.f64 (.f64 a x)) (log.f64 (E.f64)))
(.f64 #s(literal 1 binary64) (expm1.f64 (.f64 a x)))
(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2/3 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 2/3 binary64)) (cbrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/2 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (expm1.f64 (.f64 a x)))
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 (.f64 a x)) (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 (.f64 a x)) (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/2 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 3/2 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) #s(literal 5 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(/.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) #s(literal -1 binary64)) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 a) x) #s(literal -1 binary64)))))
(pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (expm1.f64 (*.f64 a x))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x))))) (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)))
(fabs.f64 (expm1.f64 (*.f64 a x)))
(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)))
(expm1.f64 (*.f64 a x))
(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))
(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 a) x) #s(literal -1 binary64))
(fma.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (exp.f64 a) x)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (pow.f64 (exp.f64 a) x)) (sqrt.f64 (pow.f64 (exp.f64 a) x)) #s(literal -1 binary64))

simplify121.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

689×	`times-frac`
554×	`prod-exp`
492×	`fma-define`
387×	`associate-r`
289×	`associate-l`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	8589936880
1	407	8589936824
2	1184	8589936808
3	3807	8589936784
4	7312	8589936784

Stop Event

1×	node limit

Counts

72 → 65

Calls

Call 1

Inputs
(*.f64 a x)
(.f64 a (+.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 a (pow.f64 x #s(literal 2 binary64))))))
(.f64 a (+.f64 x (.f64 a (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 a (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))))
(.f64 a (+.f64 x (.f64 a (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64))) (.f64 a (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 a (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)))))))))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(*.f64 a x)
(.f64 x (+.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 a #s(literal 2 binary64)) x))))
(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 a #s(literal 3 binary64)) x)) (*.f64 #s(literal 1/2 binary64) (pow.f64 a #s(literal 2 binary64)))))))
(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 a #s(literal 2 binary64))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 (pow.f64 a #s(literal 4 binary64)) x)) (*.f64 #s(literal 1/6 binary64) (pow.f64 a #s(literal 3 binary64)))))))))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+.f64 (pow.f64 (exp.f64 a) x) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))))
(-.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))
(-.f64 (pow.f64 (exp.f64 a) x) (log.f64 (E.f64)))
(-.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))))
(-.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))
(.f64 (expm1.f64 (.f64 a x)) #s(literal 1 binary64))
(.f64 (expm1.f64 (.f64 a x)) (log.f64 (E.f64)))
(.f64 #s(literal 1 binary64) (expm1.f64 (.f64 a x)))
(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2/3 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 2/3 binary64)) (cbrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/2 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (expm1.f64 (.f64 a x)))
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 (.f64 a x)) (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 (.f64 a x)) (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/2 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 3/2 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) #s(literal 5 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(/.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) #s(literal -1 binary64)) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 a) x) #s(literal -1 binary64)))))
(pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (expm1.f64 (*.f64 a x))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x))))) (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)))
(fabs.f64 (expm1.f64 (*.f64 a x)))
(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)))
(expm1.f64 (*.f64 a x))
(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))
(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 a) x) #s(literal -1 binary64))
(fma.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (exp.f64 a) x)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (pow.f64 (exp.f64 a) x)) (sqrt.f64 (pow.f64 (exp.f64 a) x)) #s(literal -1 binary64))

Outputs
(*.f64 a x)
(.f64 a (+.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 a (pow.f64 x #s(literal 2 binary64))))))
(.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64))) x))
(.f64 a (+.f64 x (.f64 a (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 a (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))))
(.f64 a (fma.f64 a (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) a) #s(literal 1/2 binary64))) x))
(.f64 a (+.f64 x (.f64 a (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64))) (.f64 a (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 a (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)))))))))
(.f64 a (fma.f64 a (fma.f64 a (fma.f64 a (.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))) x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(*.f64 a x)
(.f64 x (+.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 a #s(literal 2 binary64)) x))))
(.f64 a (fma.f64 a (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64))) x))
(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 a #s(literal 3 binary64)) x)) (*.f64 #s(literal 1/2 binary64) (pow.f64 a #s(literal 2 binary64)))))))
(.f64 a (fma.f64 a (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) a) #s(literal 1/2 binary64))) x))
(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 a #s(literal 2 binary64))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 (pow.f64 a #s(literal 4 binary64)) x)) (*.f64 #s(literal 1/6 binary64) (pow.f64 a #s(literal 3 binary64)))))))))
(.f64 x (fma.f64 x (fma.f64 x (fma.f64 x (.f64 #s(literal 1/24 binary64) (pow.f64 a #s(literal 4 binary64))) (.f64 #s(literal 1/6 binary64) (pow.f64 a #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (pow.f64 a #s(literal 2 binary64)))) a))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(+.f64 (pow.f64 (exp.f64 a) x) #s(literal -1 binary64))
(expm1.f64 (*.f64 a x))
(+.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a x)))
(expm1.f64 (*.f64 a x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))))
(.f64 #s(literal 2 binary64) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))))
(-.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(-.f64 (pow.f64 (exp.f64 a) x) (log.f64 (E.f64)))
(expm1.f64 (*.f64 a x))
(-.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))))
(/.f64 (expm1.f64 (.f64 #s(literal 3 binary64) (.f64 a x))) (-.f64 (pow.f64 (exp.f64 a) (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (exp.f64 a) x))))
(-.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))
(expm1.f64 (*.f64 a x))
(.f64 (expm1.f64 (.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(.f64 (expm1.f64 (.f64 a x)) (log.f64 (E.f64)))
(expm1.f64 (*.f64 a x))
(.f64 #s(literal 1 binary64) (expm1.f64 (.f64 a x)))
(expm1.f64 (*.f64 a x))
(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2/3 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 2/3 binary64)) (cbrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2/3 binary64)))
(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
(expm1.f64 (*.f64 a x))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/2 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (expm1.f64 (.f64 a x)))
(expm1.f64 (*.f64 a x))
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 (.f64 a x)) (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) #s(literal 8 binary64))) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/2 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 (.f64 a x)) (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) #s(literal 8 binary64))) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/2 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 3/2 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/2 binary64))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) #s(literal 5 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/6 binary64)) (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 5 binary64))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64)))))
(/.f64 (expm1.f64 (.f64 #s(literal 3 binary64) (.f64 a x))) (-.f64 (pow.f64 (exp.f64 a) (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (exp.f64 a) x))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64)))
(expm1.f64 (*.f64 a x))
(/.f64 (neg.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))))
(/.f64 (expm1.f64 (.f64 #s(literal 3 binary64) (.f64 a x))) (-.f64 (pow.f64 (exp.f64 a) (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (exp.f64 a) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (exp.f64 a) x) #s(literal 1 binary64))))
(expm1.f64 (*.f64 a x))
(/.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 3 binary64)) #s(literal -1 binary64)) (+.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (exp.f64 a) x) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (.f64 #s(literal 3 binary64) (.f64 a x))) (-.f64 (pow.f64 (exp.f64 a) (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (exp.f64 a) x))))
(pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 3 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (E.f64) (log.f64 (expm1.f64 (*.f64 a x))))
(expm1.f64 (*.f64 a x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x))))) (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)))
(expm1.f64 (*.f64 a x))
(fabs.f64 (expm1.f64 (*.f64 a x)))
(expm1.f64 (*.f64 a x))
(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))
(expm1.f64 (*.f64 a x))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)))
(expm1.f64 (*.f64 a x))
(expm1.f64 (*.f64 a x))
(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))
(expm1.f64 (*.f64 a x))
(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
(expm1.f64 (*.f64 a x))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 3 binary64)))
(expm1.f64 (*.f64 a x))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1/3 binary64)))
(expm1.f64 (*.f64 a x))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64)))
(expm1.f64 (*.f64 a x))
(fma.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 a) x) #s(literal -1 binary64))
(expm1.f64 (*.f64 a x))
(fma.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 a) x) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (exp.f64 a) x)) #s(literal -1 binary64))
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 a) (*.f64 x #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 (exp.f64 a) x)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (pow.f64 (exp.f64 a) x)) (sqrt.f64 (pow.f64 (exp.f64 a) x)) #s(literal -1 binary64))
(expm1.f64 (*.f64 a x))

eval13.0ms (0.4%)

Compiler: Compiled 847 to 386 computations (54.4% saved)

prune13.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	3	66

Accuracy

100.0%

Counts

66 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	42.0%	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))
▶	67.7%	(*.f64 a x)
✓	100.0%	(expm1.f64 (*.f64 a x))

Compiler

Compiled 20 to 14 computations (30% saved)

localize90.0ms (2.8%)

Localize:

Found 3 expressions with local error:

New	Accuracy	Program
	100.0%	(expm1.f64 (*.f64 a x))
✓	99.8%	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))
✓	92.6%	(sqrt.f64 (expm1.f64 (*.f64 a x)))

Results

9.0ms	95×	256	invalid
7.0ms	29×	512	valid
10.0ms	27×	1024	invalid
5.0ms	24×	512	invalid
7.0ms	23×	1024	valid
14.0ms	21×	2048	invalid
10.0ms	20×	2048	valid
2.0ms	17×	256	valid

Compiler

Compiled 30 to 9 computations (70% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

composed: 21.0ms (36.5% of total)

ival-exp: 17.0ms (29.6% of total)

ival-pow: 6.0ms (10.4% of total)

ival-mult: 5.0ms (8.7% of total)

ival-sqrt: 4.0ms (7% of total)

ival-sub: 3.0ms (5.2% of total)

const: 1.0ms (1.7% of total)

series5.0ms (0.2%)

Counts

2 → 48

Calls

Call 1

Inputs
#<alt (sqrt.f64 (expm1.f64 (*.f64 a x)))>
#<alt (pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))>

Outputs
#<alt (sqrt.f64 (*.f64 a x))>
#<alt (+.f64 (sqrt.f64 (.f64 a x)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))>
#<alt (+.f64 (sqrt.f64 (.f64 a x)) (.f64 (pow.f64 a #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/12 binary64) (sqrt.f64 (.f64 a (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) a))))))>
#<alt (+.f64 (sqrt.f64 (.f64 a x)) (.f64 (pow.f64 a #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) a))) (.f64 a (+.f64 (.f64 #s(literal 1/12 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 5 binary64)) a))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 a x)) (-.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) a))))))))))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (*.f64 a x))>
#<alt (+.f64 (sqrt.f64 (.f64 a x)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))>
#<alt (+.f64 (sqrt.f64 (.f64 a x)) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/12 binary64) (sqrt.f64 (.f64 (pow.f64 a #s(literal 5 binary64)) x))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) x))))))>
#<alt (+.f64 (sqrt.f64 (.f64 a x)) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) x))) (.f64 x (+.f64 (.f64 #s(literal 1/12 binary64) (sqrt.f64 (/.f64 (pow.f64 a #s(literal 5 binary64)) x))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 x a)) (-.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 a #s(literal 4 binary64))) (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 a #s(literal 3 binary64)) x))))))))))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))>
#<alt (*.f64 a x)>
#<alt (.f64 a (+.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 a (pow.f64 x #s(literal 2 binary64))))))>
#<alt (.f64 a (+.f64 x (.f64 a (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 a (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))))>
#<alt (.f64 a (+.f64 x (.f64 a (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64))) (.f64 a (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 a (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)))))))))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (*.f64 a x)>
#<alt (.f64 x (+.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 a #s(literal 2 binary64)) x))))>
#<alt (.f64 x (+.f64 a (.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 a #s(literal 3 binary64)) x)) (*.f64 #s(literal 1/2 binary64) (pow.f64 a #s(literal 2 binary64)))))))>
#<alt (.f64 x (+.f64 a (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 a #s(literal 2 binary64))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 (pow.f64 a #s(literal 4 binary64)) x)) (*.f64 #s(literal 1/6 binary64) (pow.f64 a #s(literal 3 binary64)))))))))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	a	@	0	(sqrt (- (exp (* a x)) 1))
1.0ms	x	@	0	(sqrt (- (exp (* a x)) 1))
0.0ms	a	@	inf	(sqrt (- (exp (* a x)) 1))
0.0ms	a	@	-inf	(sqrt (- (exp (* a x)) 1))
0.0ms	x	@	inf	(sqrt (- (exp (* a x)) 1))

rewrite106.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

400×	`unpow-prod-down`
381×	`log1p-expm1-u`
380×	`expm1-log1p-u`
362×	`add-exp-log`
343×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	126	38
2	1136	38

Stop Event

1×	node limit

Counts

2 → 88

Calls

Call 1

Inputs
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))

Outputs
(+.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 (*.f64 a x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (expm1.f64 (.f64 a x))))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))))))
(-.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 (.f64 a x))))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/6 binary64)) (cbrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/4 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 2/3 binary64))) (pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 5/6 binary64)) #s(literal 1/3 binary64)))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 5/6 binary64))))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 4/3 binary64))) (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64))))
(.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/4 binary64))) (pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/6 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (sqrt.f64 (expm1.f64 (.f64 a x))))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64))))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/4 binary64)) #s(literal 1/3 binary64)) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64))))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/4 binary64))) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64))))
(pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)) #s(literal 3 binary64))
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (expm1.f64 (*.f64 a x))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (expm1.f64 (.f64 a x))))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (sqrt.f64 (expm1.f64 (.f64 a x))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))))) (sqrt.f64 (log.f64 (sqrt.f64 (expm1.f64 (.f64 a x))))))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(fabs.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))
(log.f64 (exp.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(exp.f64 (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/6 binary64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 2 binary64)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(.f64 (expm1.f64 (.f64 a x)) #s(literal 1 binary64))
(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 #s(literal 1 binary64) (expm1.f64 (.f64 a x)))
(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2/3 binary64)))
(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 4/3 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 2/3 binary64)) (cbrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/4 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/4 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 3/4 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/6 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (expm1.f64 (.f64 a x)))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 4/3 binary64)) #s(literal 1/2 binary64)) (cbrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) #s(literal 5 binary64)) #s(literal 1/2 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (pow.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 4/3 binary64)) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/2 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 4/3 binary64)) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
(pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)) #s(literal 6 binary64))
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/2 binary64)) #s(literal 2/3 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (E.f64) (log.f64 (expm1.f64 (*.f64 a x))))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x))))) (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)))
(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)))
(expm1.f64 (*.f64 a x))
(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))
(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)) #s(literal -1 binary64))
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 2 binary64))) (cbrt.f64 (exp.f64 (.f64 a x))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (exp.f64 (.f64 a x))) #s(literal -1 binary64))

simplify119.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

748×	`fma-define`
571×	`associate-r`
494×	`associate-+r+`
449×	`associate-l`
318×	`prod-exp`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	313	34359742608
1	642	34359742552
2	1700	34359742468
3	5282	4594

Stop Event

1×	node limit

Counts

136 → 124

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 a x))
(+.f64 (sqrt.f64 (.f64 a x)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(+.f64 (sqrt.f64 (.f64 a x)) (.f64 (pow.f64 a #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/12 binary64) (sqrt.f64 (.f64 a (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) a))))))
(+.f64 (sqrt.f64 (.f64 a x)) (.f64 (pow.f64 a #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) a))) (.f64 a (+.f64 (.f64 #s(literal 1/12 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 5 binary64)) a))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 a x)) (-.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) a))))))))))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (*.f64 a x))
(+.f64 (sqrt.f64 (.f64 a x)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(+.f64 (sqrt.f64 (.f64 a x)) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/12 binary64) (sqrt.f64 (.f64 (pow.f64 a #s(literal 5 binary64)) x))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) x))))))
(+.f64 (sqrt.f64 (.f64 a x)) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) x))) (.f64 x (+.f64 (.f64 #s(literal 1/12 binary64) (sqrt.f64 (/.f64 (pow.f64 a #s(literal 5 binary64)) x))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 x a)) (-.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 a #s(literal 4 binary64))) (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 a #s(literal 3 binary64)) x))))))))))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(*.f64 a x)
(.f64 a (+.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 a (pow.f64 x #s(literal 2 binary64))))))
(.f64 a (+.f64 x (.f64 a (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 a (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))))
(.f64 a (+.f64 x (.f64 a (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 2 binary64))) (.f64 a (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 a (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)))))))))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(*.f64 a x)
(.f64 x (+.f64 a (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 a #s(literal 2 binary64)) x))))
(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 a #s(literal 3 binary64)) x)) (*.f64 #s(literal 1/2 binary64) (pow.f64 a #s(literal 2 binary64)))))))
(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 a #s(literal 2 binary64))) (.f64 x (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 (pow.f64 a #s(literal 4 binary64)) x)) (*.f64 #s(literal 1/6 binary64) (pow.f64 a #s(literal 3 binary64)))))))))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(+.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 (*.f64 a x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (expm1.f64 (.f64 a x))))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))))))
(-.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 (.f64 a x))))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/6 binary64)) (cbrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/4 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 2/3 binary64))) (pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 5/6 binary64)) #s(literal 1/3 binary64)))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 5/6 binary64))))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 4/3 binary64))) (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64))))
(.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/4 binary64))) (pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/6 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (sqrt.f64 (expm1.f64 (.f64 a x))))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64))))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/4 binary64)) #s(literal 1/3 binary64)) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64))))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/4 binary64))) (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64))))
(pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)) #s(literal 3 binary64))
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (expm1.f64 (*.f64 a x))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (expm1.f64 (.f64 a x))))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (sqrt.f64 (expm1.f64 (.f64 a x))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (expm1.f64 (.f64 a x)))))) (sqrt.f64 (log.f64 (sqrt.f64 (expm1.f64 (.f64 a x))))))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(fabs.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))
(log.f64 (exp.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(exp.f64 (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/6 binary64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 2 binary64)))
(+.f64 (exp.f64 (*.f64 a x)) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (.f64 a x))))))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(.f64 (expm1.f64 (.f64 a x)) #s(literal 1 binary64))
(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 #s(literal 1 binary64) (expm1.f64 (.f64 a x)))
(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2/3 binary64)))
(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 4/3 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 2/3 binary64)) (cbrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 1/4 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/4 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 3/4 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/6 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (expm1.f64 (.f64 a x)))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 4/3 binary64)) #s(literal 1/2 binary64)) (cbrt.f64 (expm1.f64 (*.f64 a x))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) #s(literal 5 binary64)) #s(literal 1/2 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (pow.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 4/3 binary64)) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 5/2 binary64))) (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 4/3 binary64)) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
(pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)) #s(literal 6 binary64))
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/2 binary64)) #s(literal 2/3 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (E.f64) (log.f64 (expm1.f64 (*.f64 a x))))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x))))) (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)))
(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)))
(expm1.f64 (*.f64 a x))
(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))
(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)) #s(literal -1 binary64))
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 2 binary64))) (cbrt.f64 (exp.f64 (.f64 a x))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (exp.f64 (.f64 a x))) #s(literal -1 binary64))

Outputs
(sqrt.f64 (*.f64 a x))
(+.f64 (sqrt.f64 (.f64 a x)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (pow.f64 (.f64 a x) #s(literal 3 binary64))) (sqrt.f64 (.f64 a x)))
(+.f64 (sqrt.f64 (.f64 a x)) (.f64 (pow.f64 a #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/12 binary64) (sqrt.f64 (.f64 a (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) a))))))
(fma.f64 (pow.f64 a #s(literal 2 binary64)) (fma.f64 #s(literal 1/12 binary64) (sqrt.f64 (.f64 a (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) a)))) (sqrt.f64 (*.f64 a x)))
(+.f64 (sqrt.f64 (.f64 a x)) (.f64 (pow.f64 a #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) a))) (.f64 a (+.f64 (.f64 #s(literal 1/12 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 5 binary64)) a))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 a x)) (-.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) a))))))))))
(fma.f64 (pow.f64 a #s(literal 2 binary64)) (fma.f64 a (fma.f64 #s(literal 1/12 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 5 binary64)) a)) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 a x)) (fma.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) a) #s(literal -1/16 binary64)))))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) a)))) (sqrt.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64)))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (*.f64 a x))
(+.f64 (sqrt.f64 (.f64 a x)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (pow.f64 (.f64 a x) #s(literal 3 binary64))) (sqrt.f64 (.f64 a x)))
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(.f64 (cbrt.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 4/3 binary64)) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) #s(literal 8/3 binary64))) (cbrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))))
(/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))))
(/.f64 (expm1.f64 (.f64 #s(literal 3 binary64) (.f64 a x))) (+.f64 (pow.f64 (exp.f64 a) x) (+.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 a x)))))
(/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (exp.f64 (.f64 a x)) #s(literal 1 binary64)))
(expm1.f64 (*.f64 a x))
(pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/6 binary64)) #s(literal 6 binary64))
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 3 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3/2 binary64)) #s(literal 2/3 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(expm1.f64 (*.f64 a x))
(pow.f64 (E.f64) (log.f64 (expm1.f64 (*.f64 a x))))
(expm1.f64 (*.f64 a x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
(expm1.f64 (*.f64 a x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x))))) (sqrt.f64 (log.f64 (expm1.f64 (.f64 a x)))))
(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 2 binary64)))
(expm1.f64 (*.f64 a x))
(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))
(expm1.f64 (*.f64 a x))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) #s(literal 3 binary64)))
(expm1.f64 (*.f64 a x))
(expm1.f64 (*.f64 a x))
(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))
(expm1.f64 (*.f64 a x))
(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
(expm1.f64 (*.f64 a x))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (expm1.f64 (.f64 a x)))) #s(literal 3 binary64)))
(expm1.f64 (*.f64 a x))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1/2 binary64)))
(expm1.f64 (*.f64 a x))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 (expm1.f64 (*.f64 a x)))) #s(literal 1/3 binary64)))
(expm1.f64 (*.f64 a x))
(fma.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a x)) #s(literal -1 binary64))
(expm1.f64 (*.f64 a x))
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 (.f64 a x)) #s(literal 2 binary64))) (cbrt.f64 (exp.f64 (.f64 a x))) #s(literal -1 binary64))
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 a x))) (cbrt.f64 (pow.f64 (exp.f64 a) x)) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (exp.f64 (.f64 a x))) (sqrt.f64 (exp.f64 (.f64 a x))) #s(literal -1 binary64))
(expm1.f64 (*.f64 a x))

eval50.0ms (1.6%)

Compiler: Compiled 2789 to 1432 computations (48.7% saved)

prune27.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	189	3	192

Accuracy

100.0%

Counts

192 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	42.0%	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))
✓	67.7%	(*.f64 a x)
✓	100.0%	(expm1.f64 (*.f64 a x))

Compiler

Compiled 42 to 24 computations (42.9% saved)

regimes7.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
(*.f64 a x)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) #s(literal 2 binary64))

Outputs
(expm1.f64 (*.f64 a x))

Calls

5 calls:

2.0ms	a
2.0ms	x
2.0ms	(*.f64 a x)
1.0ms	(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))
1.0ms	(exp.f64 (*.f64 a x))

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`x`
100.0%	1	`(-.f64 (exp.f64 (*.f64 a x)) #s(literal 1 binary64))`
100.0%	1	`(exp.f64 (*.f64 a x))`
100.0%	1	`(*.f64 a x)`

Compiler

Compiled 25 to 17 computations (32% saved)

regimes2.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 a x)

Outputs
(*.f64 a x)

Calls

3 calls:

0.0ms	(*.f64 a x)
0.0ms	a
0.0ms	x

Results

Accuracy	Segments	Branch
67.7%	1	`a`
67.7%	1	`x`
67.7%	1	`(*.f64 a x)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	11	30

Stop Event

1×

saturated

Calls

Call 1

Inputs
(expm1.f64 (*.f64 a x))
(*.f64 a x)

Outputs
(expm1.f64 (*.f64 a x))
(*.f64 a x)

soundness23.0ms (0.7%)

Rules

48×	`fma-define`
22×	`sub-neg`
20×	`exp-sum`
19×	`fma-neg`
12×	`exp-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	143
1	58	143
2	88	143
3	126	143
4	169	143
5	203	143
6	248	143
7	298	143
8	315	143
9	331	143
10	335	143

Stop Event

1×	done
1×	saturated

Compiler

Compiled 21 to 11 computations (47.6% saved)

preprocess42.0ms (1.3%)

Remove: (sort a x)
Compiler: Compiled 82 to 52 computations (36.6% saved)

expax (section 3.5)

analyze27.0ms (0.8%)

sample1.9s (59.1%)

preprocess50.0ms (1.6%)

explain187.0ms (5.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize82.0ms (2.5%)

series3.0ms (0.1%)

rewrite342.0ms (10.7%)

simplify121.0ms (3.8%)

eval13.0ms (0.4%)

prune13.0ms (0.4%)

localize90.0ms (2.8%)

series5.0ms (0.2%)

rewrite106.0ms (3.3%)

simplify119.0ms (3.7%)

eval50.0ms (1.6%)

prune27.0ms (0.8%)

regimes7.0ms (0.2%)

regimes2.0ms (0%)

simplify2.0ms (0.1%)

soundness23.0ms (0.7%)

preprocess42.0ms (1.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	25	143
1	58	143
2	88	143
3	126	143
4	169	143
5	203	143
6	248	143
7	298	143
8	315	143
9	331	143
10	335	143

Iter	Nodes	Cost
0	25	143
1	58	143
2	88	143
3	126	143
4	169	143
5	203	143
6	248	143
7	298	143
8	315	143
9	331	143
10	335	143

Iter	Nodes	Cost
0	25	143
1	58	143
2	88	143
3	126	143
4	169	143
5	203	143
6	248	143
7	298	143
8	315	143
9	331	143
10	335	143

Iter	Nodes	Cost
0	25	143
1	58	143
2	88	143
3	126	143
4	169	143
5	203	143
6	248	143
7	298	143
8	315	143
9	331	143
10	335	143

Iter	Nodes	Cost
0	25	143
1	58	143
2	88	143
3	126	143
4	169	143
5	203	143
6	248	143
7	298	143
8	315	143
9	331	143
10	335	143

Iter	Nodes	Cost
0	25	143
1	58	143
2	88	143
3	126	143
4	169	143
5	203	143
6	248	143
7	298	143
8	315	143
9	331	143
10	335	143