Metrics for sqrt sqr

analyze2.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 14 to 9 computations (35.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-div: 0.0ms (0% of total)

ival-sub: 0.0ms (0% of total)

ival-mult: 0.0ms (0% of total)

const: 0.0ms (0% of total)

ival-sqrt: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample2.7s (55.2%)

Results

1.6s	4117×	2	valid
626.0ms	4139×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-div: 674.0ms (41.4% of total)

ival-mult: 389.0ms (23.9% of total)

backward-pass: 231.0ms (14.2% of total)

ival-sqrt: 160.0ms (9.8% of total)

ival-sub: 156.0ms (9.6% of total)

const: 16.0ms (1% of total)

Bogosity

preprocess65.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

85×	`fma-define`
67×	`fmm-def`
22×	`distribute-lft-neg-in`
19×	`cancel-sign-sub-inv`
19×	`sub-neg`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	128
1	69	92
2	141	92
3	258	92
4	412	92
5	539	92
6	574	92
7	584	92

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))
(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))
(-.f64 (/.f64 (neg.f64 x) (neg.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (sqrt.f64 (.f64 (neg.f64 x) (neg.f64 x)))))
(neg.f64 (-.f64 (/.f64 (neg.f64 x) (neg.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (sqrt.f64 (.f64 (neg.f64 x) (neg.f64 x))))))

Outputs
(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))
(-.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (fabs.f64 x)))
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))
(-.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (fabs.f64 x)))
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
(-.f64 (/.f64 (neg.f64 x) (neg.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (sqrt.f64 (.f64 (neg.f64 x) (neg.f64 x)))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (neg.f64 x)))
(+.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
(neg.f64 (-.f64 (/.f64 (neg.f64 x) (neg.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (sqrt.f64 (.f64 (neg.f64 x) (neg.f64 x))))))
(neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (neg.f64 x))))
(-.f64 #s(literal -1 binary64) (/.f64 (fabs.f64 x) x))

explain266.0ms (5.5%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
128	-	3	(9.584468272170066e-157)	`(sqrt.f64 (*.f64 x x))`
0	-	0	-	`x`
0	-	0	-	`(/.f64 x x)`
0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x)))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))`
0	-	0	-	`(/.f64 #s(literal 1 binary64) x)`
0	-	0	-	`#s(literal 1 binary64)`

Results

124.0ms	244×	2	valid
27.0ms	268×	0	valid

Compiler

Compiled 87 to 26 computations (70.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 116.0ms

ival-mult: 72.0ms (62.2% of total)

ival-div: 20.0ms (17.3% of total)

ival-sqrt: 9.0ms (7.8% of total)

backward-pass: 7.0ms (6% of total)

ival-sub: 5.0ms (4.3% of total)

const: 1.0ms (0.9% of total)

eval0.0ms (0%)

Compiler: Compiled 15 to 8 computations (46.7% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize46.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fabs.f64 x)
✓	cost-diff	0	(/.f64 (fabs.f64 x) x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
✓	accuracy	100.0%	(/.f64 (fabs.f64 x) x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
✓	accuracy	100.0%	(fabs.f64 x)

Rules

95×	`fmm-def`
68×	`fma-define`
23×	`times-frac`
21×	`sub-neg`
13×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	53
1	17	53
2	25	53
3	36	53
4	52	53
5	68	53
6	90	53
7	113	53
8	128	53
9	148	53
10	182	53
11	249	53
12	373	53
13	427	53
14	451	53
15	481	53

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
#s(literal 1 binary64)
(/.f64 (fabs.f64 x) x)
(fabs.f64 x)
x

Outputs
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
#s(literal 1 binary64)
(/.f64 (fabs.f64 x) x)
(fabs.f64 x)
x

Results

14.0ms

256×

valid

Compiler

Compiled 16 to 6 computations (62.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 2.0ms (38.5% of total)

ival-fabs: 2.0ms (38.5% of total)

ival-sub: 1.0ms (19.3% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series3.0ms (0.1%)

Counts

3 → 12

Calls

Call 1

Inputs
#<alt (fabs.f64 x)>
#<alt (-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))>
#<alt (/.f64 (fabs.f64 x) x)>

Outputs
#<alt (*.f64 #s(literal -1 binary64) (/.f64 (fabs.f64 x) x))>
#<alt (/.f64 (-.f64 x (fabs.f64 x)) x)>
#<alt (/.f64 (-.f64 x (fabs.f64 x)) x)>
#<alt (/.f64 (-.f64 x (fabs.f64 x)) x)>
#<alt #s(literal 1 binary64)>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fabs.f64 x) x)))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fabs.f64 x) x)))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fabs.f64 x) x)))>
#<alt #s(literal 1 binary64)>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fabs.f64 x) x)))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fabs.f64 x) x)))>
#<alt (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fabs.f64 x) x)))>

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(- 1 (/ (fabs x) x))
0.0ms	x	@	0	(- 1 (/ (fabs x) x))
0.0ms	x	@	-inf	(/ (fabs x) x)
0.0ms	x	@	inf	(- 1 (/ (fabs x) x))
0.0ms	x	@	0	(/ (fabs x) x)

rewrite795.0ms (16.3%)

Algorithm

1×	batch-egg-rewrite

Rules

420×	`log1p-expm1-u`
420×	`expm1-log1p-u`
415×	`unpow-prod-down`
368×	`add-exp-log`
354×	`prod-diff`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	48
1	109	36
2	1525	6

Stop Event

1×	node limit

Counts

3 → 34

Calls

Call 1

Inputs
(fabs.f64 x)
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
(/.f64 (fabs.f64 x) x)

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

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

892×	`fma-define`
694×	`distribute-lft-in`
575×	`distribute-rgt-in`
342×	`unswap-sqr`
316×	`fmm-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	637
1	165	364
2	548	358
3	2151	358

Stop Event

1×	node limit

Counts

46 → 47

Calls

Call 1

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

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

eval6.0ms (0.1%)

Compiler: Compiled 456 to 190 computations (58.3% saved)

prune58.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	3	48

Accuracy

100.0%

Counts

48 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
▶	11.3%	#s(literal 1 binary64)
▶	49.3%	#s(literal 0 binary64)

Compiler

Compiled 11 to 9 computations (18.2% saved)

localize14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

3× 1-exp

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	2
1	8	2

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)

Outputs
#s(literal 0 binary64)
#s(literal 1 binary64)

Results

5.0ms

256×

valid

Compiler

Compiled 4 to 4 computations (0% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	1	1
Total	3	3

Accuracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
✓	11.3%	#s(literal 1 binary64)
✓	49.3%	#s(literal 0 binary64)

Compiler

Compiled 32 to 21 computations (34.4% saved)

regimes4.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))
(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))

Outputs
(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes2.0ms (0%)

Counts

2 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)
#s(literal 0 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
57.5%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
49.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch20.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	-8.648808981689132e-307	5.729665174279767e-308

Results

8.0ms	32×	2	valid
6.0ms	96×	0	valid

Compiler

Compiled 65 to 59 computations (9.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-div: 4.0ms (40.5% of total)

ival-mult: 3.0ms (30.4% of total)

ival-sqrt: 2.0ms (20.2% of total)

backward-pass: 1.0ms (10.1% of total)

ival-sub: 1.0ms (10.1% of total)

const: 0.0ms (0% of total)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`sub-neg`
4×	`+-commutative`
3×	`1-exp`
3×	`*-commutative`
3×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	38
1	23	38
2	31	38
3	37	38
4	42	38
5	44	38

Stop Event

1×

saturated

Calls

Call 1

Inputs

(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))

(if (<=.f64 x #s(literal -5060056332683/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(literal 1 binary64) #s(literal 0 binary64))

#s(literal 0 binary64)

Outputs

(-.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 x) x))

(if (<=.f64 x #s(literal -5060056332683/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(literal 1 binary64) #s(literal 0 binary64))

#s(literal 0 binary64)

soundness618.0ms (12.7%)

Rules

892×	`fma-define`
694×	`distribute-lft-in`
575×	`distribute-rgt-in`
342×	`unswap-sqr`
316×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	128
1	69	92
2	141	92
3	258	92
4	412	92
5	539	92
6	574	92
7	584	92
0	95	637
1	165	364
2	548	358
3	2151	358

Stop Event

1×	done
1×	node limit
1×	saturated

Compiler

Compiled 289 to 85 computations (70.6% saved)

preprocess233.0ms (4.8%)

Compiler: Compiled 68 to 44 computations (35.3% saved)

sqrt sqr

analyze2.0ms (0%)

sample2.7s (55.2%)

preprocess65.0ms (1.3%)

explain266.0ms (5.5%)

eval0.0ms (0%)

prune1.0ms (0%)

localize46.0ms (0.9%)

series3.0ms (0.1%)

rewrite795.0ms (16.3%)

simplify45.0ms (0.9%)

eval6.0ms (0.1%)

prune58.0ms (1.2%)

localize14.0ms (0.3%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes4.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

bsearch20.0ms (0.4%)

simplify4.0ms (0.1%)

soundness618.0ms (12.7%)

preprocess233.0ms (4.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	53
1	17	53
2	25	53
3	36	53
4	52	53
5	68	53
6	90	53
7	113	53
8	128	53
9	148	53
10	182	53
11	249	53
12	373	53
13	427	53
14	451	53
15	481	53

Iter	Nodes	Cost
0	10	53
1	17	53
2	25	53
3	36	53
4	52	53
5	68	53
6	90	53
7	113	53
8	128	53
9	148	53
10	182	53
11	249	53
12	373	53
13	427	53
14	451	53
15	481	53

Iter	Nodes	Cost
0	10	53
1	17	53
2	25	53
3	36	53
4	52	53
5	68	53
6	90	53
7	113	53
8	128	53
9	148	53
10	182	53
11	249	53
12	373	53
13	427	53
14	451	53
15	481	53