Metrics for expq2 (section 3.11)

analyze151.0ms (3.4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	75.2%	24.8%	0%	0%	0%	0
0%	0%	75.2%	24.8%	0%	0%	0%	1
0%	0%	75.2%	24.8%	0%	0%	0%	2
25%	18.8%	56.4%	24.8%	0%	0%	0%	3
37.5%	28.2%	47%	24.8%	0%	0%	0%	4
37.5%	28.2%	47%	24.8%	0%	0%	0%	5
40.6%	30.5%	44.6%	24.8%	0%	0%	0%	6
42.2%	31.7%	43.5%	24.8%	0%	0%	0%	7
42.2%	31.7%	43.5%	24.8%	0%	0%	0%	8
43%	32.3%	42.9%	24.8%	0%	0%	0%	9
43%	32.3%	42.9%	24.8%	0%	0%	0%	10
43.1%	32.4%	42.8%	24.8%	0%	0%	0%	11
43.1%	32.4%	42.8%	24.8%	0%	0%	0%	12

Compiler

Compiled 11 to 7 computations (36.4% saved)

Precisions

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

Operation ival-sub, time spent: 19.0ms, 33.0% of total-time

Operation ival-exp, time spent: 17.0ms, 29.0% of total-time

Operation ival->, time spent: 11.0ms, 19.0% of total-time

Operation ival-div, time spent: 7.0ms, 12.0% of total-time

Operation const, time spent: 4.0ms, 7.0% of total-time

sample1.8s (41.6%)

Results

446.0ms	4006×	256	valid
853.0ms	2723×	1024	valid
284.0ms	1351×	512	valid
94.0ms	174×	2048	valid
0.0ms	1×	512	valid
0.0ms	1×	1024	infinite

Precisions

Click to see histograms. Total time spent on operations: 837.0ms

Operation ival-exp, time spent: 458.0ms, 55.0% of total-time

Operation ival->, time spent: 140.0ms, 17.0% of total-time

Operation ival-div, time spent: 112.0ms, 13.0% of total-time

Operation ival-sub, time spent: 102.0ms, 12.0% of total-time

Operation const, time spent: 24.0ms, 3.0% of total-time

Bogosity

preprocess522.0ms (11.8%)

Algorithm

1×	egg-herbie

Rules

2412×	`fma-neg`
1494×	`div-sub`
1056×	`fma-define`
452×	`distribute-lft-neg-in`
436×	`associate-+r-`

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
161	1	(0.00348655734421175)	-	`(-.f64 (exp.f64 x) 1)`
0	0	-	-	`x`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
0	0	-	-	`1`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	15	104
1	35	102
2	56	102
3	94	102
4	153	76
5	292	68
6	469	68
7	837	64
8	2147	64
9	3590	64
10	4606	64
11	5606	64
12	6702	64

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 (neg.f64 x)) 1))
(neg.f64 (/.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 (neg.f64 x)) 1)))

Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 (exp.f64 (neg.f64 x)) (expm1.f64 (neg.f64 x)))
(/.f64 1 (-.f64 1 (exp.f64 x)))
(/.f64 1 (neg.f64 (expm1.f64 x)))
(/.f64 -1 (expm1.f64 x))
(neg.f64 (/.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 (neg.f64 x)) 1)))
(/.f64 (exp.f64 (neg.f64 x)) (neg.f64 (expm1.f64 (neg.f64 x))))
(/.f64 (/.f64 -1 (exp.f64 x)) (expm1.f64 (neg.f64 x)))
(/.f64 -1 (*.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))))
(/.f64 1 (expm1.f64 x))

Compiler

Compiled 42 to 23 computations (45.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

Operation ival-exp, time spent: 23.0ms, 52.0% of total-time

Operation ival-sub, time spent: 11.0ms, 25.0% of total-time

Operation ival-div, time spent: 9.0ms, 20.0% of total-time

Operation const, time spent: 3.0ms, 7.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 -1 (expm1.f64 (neg.f64 x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize58.0ms (1.3%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f64 -1 (expm1.f64 (neg.f64 x)))

Compiler

Compiled 14 to 7 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

Operation composed, time spent: 16.0ms, 43.0% of total-time

Operation ival-exp, time spent: 11.0ms, 30.0% of total-time

Operation ival-div, time spent: 3.0ms, 8.0% of total-time

Operation ival-sub, time spent: 3.0ms, 8.0% of total-time

Operation ival-neg, time spent: 2.0ms, 5.0% of total-time

Operation const, time spent: 1.0ms, 3.0% of total-time

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 -1 (expm1.f64 (neg.f64 x)))
1.0ms	x	@	-inf	(/.f64 -1 (expm1.f64 (neg.f64 x)))
1.0ms	x	@	0	(/.f64 -1 (expm1.f64 (neg.f64 x)))

rewrite167.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

982×	`frac-times`
552×	`unpow-prod-down`
330×	`log-prod`
328×	`cbrt-prod`
302×	`log1p-expm1-u`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	91	14
2	1094	8

Stop Event

1×	node limit

Counts

1 → 71

Calls

Call 1

Inputs
(/.f64 -1 (expm1.f64 (neg.f64 x)))

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

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1730×	`prod-exp`
936×	`fma-neg`
704×	`distribute-lft-out`
700×	`cancel-sign-sub-inv`
540×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	4294968763
1	307	4294968701
2	727	4294968677
3	2799	4294968489
4	7856	4294968489

Stop Event

1×	node limit

Counts

83 → 102

Calls

Call 1

Inputs
(/.f64 1 x)
(/.f64 (+.f64 1 (*.f64 1/2 x)) x)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 1/12 x)))) x)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2))))))) x)
(/.f64 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))
(+.f64 (exp.f64 x) -1)
(+.f64 0 (expm1.f64 x))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (expm1.f64 x)) 2))) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))))
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) (log.f64 (E.f64)))
(-.f64 0 (expm1.f64 x))
(-.f64 (/.f64 (exp.f64 x) -1) -1)
(*.f64 -1 (expm1.f64 x))
(*.f64 (expm1.f64 x) -1)
(*.f64 (expm1.f64 x) 1)
(*.f64 (expm1.f64 x) (log.f64 (E.f64)))
(*.f64 (expm1.f64 x) (log.f64 (exp.f64 -1)))
(*.f64 1 (expm1.f64 x))
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (neg.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 (cbrt.f64 (expm1.f64 x)) -1))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (neg.f64 (cbrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (/.f64 (cbrt.f64 (expm1.f64 x)) -1) -1))
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) -1))
(*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) -1))
(*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) -1) -1))
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)))
(*.f64 (sqrt.f64 -1) (expm1.f64 x))
(*.f64 (neg.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(*.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 1 1/3) (expm1.f64 x))
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 5/2) 1/3) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (pow.f64 (cbrt.f64 -1) 3) (expm1.f64 x))
(.f64 (pow.f64 (.f64 (pow.f64 (expm1.f64 x) 2) -1) 1/3) (cbrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 -1) 2) (expm1.f64 x))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) -1) (sqrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1) (cbrt.f64 (expm1.f64 x)))
(*.f64 (exp.f64 (log.f64 -1)) (expm1.f64 x))
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)) (pow.f64 (expm1.f64 x) 1/6))
(.f64 (cbrt.f64 (.f64 (pow.f64 (expm1.f64 x) 2) -1)) (cbrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)) (pow.f64 (expm1.f64 x) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 5)) (pow.f64 (expm1.f64 x) 1/6))
(pow.f64 (expm1.f64 x) -1)
(pow.f64 (expm1.f64 x) 1)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(pow.f64 (cbrt.f64 (expm1.f64 x)) -3)
(pow.f64 (pow.f64 (expm1.f64 x) 2) 1/2)
(pow.f64 (pow.f64 (expm1.f64 x) 2) -1/2)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(pow.f64 (pow.f64 (expm1.f64 x) 3) -1/3)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(pow.f64 (sqrt.f64 (expm1.f64 x)) -2)
(pow.f64 (E.f64) (log.f64 (expm1.f64 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 x))) 2)) (cbrt.f64 (log.f64 (expm1.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 x)))) (sqrt.f64 (log.f64 (expm1.f64 x))))
(neg.f64 (expm1.f64 x))
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(fabs.f64 (expm1.f64 x))
(log.f64 (exp.f64 (expm1.f64 x)))
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
(expm1.f64 x)
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(exp.f64 (log.f64 (expm1.f64 x)))
(exp.f64 (*.f64 (log.f64 (expm1.f64 x)) -1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (expm1.f64 x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
(fma.f64 1 (exp.f64 x) -1)
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) -1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -1)

Outputs
(/.f64 1 x)
(/.f64 (+.f64 1 (*.f64 1/2 x)) x)
(/.f64 (+.f64 1 (*.f64 x 1/2)) x)
(/.f64 (fma.f64 x 1/2 1) x)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 1/12 x)))) x)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/12)))) x)
(/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2))))))) x)
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 -1/720 (pow.f64 x 2) 1/12) 1/2) 1) x)
(/.f64 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 -1 (-.f64 (exp.f64 (neg.f64 x)) 1))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 -1 (-.f64 (exp.f64 (*.f64 -1 x)) 1))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(+.f64 0 (expm1.f64 x))
(expm1.f64 x)
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (expm1.f64 x)) 2))) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))
(+.f64 0 (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))))
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) (log.f64 (E.f64)))
(expm1.f64 x)
(-.f64 0 (expm1.f64 x))
(expm1.f64 x)
(-.f64 (/.f64 (exp.f64 x) -1) -1)
(expm1.f64 x)
(*.f64 -1 (expm1.f64 x))
(expm1.f64 x)
(*.f64 (expm1.f64 x) -1)
(expm1.f64 x)
(*.f64 (expm1.f64 x) 1)
(expm1.f64 x)
(*.f64 (expm1.f64 x) (log.f64 (E.f64)))
(expm1.f64 x)
(*.f64 (expm1.f64 x) (log.f64 (exp.f64 -1)))
(expm1.f64 x)
(*.f64 1 (expm1.f64 x))
(expm1.f64 x)
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(expm1.f64 x)
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (neg.f64 (cbrt.f64 (expm1.f64 x))))
(expm1.f64 x)
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 (cbrt.f64 (expm1.f64 x)) -1))
(expm1.f64 x)
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (neg.f64 (cbrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 1 (neg.f64 (cbrt.f64 (expm1.f64 x)))))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 -1 (cbrt.f64 (expm1.f64 x))))
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (neg.f64 (cbrt.f64 (expm1.f64 x))))
(neg.f64 (cbrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (/.f64 (cbrt.f64 (expm1.f64 x)) -1) -1))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 1 (neg.f64 (cbrt.f64 (expm1.f64 x)))))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 -1 (cbrt.f64 (expm1.f64 x))))
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (neg.f64 (cbrt.f64 (expm1.f64 x))))
(neg.f64 (cbrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (sqrt.f64 (expm1.f64 x)) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(expm1.f64 x)
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) -1))
(expm1.f64 x)
(*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) -1))
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 -1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (neg.f64 (sqrt.f64 (expm1.f64 x))))
-1
(*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) -1) -1))
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 -1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (neg.f64 (sqrt.f64 (expm1.f64 x))))
-1
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)))
(*.f64 (sqrt.f64 -1) (expm1.f64 x))
(*.f64 (expm1.f64 x) (sqrt.f64 -1))
(*.f64 (neg.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (pow.f64 1 1/3) (expm1.f64 x))
(expm1.f64 x)
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 8)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 5/2) 1/3) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (pow.f64 (cbrt.f64 -1) 3) (expm1.f64 x))
(expm1.f64 x)
(.f64 (pow.f64 (.f64 (pow.f64 (expm1.f64 x) 2) -1) 1/3) (cbrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (pow.f64 (sqrt.f64 -1) 2) (expm1.f64 x))
(expm1.f64 x)
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) -1) (sqrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 -1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (neg.f64 (sqrt.f64 (expm1.f64 x))))
-1
(*.f64 (pow.f64 (neg.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1) (cbrt.f64 (expm1.f64 x)))
(*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))))
(*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 -1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(/.f64 (cbrt.f64 (expm1.f64 x)) (neg.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(/.f64 -1 (cbrt.f64 (expm1.f64 x)))
(*.f64 (exp.f64 (log.f64 -1)) (expm1.f64 x))
(expm1.f64 x)
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 8)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)) (pow.f64 (expm1.f64 x) 1/6))
(.f64 (cbrt.f64 (.f64 (pow.f64 (expm1.f64 x) 2) -1)) (cbrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)) (pow.f64 (expm1.f64 x) 1/4))
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 5)) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 5)))
(pow.f64 (expm1.f64 x) -1)
(/.f64 1 (expm1.f64 x))
(pow.f64 (expm1.f64 x) 1)
(expm1.f64 x)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(expm1.f64 x)
(pow.f64 (cbrt.f64 (expm1.f64 x)) -3)
(/.f64 1 (expm1.f64 x))
(pow.f64 (pow.f64 (expm1.f64 x) 2) 1/2)
(expm1.f64 x)
(pow.f64 (pow.f64 (expm1.f64 x) 2) -1/2)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(expm1.f64 x)
(pow.f64 (pow.f64 (expm1.f64 x) 3) -1/3)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(expm1.f64 x)
(pow.f64 (sqrt.f64 (expm1.f64 x)) -2)
(/.f64 1 (expm1.f64 x))
(pow.f64 (E.f64) (log.f64 (expm1.f64 x)))
(expm1.f64 x)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 x))) 2)) (cbrt.f64 (log.f64 (expm1.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 x)))) (sqrt.f64 (log.f64 (expm1.f64 x))))
(neg.f64 (expm1.f64 x))
(expm1.f64 x)
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(expm1.f64 x)
(fabs.f64 (expm1.f64 x))
(expm1.f64 x)
(log.f64 (exp.f64 (expm1.f64 x)))
(expm1.f64 x)
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
(expm1.f64 x)
(expm1.f64 x)
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(expm1.f64 x)
(exp.f64 (log.f64 (expm1.f64 x)))
(expm1.f64 x)
(exp.f64 (*.f64 (log.f64 (expm1.f64 x)) -1))
(/.f64 1 (expm1.f64 x))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (expm1.f64 x))) 3))
(expm1.f64 x)
(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
(expm1.f64 x)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
(expm1.f64 x)
(fma.f64 1 (exp.f64 x) -1)
(expm1.f64 x)
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) -1)
(expm1.f64 x)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -1)
(expm1.f64 x)

eval21.0ms (0.5%)

Compiler: Compiled 789 to 392 computations (50.3% saved)

prune14.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	5	103

Accuracy

100.0%

Counts

103 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.9%	(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/12)))) x)
▶	63.9%	(/.f64 (+.f64 1 (*.f64 x 1/2)) x)
▶	64.0%	(/.f64 1 x)
✓	100.0%	(/.f64 -1 (expm1.f64 (neg.f64 x)))
▶	3.0%	-1

Compiler

Compiled 32 to 25 computations (21.9% saved)

localize119.0ms (2.7%)

Localize:

Found 4 expressions with local error:

New	Accuracy	Program
✓	99.9%	(.f64 x (+.f64 1/2 (.f64 x 1/12)))
✓	99.4%	(*.f64 x 1/12)
✓	82.7%	(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/12)))) x)
✓	100.0%	(/.f64 (+.f64 1 (*.f64 x 1/2)) x)

Compiler

Compiled 65 to 48 computations (26.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

Operation ival-mult, time spent: 21.0ms, 50.0% of total-time

Operation ival-add, time spent: 11.0ms, 26.0% of total-time

Operation ival-div, time spent: 6.0ms, 14.0% of total-time

Operation const, time spent: 3.0ms, 7.0% of total-time

series14.0ms (0.3%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(/.f64 (+.f64 1 (*.f64 x 1/2)) x)
1.0ms	x	@	inf	(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/12)))) x)
1.0ms	x	@	-inf	(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/12)))) x)
1.0ms	x	@	inf	(/.f64 (+.f64 1 (*.f64 x 1/2)) x)
1.0ms	x	@	-inf	(/.f64 (+.f64 1 (*.f64 x 1/2)) x)

rewrite131.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

1304×	`fma-define`
855×	`log1p-expm1-u`
855×	`expm1-log1p-u`
502×	`fma-neg`
404×	`expm1-undefine`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	100
1	241	84
2	3637	84

Stop Event

1×	node limit

Counts

4 → 154

Calls

Call 1

Inputs
(/.f64 (+.f64 1 (*.f64 x 1/2)) x)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/12)))) x)
(*.f64 x 1/12)
(.f64 x (+.f64 1/2 (.f64 x 1/12)))

Outputs
(-.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 x 1/2 1) x))) 1)
(*.f64 1 (/.f64 (fma.f64 x 1/2 1) x))
(*.f64 (fma.f64 x 1/2 1) (/.f64 1 x))
(*.f64 (/.f64 (fma.f64 x 1/2 1) x) 1)
(*.f64 (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) 2) (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) (/.f64 (cbrt.f64 (fma.f64 x 1/2 1)) x))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) (.f64 (cbrt.f64 (fma.f64 x 1/2 1)) (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) (sqrt.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(*.f64 (sqrt.f64 (fma.f64 x 1/2 1)) (/.f64 (sqrt.f64 (fma.f64 x 1/2 1)) x))
(.f64 (sqrt.f64 (fma.f64 x 1/2 1)) (.f64 (sqrt.f64 (fma.f64 x 1/2 1)) (/.f64 1 x)))
(*.f64 (neg.f64 (fma.f64 x 1/2 1)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (fma.f64 x 1/2 1))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (fma.f64 x 1/2 1) (cbrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) 1) (/.f64 (cbrt.f64 (fma.f64 x 1/2 1)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (fma.f64 x 1/2 1)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 x 1/2 1)) 1) (/.f64 (sqrt.f64 (fma.f64 x 1/2 1)) x))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 x 1/2 1)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (fma.f64 x 1/2 1)) (cbrt.f64 x)))
(pow.f64 (/.f64 (fma.f64 x 1/2 1) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) 3)
(pow.f64 (pow.f64 (/.f64 (fma.f64 x 1/2 1) x) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) 2)
(pow.f64 (/.f64 x (fma.f64 x 1/2 1)) -1)
(neg.f64 (/.f64 (fma.f64 x 1/2 1) (neg.f64 x)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x 1/2 1)) x))
(sqrt.f64 (pow.f64 (/.f64 (fma.f64 x 1/2 1) x) 2))
(log.f64 (exp.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (fma.f64 x 1/2 1) x))))
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1/2 1) x) 3))
(cbrt.f64 (/.f64 (pow.f64 (fma.f64 x 1/2 1) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(log1p.f64 (expm1.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(exp.f64 (log.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 x 1/2 1) x)) 1))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x))) 1)
(*.f64 1 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x))
(*.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) (/.f64 1 x))
(*.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x) 1)
(*.f64 (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) 2) (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) (/.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) x))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) (sqrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) x))
(.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (/.f64 1 x)))
(*.f64 (neg.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x 1/12 1/2) 1))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) (cbrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) 1) (/.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 1) (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) x))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (cbrt.f64 x)))
(pow.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) 3)
(pow.f64 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) 2)
(pow.f64 (/.f64 x (fma.f64 x (fma.f64 x 1/12 1/2) 1)) -1)
(neg.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) (neg.f64 x)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) x))
(sqrt.f64 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x) 2))
(log.f64 (exp.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x))))
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x) 3))
(cbrt.f64 (/.f64 (pow.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(log1p.f64 (expm1.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(exp.f64 (log.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x 1/12))) 1)
(pow.f64 (*.f64 x 1/12) 1)
(pow.f64 (cbrt.f64 (*.f64 x 1/12)) 3)
(pow.f64 (*.f64 (pow.f64 x 3) 1/1728) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x 1/12)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 2) 1/144))
(log.f64 (pow.f64 (exp.f64 1/12) x))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x 1/12))))
(cbrt.f64 (*.f64 (pow.f64 x 3) 1/1728))
(expm1.f64 (log1p.f64 (*.f64 x 1/12)))
(log1p.f64 (expm1.f64 (*.f64 x 1/12)))
(exp.f64 (log.f64 (*.f64 x 1/12)))
(exp.f64 (.f64 (log.f64 (.f64 x 1/12)) 1))
(+.f64 (.f64 x 1/2) (.f64 1/12 (pow.f64 x 2)))
(+.f64 (.f64 x 1/2) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(+.f64 (.f64 1/12 (pow.f64 x 2)) (.f64 x 1/2))
(-.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) 1)
(/.f64 (fma.f64 1/8 (pow.f64 x 3) (pow.f64 (.f64 1/12 (pow.f64 x 2)) 3)) (fma.f64 (pow.f64 x 2) 1/4 (fma.f64 (.f64 1/12 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)) (neg.f64 (.f64 (.f64 x 1/2) (.f64 1/12 (pow.f64 x 2)))))))
(/.f64 (-.f64 (.f64 (pow.f64 x 2) 1/4) (.f64 (.f64 1/12 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (-.f64 (.f64 x 1/2) (.f64 1/12 (pow.f64 x 2))))
(/.f64 (.f64 x (fma.f64 (pow.f64 x 3) 1/1728 1/8)) (fma.f64 (.f64 x 1/12) (fma.f64 x 1/12 -1/2) 1/4))
(/.f64 (.f64 x (-.f64 1/4 (.f64 (pow.f64 x 2) 1/144))) (+.f64 1/2 (*.f64 -1/12 x)))
(/.f64 (.f64 (fma.f64 (pow.f64 x 3) 1/1728 1/8) x) (fma.f64 (.f64 x 1/12) (fma.f64 x 1/12 -1/2) 1/4))
(/.f64 (.f64 (-.f64 1/4 (.f64 (pow.f64 x 2) 1/144)) x) (+.f64 1/2 (*.f64 -1/12 x)))
(pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/12 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x 1/12 1/2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/12 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 x 1/12 1/2)))))
(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/12 1/2))))
(expm1.f64 (.f64 (log1p.f64 (.f64 x (fma.f64 x 1/12 1/2))) 1))
(log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x 1/12 1/2))))
(exp.f64 (log.f64 (*.f64 x (fma.f64 x 1/12 1/2))))
(exp.f64 (.f64 (log.f64 (.f64 x (fma.f64 x 1/12 1/2))) 1))
(fma.f64 1 (.f64 x 1/2) (.f64 1/12 (pow.f64 x 2)))
(fma.f64 1 (.f64 x 1/2) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 1 (fma.f64 x (fma.f64 x 1/12 1/2) 1) -1)
(fma.f64 1 (.f64 1/12 (pow.f64 x 2)) (.f64 x 1/2))
(fma.f64 x 1/2 (*.f64 1/12 (pow.f64 x 2)))
(fma.f64 x 1/2 (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 x (.f64 x 1/12) (.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/12 (pow.f64 x 2)))
(fma.f64 1/2 x (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (.f64 x 1/2) 1 (.f64 1/12 (pow.f64 x 2)))
(fma.f64 (.f64 x 1/2) 1 (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 1/12 (pow.f64 x 2) (*.f64 x 1/2))
(fma.f64 (.f64 x 1/12) x (.f64 x 1/2))
(fma.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) 1 -1)
(fma.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) -1)
(fma.f64 (cbrt.f64 (.f64 x 1/2)) (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (*.f64 1/12 (pow.f64 x 2)))
(fma.f64 (cbrt.f64 (.f64 x 1/2)) (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (cbrt.f64 (.f64 x 1/2)) (*.f64 1/12 (pow.f64 x 2)))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (cbrt.f64 (.f64 x 1/2)) (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (cbrt.f64 (.f64 (pow.f64 x 2) 1/144)) (.f64 (cbrt.f64 (.f64 x 1/12)) x) (.f64 x 1/2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/2) (.f64 1/12 (pow.f64 x 2)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/2) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (.f64 x 1/12)) (*.f64 x 1/2))
(fma.f64 (pow.f64 x 2) 1/12 (*.f64 x 1/2))
(fma.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) -1)
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (*.f64 1/12 (pow.f64 x 2)))
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (sqrt.f64 (.f64 x 1/12)) (.f64 (sqrt.f64 (.f64 x 1/12)) x) (.f64 x 1/2))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/2) (.f64 1/12 (pow.f64 x 2)))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/2) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 x 1/12)) (*.f64 x 1/2))
(fma.f64 (+.f64 1 (pow.f64 (.f64 x (fma.f64 x 1/12 1/2)) 3)) (/.f64 1 (fma.f64 (.f64 x (fma.f64 x 1/12 1/2)) (fma.f64 x (fma.f64 x 1/12 1/2) -1) 1)) -1)
(fma.f64 (-.f64 1 (pow.f64 (.f64 x (fma.f64 x 1/12 1/2)) 2)) (/.f64 1 (-.f64 1 (.f64 x (fma.f64 x 1/12 1/2)))) -1)
(fma.f64 (.f64 (cbrt.f64 (.f64 1/12 (pow.f64 x 2))) (cbrt.f64 (.f64 1/12 (pow.f64 x 2)))) (cbrt.f64 (.f64 1/12 (pow.f64 x 2))) (*.f64 x 1/2))
(fma.f64 (sqrt.f64 (.f64 1/12 (pow.f64 x 2))) (sqrt.f64 (.f64 1/12 (pow.f64 x 2))) (*.f64 x 1/2))
(fma.f64 (.f64 (sqrt.f64 (.f64 x 1/12)) (sqrt.f64 x)) (.f64 (sqrt.f64 (.f64 x 1/12)) (sqrt.f64 x)) (*.f64 x 1/2))
(fma.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/12))) (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/12))) (*.f64 x 1/2))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 1/12 (pow.f64 x 2)))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (.f64 1/12 (pow.f64 x 2)))
(fma.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (.f64 (.f64 x 1/12) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x 1/2))
(fma.f64 (.f64 (.f64 x 1/12) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x 1/2))
(fma.f64 (.f64 x (cbrt.f64 (.f64 (pow.f64 x 2) 1/144))) (cbrt.f64 (.f64 x 1/12)) (.f64 x 1/2))
(fma.f64 (.f64 x (sqrt.f64 (.f64 x 1/12))) (sqrt.f64 (.f64 x 1/12)) (.f64 x 1/2))

simplify128.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1688×	`fma-neg`
1222×	`fma-define`
728×	`distribute-lft-in`
712×	`distribute-rgt-in`
648×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	5069
1	779	5013
2	2074	4639
3	7727	4639

Stop Event

1×	node limit

Counts

202 → 198

Calls

Call 1

Inputs
(/.f64 1 x)
(/.f64 (+.f64 1 (*.f64 1/2 x)) x)
(/.f64 (+.f64 1 (*.f64 1/2 x)) x)
(/.f64 (+.f64 1 (*.f64 1/2 x)) x)
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
(/.f64 1 x)
(/.f64 (+.f64 1 (*.f64 1/2 x)) x)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 1/12 x)))) x)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 1/12 x)))) x)
(*.f64 1/12 x)
(.f64 x (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(.f64 x (+.f64 1/12 (+.f64 (.f64 1/2 (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))))
(.f64 x (+.f64 1/12 (+.f64 (.f64 1/2 (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))))
(*.f64 1/12 x)
(.f64 x (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 (/.f64 (+.f64 1/2 (/.f64 1 x)) x)) 1/12)))
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 (/.f64 (+.f64 1/2 (/.f64 1 x)) x)) 1/12)))
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/2 x)
(.f64 x (+.f64 1/2 (.f64 1/12 x)))
(.f64 x (+.f64 1/2 (.f64 1/12 x)))
(.f64 x (+.f64 1/2 (.f64 1/12 x)))
(*.f64 1/12 (pow.f64 x 2))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(*.f64 1/12 (pow.f64 x 2))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 x 1/2 1) x))) 1)
(*.f64 1 (/.f64 (fma.f64 x 1/2 1) x))
(*.f64 (fma.f64 x 1/2 1) (/.f64 1 x))
(*.f64 (/.f64 (fma.f64 x 1/2 1) x) 1)
(*.f64 (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) 2) (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) (/.f64 (cbrt.f64 (fma.f64 x 1/2 1)) x))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) (.f64 (cbrt.f64 (fma.f64 x 1/2 1)) (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) (sqrt.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(*.f64 (sqrt.f64 (fma.f64 x 1/2 1)) (/.f64 (sqrt.f64 (fma.f64 x 1/2 1)) x))
(.f64 (sqrt.f64 (fma.f64 x 1/2 1)) (.f64 (sqrt.f64 (fma.f64 x 1/2 1)) (/.f64 1 x)))
(*.f64 (neg.f64 (fma.f64 x 1/2 1)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (fma.f64 x 1/2 1))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (fma.f64 x 1/2 1) (cbrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) 1) (/.f64 (cbrt.f64 (fma.f64 x 1/2 1)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (fma.f64 x 1/2 1)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 x 1/2 1)) 1) (/.f64 (sqrt.f64 (fma.f64 x 1/2 1)) x))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 x 1/2 1)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (fma.f64 x 1/2 1)) (cbrt.f64 x)))
(pow.f64 (/.f64 (fma.f64 x 1/2 1) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) 3)
(pow.f64 (pow.f64 (/.f64 (fma.f64 x 1/2 1) x) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) 2)
(pow.f64 (/.f64 x (fma.f64 x 1/2 1)) -1)
(neg.f64 (/.f64 (fma.f64 x 1/2 1) (neg.f64 x)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x 1/2 1)) x))
(sqrt.f64 (pow.f64 (/.f64 (fma.f64 x 1/2 1) x) 2))
(log.f64 (exp.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (fma.f64 x 1/2 1) x))))
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1/2 1) x) 3))
(cbrt.f64 (/.f64 (pow.f64 (fma.f64 x 1/2 1) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(log1p.f64 (expm1.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(exp.f64 (log.f64 (/.f64 (fma.f64 x 1/2 1) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 x 1/2 1) x)) 1))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x))) 1)
(*.f64 1 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x))
(*.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) (/.f64 1 x))
(*.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x) 1)
(*.f64 (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) 2) (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) (/.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) x))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) (sqrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) x))
(.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (/.f64 1 x)))
(*.f64 (neg.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x 1/12 1/2) 1))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) (cbrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) 1) (/.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 1) (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) x))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (cbrt.f64 x)))
(pow.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) 3)
(pow.f64 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) 2)
(pow.f64 (/.f64 x (fma.f64 x (fma.f64 x 1/12 1/2) 1)) -1)
(neg.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) (neg.f64 x)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) x))
(sqrt.f64 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x) 2))
(log.f64 (exp.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x))))
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x) 3))
(cbrt.f64 (/.f64 (pow.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(log1p.f64 (expm1.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(exp.f64 (log.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x 1/12))) 1)
(pow.f64 (*.f64 x 1/12) 1)
(pow.f64 (cbrt.f64 (*.f64 x 1/12)) 3)
(pow.f64 (*.f64 (pow.f64 x 3) 1/1728) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x 1/12)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 2) 1/144))
(log.f64 (pow.f64 (exp.f64 1/12) x))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x 1/12))))
(cbrt.f64 (*.f64 (pow.f64 x 3) 1/1728))
(expm1.f64 (log1p.f64 (*.f64 x 1/12)))
(log1p.f64 (expm1.f64 (*.f64 x 1/12)))
(exp.f64 (log.f64 (*.f64 x 1/12)))
(exp.f64 (.f64 (log.f64 (.f64 x 1/12)) 1))
(+.f64 (.f64 x 1/2) (.f64 1/12 (pow.f64 x 2)))
(+.f64 (.f64 x 1/2) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(+.f64 (.f64 1/12 (pow.f64 x 2)) (.f64 x 1/2))
(-.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) 1)
(/.f64 (fma.f64 1/8 (pow.f64 x 3) (pow.f64 (.f64 1/12 (pow.f64 x 2)) 3)) (fma.f64 (pow.f64 x 2) 1/4 (fma.f64 (.f64 1/12 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)) (neg.f64 (.f64 (.f64 x 1/2) (.f64 1/12 (pow.f64 x 2)))))))
(/.f64 (-.f64 (.f64 (pow.f64 x 2) 1/4) (.f64 (.f64 1/12 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (-.f64 (.f64 x 1/2) (.f64 1/12 (pow.f64 x 2))))
(/.f64 (.f64 x (fma.f64 (pow.f64 x 3) 1/1728 1/8)) (fma.f64 (.f64 x 1/12) (fma.f64 x 1/12 -1/2) 1/4))
(/.f64 (.f64 x (-.f64 1/4 (.f64 (pow.f64 x 2) 1/144))) (+.f64 1/2 (*.f64 -1/12 x)))
(/.f64 (.f64 (fma.f64 (pow.f64 x 3) 1/1728 1/8) x) (fma.f64 (.f64 x 1/12) (fma.f64 x 1/12 -1/2) 1/4))
(/.f64 (.f64 (-.f64 1/4 (.f64 (pow.f64 x 2) 1/144)) x) (+.f64 1/2 (*.f64 -1/12 x)))
(pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/12 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x 1/12 1/2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/12 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 x 1/12 1/2)))))
(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/12 1/2))))
(expm1.f64 (.f64 (log1p.f64 (.f64 x (fma.f64 x 1/12 1/2))) 1))
(log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x 1/12 1/2))))
(exp.f64 (log.f64 (*.f64 x (fma.f64 x 1/12 1/2))))
(exp.f64 (.f64 (log.f64 (.f64 x (fma.f64 x 1/12 1/2))) 1))
(fma.f64 1 (.f64 x 1/2) (.f64 1/12 (pow.f64 x 2)))
(fma.f64 1 (.f64 x 1/2) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 1 (fma.f64 x (fma.f64 x 1/12 1/2) 1) -1)
(fma.f64 1 (.f64 1/12 (pow.f64 x 2)) (.f64 x 1/2))
(fma.f64 x 1/2 (*.f64 1/12 (pow.f64 x 2)))
(fma.f64 x 1/2 (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 x (.f64 x 1/12) (.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/12 (pow.f64 x 2)))
(fma.f64 1/2 x (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (.f64 x 1/2) 1 (.f64 1/12 (pow.f64 x 2)))
(fma.f64 (.f64 x 1/2) 1 (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 1/12 (pow.f64 x 2) (*.f64 x 1/2))
(fma.f64 (.f64 x 1/12) x (.f64 x 1/2))
(fma.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) 1 -1)
(fma.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) -1)
(fma.f64 (cbrt.f64 (.f64 x 1/2)) (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (*.f64 1/12 (pow.f64 x 2)))
(fma.f64 (cbrt.f64 (.f64 x 1/2)) (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (cbrt.f64 (.f64 x 1/2)) (*.f64 1/12 (pow.f64 x 2)))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (cbrt.f64 (.f64 x 1/2)) (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (cbrt.f64 (.f64 (pow.f64 x 2) 1/144)) (.f64 (cbrt.f64 (.f64 x 1/12)) x) (.f64 x 1/2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/2) (.f64 1/12 (pow.f64 x 2)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/2) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (.f64 x 1/12)) (*.f64 x 1/2))
(fma.f64 (pow.f64 x 2) 1/12 (*.f64 x 1/2))
(fma.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) -1)
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (*.f64 1/12 (pow.f64 x 2)))
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (sqrt.f64 (.f64 x 1/12)) (.f64 (sqrt.f64 (.f64 x 1/12)) x) (.f64 x 1/2))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/2) (.f64 1/12 (pow.f64 x 2)))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/2) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 x 1/12)) (*.f64 x 1/2))
(fma.f64 (+.f64 1 (pow.f64 (.f64 x (fma.f64 x 1/12 1/2)) 3)) (/.f64 1 (fma.f64 (.f64 x (fma.f64 x 1/12 1/2)) (fma.f64 x (fma.f64 x 1/12 1/2) -1) 1)) -1)
(fma.f64 (-.f64 1 (pow.f64 (.f64 x (fma.f64 x 1/12 1/2)) 2)) (/.f64 1 (-.f64 1 (.f64 x (fma.f64 x 1/12 1/2)))) -1)
(fma.f64 (.f64 (cbrt.f64 (.f64 1/12 (pow.f64 x 2))) (cbrt.f64 (.f64 1/12 (pow.f64 x 2)))) (cbrt.f64 (.f64 1/12 (pow.f64 x 2))) (*.f64 x 1/2))
(fma.f64 (sqrt.f64 (.f64 1/12 (pow.f64 x 2))) (sqrt.f64 (.f64 1/12 (pow.f64 x 2))) (*.f64 x 1/2))
(fma.f64 (.f64 (sqrt.f64 (.f64 x 1/12)) (sqrt.f64 x)) (.f64 (sqrt.f64 (.f64 x 1/12)) (sqrt.f64 x)) (*.f64 x 1/2))
(fma.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/12))) (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/12))) (*.f64 x 1/2))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 1/12 (pow.f64 x 2)))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (.f64 1/12 (pow.f64 x 2)))
(fma.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(fma.f64 (.f64 (.f64 x 1/12) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x 1/2))
(fma.f64 (.f64 (.f64 x 1/12) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x 1/2))
(fma.f64 (.f64 x (cbrt.f64 (.f64 (pow.f64 x 2) 1/144))) (cbrt.f64 (.f64 x 1/12)) (.f64 x 1/2))
(fma.f64 (.f64 x (sqrt.f64 (.f64 x 1/12))) (sqrt.f64 (.f64 x 1/12)) (.f64 x 1/2))

Outputs
(/.f64 1 x)
(/.f64 (+.f64 1 (*.f64 1/2 x)) x)
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(/.f64 (+.f64 1 (*.f64 1/2 x)) x)
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(/.f64 (+.f64 1 (*.f64 1/2 x)) x)
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
1/2
(+.f64 1/2 (/.f64 1 x))
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
1/2
(+.f64 1/2 (/.f64 1 x))
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(/.f64 1 x)
(/.f64 (+.f64 1 (*.f64 1/2 x)) x)
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 1/12 x)))) x)
(/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 1/12 x)))) x)
(/.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) x)
(*.f64 1/12 x)
(*.f64 x 1/12)
(.f64 x (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(*.f64 x (+.f64 1/12 (/.f64 1/2 x)))
(fma.f64 x 1/12 1/2)
(.f64 x (+.f64 1/12 (+.f64 (.f64 1/2 (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))))
(*.f64 x (+.f64 1/12 (+.f64 (/.f64 1/2 x) (/.f64 1 (pow.f64 x 2)))))
(*.f64 x (+.f64 (+.f64 1/12 (/.f64 1/2 x)) (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(.f64 x (+.f64 1/12 (+.f64 (.f64 1/2 (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))))
(*.f64 x (+.f64 1/12 (+.f64 (/.f64 1/2 x) (/.f64 1 (pow.f64 x 2)))))
(*.f64 x (+.f64 (+.f64 1/12 (/.f64 1/2 x)) (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(*.f64 1/12 x)
(*.f64 x 1/12)
(.f64 x (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(*.f64 x (+.f64 1/12 (/.f64 1/2 x)))
(fma.f64 x 1/12 1/2)
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 (/.f64 (+.f64 1/2 (/.f64 1 x)) x)) 1/12)))
(*.f64 x (+.f64 1/12 (+.f64 (/.f64 1/2 x) (/.f64 1 (pow.f64 x 2)))))
(*.f64 x (+.f64 (+.f64 1/12 (/.f64 1/2 x)) (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(.f64 -1 (.f64 x (-.f64 (*.f64 -1 (/.f64 (+.f64 1/2 (/.f64 1 x)) x)) 1/12)))
(*.f64 x (+.f64 1/12 (+.f64 (/.f64 1/2 x) (/.f64 1 (pow.f64 x 2)))))
(*.f64 x (+.f64 (+.f64 1/12 (/.f64 1/2 x)) (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/12 x)
(*.f64 x 1/12)
(*.f64 1/2 x)
(*.f64 x 1/2)
(.f64 x (+.f64 1/2 (.f64 1/12 x)))
(*.f64 x (fma.f64 x 1/12 1/2))
(.f64 x (+.f64 1/2 (.f64 1/12 x)))
(*.f64 x (fma.f64 x 1/12 1/2))
(.f64 x (+.f64 1/2 (.f64 1/12 x)))
(*.f64 x (fma.f64 x 1/12 1/2))
(*.f64 1/12 (pow.f64 x 2))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(*.f64 x (fma.f64 x 1/12 1/2))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(*.f64 x (fma.f64 x 1/12 1/2))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(*.f64 x (fma.f64 x 1/12 1/2))
(*.f64 1/12 (pow.f64 x 2))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(*.f64 x (fma.f64 x 1/12 1/2))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(*.f64 x (fma.f64 x 1/12 1/2))
(.f64 (pow.f64 x 2) (+.f64 1/12 (.f64 1/2 (/.f64 1 x))))
(*.f64 x (fma.f64 x 1/12 1/2))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 x 1/2 1) x))) 1)
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(*.f64 1 (/.f64 (fma.f64 x 1/2 1) x))
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(*.f64 (fma.f64 x 1/2 1) (/.f64 1 x))
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(*.f64 (/.f64 (fma.f64 x 1/2 1) x) 1)
(/.f64 (fma.f64 x 1/2 1) x)
(+.f64 (/.f64 1 x) 1/2)
(*.f64 (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x 1/2 1) x)) 2))
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(/.f64 (.f64 (-.f64 1/4 (.f64 (pow.f64 x 2) 1/144)) x) (+.f64 1/2 (*.f64 -1/12 x)))
(.f64 (-.f64 1/4 (.f64 (pow.f64 x 2) 1/144)) (/.f64 x (+.f64 1/2 (*.f64 x -1/12))))
(.f64 (+.f64 1/4 (.f64 (pow.f64 x 2) -1/144)) (/.f64 x (fma.f64 x -1/12 1/2)))
(*.f64 x (/.f64 (fma.f64 (pow.f64 x 2) -1/144 1/4) (fma.f64 x -1/12 1/2)))
(pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 1)
(*.f64 x (fma.f64 x 1/12 1/2))
(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/12 1/2))) 3)
(*.f64 x (fma.f64 x 1/12 1/2))
(pow.f64 (pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 3) 1/3)
(*.f64 x (fma.f64 x 1/12 1/2))
(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x 1/12 1/2))) 2)
(*.f64 x (fma.f64 x 1/12 1/2))
(sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 2))
(*.f64 x (fma.f64 x 1/12 1/2))
(log.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/12 1/2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 x 1/12 1/2)))))
(*.f64 x (fma.f64 x 1/12 1/2))
(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 3))
(*.f64 x (fma.f64 x 1/12 1/2))
(expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/12 1/2))))
(*.f64 x (fma.f64 x 1/12 1/2))
(expm1.f64 (.f64 (log1p.f64 (.f64 x (fma.f64 x 1/12 1/2))) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x 1/12 1/2))))
(*.f64 x (fma.f64 x 1/12 1/2))
(exp.f64 (log.f64 (*.f64 x (fma.f64 x 1/12 1/2))))
(*.f64 x (fma.f64 x 1/12 1/2))
(exp.f64 (.f64 (log.f64 (.f64 x (fma.f64 x 1/12 1/2))) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 1 (.f64 x 1/2) (.f64 1/12 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 1 (.f64 x 1/2) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 1 (fma.f64 x (fma.f64 x 1/12 1/2) 1) -1)
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 1 (.f64 1/12 (pow.f64 x 2)) (.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 x 1/2 (*.f64 1/12 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 x 1/2 (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 x (.f64 x 1/12) (.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 1/2 x (*.f64 1/12 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 1/2 x (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 x 1/2) 1 (.f64 1/12 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 x 1/2) 1 (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 1/12 (pow.f64 x 2) (*.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 x 1/12) x (.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1) 1 -1)
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) -1)
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) 2) (cbrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) -1)
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (cbrt.f64 (.f64 x 1/2)) (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (*.f64 1/12 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (cbrt.f64 (.f64 x 1/2)) (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (cbrt.f64 (.f64 x 1/2)) (*.f64 1/12 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (cbrt.f64 (.f64 x 1/2)) (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (cbrt.f64 (.f64 (pow.f64 x 2) 1/144)) (.f64 (cbrt.f64 (.f64 x 1/12)) x) (.f64 x 1/2))
(fma.f64 (cbrt.f64 (.f64 (pow.f64 x 2) 1/144)) (.f64 x (cbrt.f64 (.f64 x 1/12))) (.f64 x 1/2))
(.f64 x (+.f64 1/2 (.f64 (cbrt.f64 (.f64 x 1/12)) (cbrt.f64 (.f64 (pow.f64 x 2) 1/144)))))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/2) (.f64 1/12 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/2) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (.f64 x 1/12)) (*.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (pow.f64 x 2) 1/12 (*.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 1/12 1/2) 1)) -1)
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (*.f64 1/12 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (.f64 (.f64 1/12 (pow.f64 x 2)) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (sqrt.f64 (.f64 x 1/12)) (.f64 (sqrt.f64 (.f64 x 1/12)) x) (.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/2) (.f64 1/12 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/2) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 x 1/12)) (*.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (+.f64 1 (pow.f64 (.f64 x (fma.f64 x 1/12 1/2)) 3)) (/.f64 1 (fma.f64 (.f64 x (fma.f64 x 1/12 1/2)) (fma.f64 x (fma.f64 x 1/12 1/2) -1) 1)) -1)
(+.f64 -1 (/.f64 (+.f64 1 (pow.f64 (.f64 x (fma.f64 x 1/12 1/2)) 3)) (fma.f64 x (.f64 (fma.f64 x 1/12 1/2) (fma.f64 x (fma.f64 x 1/12 1/2) -1)) 1)))
(fma.f64 (-.f64 1 (pow.f64 (.f64 x (fma.f64 x 1/12 1/2)) 2)) (/.f64 1 (-.f64 1 (.f64 x (fma.f64 x 1/12 1/2)))) -1)
(+.f64 -1 (/.f64 (-.f64 1 (pow.f64 (*.f64 x (fma.f64 x 1/12 1/2)) 2)) (fma.f64 (neg.f64 x) (fma.f64 x 1/12 1/2) 1)))
(fma.f64 (.f64 (cbrt.f64 (.f64 1/12 (pow.f64 x 2))) (cbrt.f64 (.f64 1/12 (pow.f64 x 2)))) (cbrt.f64 (.f64 1/12 (pow.f64 x 2))) (*.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (sqrt.f64 (.f64 1/12 (pow.f64 x 2))) (sqrt.f64 (.f64 1/12 (pow.f64 x 2))) (*.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 (sqrt.f64 (.f64 x 1/12)) (sqrt.f64 x)) (.f64 (sqrt.f64 (.f64 x 1/12)) (sqrt.f64 x)) (*.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/12))) (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/12))) (*.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 1/12 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (.f64 1/12 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (.f64 (*.f64 1/12 (pow.f64 x 2)) 1))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 (.f64 x 1/12) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 (.f64 x 1/12) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))
(fma.f64 (.f64 x (cbrt.f64 (.f64 (pow.f64 x 2) 1/144))) (cbrt.f64 (.f64 x 1/12)) (.f64 x 1/2))
(fma.f64 (cbrt.f64 (.f64 (pow.f64 x 2) 1/144)) (.f64 x (cbrt.f64 (.f64 x 1/12))) (.f64 x 1/2))
(.f64 x (+.f64 1/2 (.f64 (cbrt.f64 (.f64 x 1/12)) (cbrt.f64 (.f64 (pow.f64 x 2) 1/144)))))
(fma.f64 (.f64 x (sqrt.f64 (.f64 x 1/12))) (sqrt.f64 (.f64 x 1/12)) (.f64 x 1/2))
(*.f64 x (fma.f64 x 1/12 1/2))

eval89.0ms (2%)

Compiler: Compiled 3048 to 2299 computations (24.6% saved)

prune26.0ms (0.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	197	6	203

Accuracy

100.0%

Counts

203 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.9%	(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/12)))) x)
✓	64.0%	(/.f64 1 x)
✓	100.0%	(/.f64 -1 (expm1.f64 (neg.f64 x)))
▶	63.9%	(+.f64 (/.f64 1 x) 1/2)
▶	3.3%	1/2
✓	3.0%	-1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize30.0ms (0.7%)

Compiler: Compiled 14 to 11 computations (21.4% saved)
Precisions: Click to see histograms. Total time spent on operations: 9.0ms
Operation ival-div, time spent: 7.0ms, 77.0% of total-time
Operation const, time spent: 1.0ms, 11.0% of total-time
Operation ival-add, time spent: 1.0ms, 11.0% of total-time

eval0.0ms (0%)

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

prune4.0ms (0.1%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	4	4
Total	6	6

Accuracy

100.0%

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.9%	(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/12)))) x)
✓	64.0%	(/.f64 1 x)
✓	100.0%	(/.f64 -1 (expm1.f64 (neg.f64 x)))
✓	63.9%	(+.f64 (/.f64 1 x) 1/2)
✓	3.3%	1/2
✓	3.0%	-1

Compiler

Compiled 73 to 56 computations (23.3% saved)

regimes12.0ms (0.3%)

Counts

8 → 1

Calls

Call 1

Inputs
-1
1/2
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(/.f64 (+.f64 1 (*.f64 x 1/2)) x)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/12)))) x)
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Outputs
(/.f64 -1 (expm1.f64 (neg.f64 x)))

Calls

3 calls:

6.0ms	x
3.0ms	(exp.f64 x)
2.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
100.0%	1	`(exp.f64 x)`

Compiler

Compiled 13 to 8 computations (38.5% saved)

regimes5.0ms (0.1%)

Counts

6 → 1

Calls

Call 1

Inputs
-1
1/2
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(/.f64 (+.f64 1 (*.f64 x 1/2)) x)
(/.f64 (+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/12)))) x)

Outputs
(/.f64 1 x)

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
64.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

Inputs
-1
1/2

Outputs
1/2

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
3.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
-1

Outputs
-1

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
3.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`1-exp`
2×	`sub-neg`
2×	`*-commutative`
2×	`neg-sub0`
2×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	20	30
2	22	30
3	23	30

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 1 x)
1/2
-1

Outputs
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 1 x)
1/2
-1

Compiler

Compiled 14 to 12 computations (14.3% saved)

soundness927.0ms (21%)

Rules

2412×	`fma-neg`
1730×	`prod-exp`
1494×	`div-sub`
1056×	`fma-define`
982×	`frac-times`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	104
1	35	102
2	56	102
3	94	102
4	153	76
5	292	68
6	469	68
7	837	64
8	2147	64
9	3590	64
10	4606	64
11	5606	64
12	6702	64
0	10	18
1	91	14
2	1094	8
0	191	4294968763
1	307	4294968701
2	727	4294968677
3	2799	4294968489
4	7856	4294968489

Stop Event

1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 264 to 127 computations (51.9% saved)

end0.0ms (0%)

preprocess49.0ms (1.1%)

Compiler: Compiled 52 to 40 computations (23.1% saved)

analyze151.0ms (3.4%)

sample1.8s (41.6%)

preprocess522.0ms (11.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize58.0ms (1.3%)

series3.0ms (0.1%)

rewrite167.0ms (3.8%)

simplify91.0ms (2.1%)

eval21.0ms (0.5%)

prune14.0ms (0.3%)

localize119.0ms (2.7%)

series14.0ms (0.3%)

rewrite131.0ms (3%)

simplify128.0ms (2.9%)

eval89.0ms (2%)

prune26.0ms (0.6%)

localize30.0ms (0.7%)

eval0.0ms (0%)

prune4.0ms (0.1%)

regimes12.0ms (0.3%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

simplify3.0ms (0.1%)

soundness927.0ms (21%)

end0.0ms (0%)

preprocess49.0ms (1.1%)

Profiling