Details

analyze429.0ms (6.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 39 to 31 computations (20.5% saved)

sample2.2s (32.5%)

Results

2.2s	8256×	body	128	valid
2.0ms	5×	body	128	invalid

Compiler

Compiled 78 to 62 computations (20.5% saved)

preprocess36.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

104×	`fma-neg_binary32`
95×	`fma-def_binary32`
60×	`sub-neg_binary32`
45×	`cancel-sign-sub-inv_binary32`
30×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

40×	`fma-neg_binary32`
22×	`sub-neg_binary32`
17×	`cancel-sign-sub-inv_binary32`
13×	`fma-def_binary32`
10×	`*-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Stop Event

1×

saturated

Counts

1 → 2

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	12.7b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
✓	0.2b	(sin.f32 (.f32 2 (.f32 (PI.f32) u2)))
✓	0.3b	(*.f32 (PI.f32) u2)
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))

series152.0ms (2.3%)

Counts

4 → 32

Calls

15 calls:

64.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u2	inf
55.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u2	-inf
6.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u2	0
5.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u1	0
5.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u1	inf

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

653×	`prod-diff_binary32`
202×	`expm1-udef_binary32`
202×	`log1p-udef_binary32`
131×	`add-sqr-sqrt_binary32`
123×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	265	37
2	3249	37

Stop Event

1×	node limit

Counts

4 → 76

simplify47.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

538×	`cancel-sign-sub-inv_binary32`
348×	`times-frac_binary32`
276×	`associate-*l/_binary32`
248×	`associate-/r*_binary32`
218×	`associate-/l*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2008
1	588	1830
2	2199	1690

Stop Event

1×	node limit

Counts

108 → 124

prune136.0ms (2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	110	14	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	112	14	126

Error

0.2b

Counts

126 → 14

Alt Table

Status	Error	Program
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))))))
	14.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32))))))
	8.5b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2)))) 2)))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))
	8.6b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))) 3)
	1.0b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3))))
	2.6b	(fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 u2 3) -4/3)))))
	8.5b	(cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))) 3)))
	8.8b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (log1p.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (pow.f32 (sqrt.f32 (*.f32 (PI.f32) u2)) 2))))
	1.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (sqrt.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2)))) 2))
	2.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (exp.f32 (log.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))))
	2.0b	(-.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 u2 (PI.f32)) (.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 u2 7) (pow.f32 (PI.f32) 7))))))

Compiler

Compiled 4009 to 2720 computations (32.2% saved)

localize47.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sin.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3)))))
✓	0.3b	(*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))))))
✓	1.0b	(pow.f32 (PI.f32) 3)

series194.0ms (2.9%)

Counts

4 → 32

Calls

12 calls:

80.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))))))	u2	-inf
55.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))))))	u2	inf
24.0ms	(sin.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3)))))	u2	0
6.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))))))	u1	0
5.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))))))	u2	0

rewrite54.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

469×	`prod-diff_binary32`
251×	`log1p-udef_binary32`
163×	`add-sqr-sqrt_binary32`
155×	`expm1-log1p-u_binary32`
154×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	349	40
2	4083	40

Stop Event

1×	node limit

Counts

4 → 73

simplify40.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary32`
573×	`associate-l_binary32`
366×	`cancel-sign-sub-inv_binary32`
160×	`associate-*l/_binary32`
160×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	1528
1	428	1418
2	1508	1320

Stop Event

1×	node limit

Counts

105 → 113

prune145.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	7	6	13
Picked	0	1	1
Done	0	0	0
Total	119	8	127

Error

0.1b

Counts

127 → 8

Alt Table

Status	Error	Program
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2)))) 2)))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))
✓	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))))))
	8.6b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))) 3)
	2.6b	(fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 u2 3) -4/3)))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (pow.f32 (sqrt.f32 (*.f32 (PI.f32) u2)) 2))))
	2.0b	(-.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 u2 (PI.f32)) (.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 u2 7) (pow.f32 (PI.f32) 7))))))

Compiler

Compiled 3247 to 2135 computations (34.2% saved)

localize68.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sin.f32 (.f32 2 (cbrt.f32 (.f32 (*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3)))))
✓	0.3b	(.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))
✓	1.0b	(pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3)

series158.0ms (2.4%)

Counts

4 → 44

Calls

12 calls:

63.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))	u2	-inf
57.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))	u2	inf
7.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))	u2	0
5.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))	u1	0
5.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))	u1	inf

rewrite58.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

469×	`prod-diff_binary32`
185×	`add-sqr-sqrt_binary32`
181×	`expm1-log1p-u_binary32`
180×	`log1p-expm1-u_binary32`
177×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	77
1	411	40
2	4746	40

Stop Event

1×	node limit

Counts

4 → 77

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary32`
574×	`associate-l_binary32`
366×	`cancel-sign-sub-inv_binary32`
160×	`associate-*l/_binary32`
160×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1660
1	428	1550
2	1508	1452

Stop Event

1×	node limit

Counts

121 → 117

prune109.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	116	9	125

Error

0.1b

Counts

125 → 9

Alt Table

Status	Error	Program
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2)))) 2)))
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))
✓	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))
✓	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))))))
	8.6b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))) 3)
	2.6b	(fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 u2 3) -4/3)))))
	2.6b	(fma.f32 2 (.f32 (PI.f32) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) u2)) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 u2 3) -4/3)))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (pow.f32 (sqrt.f32 (*.f32 (PI.f32) u2)) 2))))
	2.0b	(-.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 u2 (PI.f32)) (.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 u2 7) (pow.f32 (PI.f32) 7))))))

Compiler

Compiled 3485 to 2277 computations (34.7% saved)

localize77.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sin.f32 (*.f32 (PI.f32) u2))
✓	0.2b	(.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))
	0.3b	(*.f32 (PI.f32) u2)
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))

series162.0ms (2.4%)

Counts

3 → 40

Calls

12 calls:

59.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))	u2	-inf
58.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))	u2	inf
10.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))	u2	0
9.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))	u1	0
8.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))	u1	inf

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

240×	`expm1-udef_binary32`
240×	`log1p-udef_binary32`
237×	`fma-def_binary32`
155×	`add-sqr-sqrt_binary32`
153×	`fma-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	44
1	310	40
2	4007	40

Stop Event

1×	node limit

Counts

3 → 52

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary32`
440×	`cancel-sign-sub-inv_binary32`
275×	`times-frac_binary32`
245×	`associate-/l*_binary32`
188×	`distribute-rgt-neg-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	1908
1	495	1776
2	1835	1659

Stop Event

1×	node limit

Counts

92 → 96

prune139.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	126	9	135

Error

0.1b

Counts

135 → 9

Alt Table

Status	Error	Program
✓	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))
✓	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))))))
	2.6b	(fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 u2 3) -4/3)))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2))))))))
	2.6b	(fma.f32 2 (.f32 (PI.f32) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) u2)) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 u2 3) -4/3)))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2)))) 2)))
	0.6b	(.f32 2 (.f32 (cos.f32 (.f32 u2 (PI.f32))) (.f32 (sin.f32 (*.f32 u2 (PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 (PI.f32) u2)) 2)) (cos.f32 (*.f32 (PI.f32) u2)))))
	2.0b	(-.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 u2 (PI.f32)) (.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 u2 7) (pow.f32 (PI.f32) 7))))))

Compiler

Compiled 3762 to 1837 computations (51.2% saved)

regimes2.0s (30.4%)

Accuracy

Total 0.4b remaining (77.5%)

Threshold costs 0.4b (77.5%)

Counts

174 → 1

Compiler

Compiled 36516 to 30454 computations (16.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary32`
2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	44
1	32	44
2	36	44
3	38	44

Stop Event

1×

saturated

end183.0ms (2.7%)

Stop Event

1×

fuel

Compiler

Compiled 318 to 248 computations (22% saved)

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Details

analyze429.0ms (6.4%)

sample2.2s (32.5%)

preprocess36.0ms (0.5%)

simplify12.0ms (0.2%)

prune5.0ms (0.1%)

localize33.0ms (0.5%)

series152.0ms (2.3%)

rewrite48.0ms (0.7%)

simplify47.0ms (0.7%)

prune136.0ms (2%)

localize47.0ms (0.7%)

series194.0ms (2.9%)

rewrite54.0ms (0.8%)

simplify40.0ms (0.6%)

prune145.0ms (2.2%)

localize68.0ms (1%)

series158.0ms (2.4%)

rewrite58.0ms (0.9%)

simplify46.0ms (0.7%)

prune109.0ms (1.6%)

localize77.0ms (1.2%)

series162.0ms (2.4%)

rewrite48.0ms (0.7%)

simplify52.0ms (0.8%)

prune139.0ms (2.1%)

regimes2.0s (30.4%)

simplify3.0ms (0%)

end183.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21