Details

analyze419.0ms (4.3%)

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)

sample2.4s (24.4%)

Results

2.3s	8256×	body	128	valid
2.0ms	7×	body	128	invalid

Compiler

Compiled 94 to 76 computations (19.1% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

40×	`fma-neg_binary32`
22×	`sub-neg_binary32`
17×	`cancel-sign-sub-inv_binary32`
15×	`fma-def_binary32`
11×	`*-commutative_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

prune5.0ms (0%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	12.8b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series199.0ms (2%)

Counts

4 → 52

Calls

4 calls:

182.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
11.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
3.0ms	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))
3.0ms	(.f32 (.f32 2 (PI.f32)) u2)

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`sqrt-prod_binary32`
18×	`add-sqr-sqrt_binary32`
14×	`associate-l_binary32`
13×	`*-un-lft-identity_binary32`
13×	`add-cube-cbrt_binary32`

Counts

4 → 82

Calls

4 calls:

6.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
4.0ms	(.f32 (.f32 2 (PI.f32)) u2)
2.0ms	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))
1.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))

simplify120.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

532×	`cancel-sign-sub-inv_binary32`
449×	`fma-neg_binary32`
324×	`times-frac_binary32`
243×	`associate-/r*_binary32`
229×	`associate-/l*_binary32`

Counts

134 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	3614
1	751	3315
2	2419	3199
3	4597	3191
4	5025	3191

prune270.0ms (2.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	156	12	168
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	157	13	170

Error

0.0b

Counts

170 → 13

Alt Table

Status	Error	Program
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	3.1b	(exp.f32 (+.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (log.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	2.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	0.5b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.5b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	2.3b	(fma.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 1) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 u2 6) -4/45) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 u2 u2) -2)))))
	0.3b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
	6.1b	(log.f32 (exp.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
▶	0.3b	(log1p.f32 (expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	12.8b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Compiler

Compiled 5147 to 3156 computations (38.7% saved)

localize46.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
✓	0.2b	(log1p.f32 (expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
✓	0.2b	(expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.3b	(.f32 (.f32 2 (PI.f32)) u2)

series458.0ms (4.7%)

Counts

2 → 40

Calls

2 calls:

245.0ms

(expm1.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))

213.0ms

(log1p.f32 (expm1.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary32`
2×	`*-un-lft-identity_binary32`
2×	`add-sqr-sqrt_binary32`
2×	`add-cube-cbrt_binary32`
2×	`add-cbrt-cube_binary32`

Counts

2 → 22

Calls

2 calls:

1.0ms

(expm1.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))

0.0ms

(log1p.f32 (expm1.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))

simplify107.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

589×	`cancel-sign-sub-inv_binary32`
270×	`fma-def_binary32`
269×	`fma-neg_binary32`
250×	`associate-r_binary32`
215×	`*-commutative_binary32`

Counts

62 → 89

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	292	4570
1	916	4278
2	3583	4278
3	5078	4278

prune320.0ms (3.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	187	5	192
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	191	14	205

Error

0.0b

Counts

205 → 14

Alt Table

Status	Error	Program
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	3.1b	(exp.f32 (+.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (log.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	3.0b	(log1p.f32 (exp.f32 (log.f32 (expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	0.4b	(log1p.f32 (expm1.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (+.f32 (log.f32 2) (log.f32 (PI.f32))) (log.f32 u2)))))))
	0.5b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	6.1b	(log1p.f32 (log.f32 (exp.f32 (expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
▶	0.3b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
	6.1b	(log.f32 (exp.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	2.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	2.9b	(log1p.f32 (expm1.f32 (+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 (PI.f32) 2) (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 2) (.f32 (*.f32 u2 u2) -2)))))))
	12.8b	(log1p.f32 (expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))))

Compiler

Compiled 8816 to 5785 computations (34.4% saved)

localize60.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
✓	0.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
	0.3b	(.f32 (.f32 2 (PI.f32)) u2)
✓	0.6b	(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

series42.0ms (0.4%)

Counts

3 → 28

Calls

3 calls:

21.0ms

(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

13.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

7.0ms

(*.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2)) (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`pow1_binary32`
61×	`sqrt-prod_binary32`
50×	`add-sqr-sqrt_binary32`
32×	`pow-prod-up_binary32`
31×	`*-un-lft-identity_binary32`

Counts

3 → 163

Calls

3 calls:

13.0ms

(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

11.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

6.0ms

(*.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2)) (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))

simplify120.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary32`
321×	`fma-neg_binary32`
218×	`associate-l_binary32`
209×	`associate-r_binary32`
166×	`times-frac_binary32`

Counts

191 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	3349
1	602	2791
2	1902	2650
3	4660	2650
4	4986	2650

prune536.0ms (5.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	324	2	326
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	327	13	340

Error

0.0b

Counts

340 → 13

Alt Table

Status	Error	Program
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	3.1b	(exp.f32 (+.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (log.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	3.0b	(log1p.f32 (exp.f32 (log.f32 (expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	0.4b	(log1p.f32 (expm1.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (+.f32 (log.f32 2) (log.f32 (PI.f32))) (log.f32 u2)))))))
	0.5b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	6.1b	(log1p.f32 (log.f32 (exp.f32 (expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	6.1b	(log.f32 (exp.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.3b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (/.f32 (+.f32 1 (cos.f32 (.f32 4 (.f32 u2 (PI.f32))))) 2) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	2.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
▶	0.3b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))
	12.8b	(log1p.f32 (expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))))

Compiler

Compiled 15027 to 7506 computations (50% saved)

localize78.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f32 (.f32 2 (PI.f32)) u2)
✓	0.4b	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))
	0.6b	(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
✓	1.4b	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

series536.0ms (5.5%)

Counts

2 → 16

Calls

2 calls:

285.0ms	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))
251.0ms	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`pow1_binary32`
16×	`log-pow_binary32`
15×	`*-un-lft-identity_binary32`
12×	`distribute-lft-out_binary32`
9×	`exp-prod_binary32`

Counts

2 → 49

Calls

2 calls:

6.0ms	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))
5.0ms	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

867×	`fma-def_binary32`
390×	`fma-neg_binary32`
272×	`prod-exp_binary32`
242×	`associate-*l/_binary32`
191×	`associate-*r/_binary32`

Counts

65 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	790
1	146	630
2	441	622
3	1728	622
4	4208	622
5	5111	622

prune412.0ms (4.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	221	3	224
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	225	12	237

Error

0.0b

Counts

237 → 12

Alt Table

Status	Error	Program
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	3.1b	(exp.f32 (+.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (log.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	0.5b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	6.1b	(log1p.f32 (log.f32 (exp.f32 (expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	0.8b	(cbrt.f32 (.f32 (.f32 (exp.f32 (log.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))))
	0.3b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))) (cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))))
	0.3b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (exp.f32 (log.f32 (/.f32 (.f32 2 (PI.f32)) (exp.f32 (neg.f32 (log.f32 u2))))))))))
	0.3b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (/.f32 (+.f32 1 (cos.f32 (.f32 4 (.f32 u2 (PI.f32))))) 2) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	3.0b	(log1p.f32 (exp.f32 (log.f32 (expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	12.8b	(log1p.f32 (expm1.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))))

Compiler

Compiled 10925 to 5266 computations (51.8% saved)

regimes3.3s (33.1%)

Accuracy

Total 0.2b remaining (78.1%)

Threshold costs 0.2b (78.1%)

Counts

240 → 1

Compiler

Compiled 78627 to 58895 computations (25.1% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary32`
7×	`distribute-rgt-neg-in_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`
5×	`distribute-lft-neg-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	69
1	41	69
2	50	69
3	64	69
4	74	69
5	76	69
6	72	69

end237.0ms (2.4%)

Compiler: Compiled 433 to 316 computations (27% saved)

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

Details

analyze419.0ms (4.3%)

sample2.4s (24.4%)

simplify15.0ms (0.2%)

prune5.0ms (0%)

localize34.0ms (0.3%)

series199.0ms (2%)

rewrite17.0ms (0.2%)

simplify120.0ms (1.2%)

prune270.0ms (2.8%)

localize46.0ms (0.5%)

series458.0ms (4.7%)

rewrite2.0ms (0%)

simplify107.0ms (1.1%)

prune320.0ms (3.3%)

localize60.0ms (0.6%)

series42.0ms (0.4%)

rewrite46.0ms (0.5%)

simplify120.0ms (1.2%)

prune536.0ms (5.5%)

localize78.0ms (0.8%)

series536.0ms (5.5%)

rewrite14.0ms (0.1%)

simplify71.0ms (0.7%)

prune412.0ms (4.2%)

regimes3.3s (33.1%)

simplify5.0ms (0%)

end237.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21