Details

analyze420.0ms (3.7%)

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 31 to 25 computations (19.4% saved)

sample61.0ms (0.5%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
10.0ms	256×	pre	128	true

Compiler

Compiled 50 to 42 computations (16% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`sub-neg_binary32`
17×	`cancel-sign-sub-inv_binary32`
11×	`*-commutative_binary32`
9×	`distribute-rgt-neg-in_binary32`
8×	`+-commutative_binary32`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	26	22
2	37	22
3	44	22
4	51	22
5	60	22
6	74	22
7	97	22
8	108	22
9	110	22
10	127	22
11	123	22
12	134	22
13	137	22
14	138	22
15	116	22

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
0.2b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
0.4b	(.f32 (.f32 2 PI.f32) u2)
13.9b	(log.f32 (-.f32 1 u1))

rewrite135.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

9.0b

Rules

25×	`sqrt-prod_binary32`
22×	`add-sqr-sqrt_binary32`
17×	`*-un-lft-identity_binary32`
17×	`pow1_binary32`
16×	`associate-l_binary32`

Counts

4 → 88

Calls

4 calls:

7.0ms	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
4.0ms	(.f32 (.f32 2 PI.f32) u2)
3.0ms	(log.f32 (-.f32 1 u1))
2.0ms	(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))

Compiler

Compiled 1523 to 1205 computations (20.9% saved)

series92.0ms (0.8%)

Error

0.4b

Counts

4 → 21

Calls

4 calls:

38.0ms	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
13.0ms	(log.f32 (-.f32 1 u1))
10.0ms	(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
9.0ms	(.f32 (.f32 2 PI.f32) u2)

Compiler

Compiled 1095 to 914 computations (16.5% saved)

simplify127.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

507×	`cancel-sign-sub-inv_binary32`
394×	`*-commutative_binary32`
254×	`neg-mul-1_binary32`
248×	`neg-sub0_binary32`
237×	`distribute-rgt-neg-in_binary32`

Counts

109 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	2024
1	413	1890
2	1172	1846
3	2097	1821
4	4616	1821
5	4996	1821
6	4928	1821

prune111.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	61	12	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	12	74

Error

0.2b

Counts

74 → 12

Alt Table

Status	Error	Program
	15.1b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (.f32 2 (log.f32 (cbrt.f32 (-.f32 1 u1)))) (log.f32 (cbrt.f32 (-.f32 1 u1)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	4.1b	(.f32 (sqrt.f32 (neg.f32 (.f32 u1 (+.f32 -1 (.f32 u1 -1/2))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	14.4b	(.f32 (sqrt.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u1 u1))) (log.f32 (+.f32 u1 1))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	13.3b	(.f32 (.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (cbrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))) (cbrt.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	7.6b	(.f32 (sqrt.f32 (neg.f32 (neg.f32 u1))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	13.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 PI.f32) u2))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))))))
▶	2.2b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	13.7b	(.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (sqrt.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	13.3b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	13.7b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	13.9b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (-.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 PI.f32 4))) 1) (.f32 2 (.f32 (.f32 u2 u2) (pow.f32 PI.f32 2)))))

Compiler

Compiled 1693 to 1317 computations (22.2% saved)

localize71.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
0.3b	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))
0.3b	(*.f32 u1 1/3)
0.4b	(.f32 (.f32 2 PI.f32) u2)

rewrite228.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

20×	`add-sqr-sqrt_binary32`
18×	`associate-l_binary32`
18×	`add-cbrt-cube_binary32`
18×	`add-exp-log_binary32`
18×	`pow1_binary32`

Counts

4 → 92

Calls

4 calls:

15.0ms	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
7.0ms	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))
4.0ms	(.f32 (.f32 2 PI.f32) u2)
3.0ms	(*.f32 u1 1/3)

Compiler

Compiled 3076 to 2162 computations (29.7% saved)

series145.0ms (1.3%)

Error

0.2b

Counts

4 → 25

Calls

4 calls:

71.0ms	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
19.0ms	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))
12.0ms	(.f32 (.f32 2 PI.f32) u2)
11.0ms	(*.f32 u1 1/3)

Compiler

Compiled 1801 to 1432 computations (20.5% saved)

simplify113.0ms (1%)

Algorithm

1×	egg-herbie

Rules

355×	`associate-l_binary32`
284×	`associate-r_binary32`
261×	`cancel-sign-sub-inv_binary32`
259×	`distribute-rgt-in_binary32`
248×	`distribute-lft-in_binary32`

Counts

117 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	3162
1	567	2886
2	1835	2672
3	4338	2672
4	4920	2672

prune203.0ms (1.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	87	7	94
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	89	17	106

Error

0.1b

Counts

106 → 17

Alt Table

Status	Error	Program
	3.3b	(.f32 (.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 PI.f32) u2))))
	13.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 PI.f32) u2))))
	2.4b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))) (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))))))
	8.2b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4)))))))
	4.2b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (log.f32 (pow.f32 (exp.f32 u1) (.f32 u1 (-.f32 -1/2 (.f32 1/3 u1))))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	15.1b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (.f32 2 (log.f32 (cbrt.f32 (-.f32 1 u1)))) (log.f32 (cbrt.f32 (-.f32 1 u1)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	4.1b	(.f32 (sqrt.f32 (neg.f32 (.f32 u1 (+.f32 -1 (.f32 u1 -1/2))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	14.4b	(.f32 (sqrt.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u1 u1))) (log.f32 (+.f32 u1 1))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	13.3b	(.f32 (.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (cbrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))) (cbrt.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	2.4b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (-.f32 (.f32 (pow.f32 u1 12) 1/64) (pow.f32 (-.f32 (.f32 u1 (.f32 u1 (-.f32 -1/2 (.f32 1/3 u1)))) u1) 3)))) (sqrt.f32 (+.f32 (.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1)) (-.f32 (.f32 (.f32 (pow.f32 u1 4) -1/4) (.f32 (pow.f32 u1 4) -1/4)) (.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))))
	13.3b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))))))
▶	2.3b	(.f32 (.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 PI.f32) u2))))
	13.7b	(.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (sqrt.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	2.6b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))) (cbrt.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))))) (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (*.f32 1/4 (pow.f32 u1 4))))))))
	13.7b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	13.9b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (-.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 PI.f32 4))) 1) (.f32 2 (.f32 (.f32 u2 u2) (pow.f32 PI.f32 2)))))

Compiler

Compiled 3548 to 2586 computations (27.1% saved)

localize102.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.3b	(*.f32 1/3 u1)
0.4b	(.f32 (.f32 2 PI.f32) u2)
0.4b	(*.f32 u2 PI.f32)
0.4b	(*.f32 u2 PI.f32)

rewrite188.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

17×	`add-sqr-sqrt_binary32`
15×	`add-cbrt-cube_binary32`
15×	`add-exp-log_binary32`
15×	`pow1_binary32`
12×	`associate-r_binary32`

Counts

4 → 72

Calls

4 calls:

4.0ms	(*.f32 1/3 u1)
4.0ms	(.f32 (.f32 2 PI.f32) u2)
3.0ms	(*.f32 u2 PI.f32)
3.0ms	(*.f32 u2 PI.f32)

Compiler

Compiled 3015 to 1965 computations (34.8% saved)

series57.0ms (0.5%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

14.0ms	(*.f32 u2 PI.f32)
13.0ms	(.f32 (.f32 2 PI.f32) u2)
13.0ms	(*.f32 u2 PI.f32)
13.0ms	(*.f32 1/3 u1)

Compiler

Compiled 1167 to 871 computations (25.4% saved)

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Rules

646×	`distribute-rgt-in_binary32`
476×	`distribute-lft-in_binary32`
310×	`associate-*l/_binary32`
293×	`*-commutative_binary32`
292×	`distribute-rgt-out_binary32`

Counts

84 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	732
1	190	634
2	566	633
3	743	633
4	897	633
5	1134	633
6	2539	633
7	4645	633
8	4999	633
9	4929	633

prune130.0ms (1.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	16	16
Picked	1	0	1
Done	0	0	0
Total	36	18	54

Error

0.1b

Counts

54 → 18

Alt Table

Status	Error	Program
	3.3b	(.f32 (.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 PI.f32) u2))))
	13.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 PI.f32) u2))))
	2.4b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))) (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))))))
	8.2b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4)))))))
	4.2b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (log.f32 (pow.f32 (exp.f32 u1) (.f32 u1 (-.f32 -1/2 (.f32 1/3 u1))))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	2.3b	(.f32 (.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 (.f32 u2 PI.f32) 2)) (cbrt.f32 (.f32 (.f32 u2 PI.f32) 2))) (cbrt.f32 (.f32 (*.f32 u2 PI.f32) 2))))))
	2.6b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))) (cbrt.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))))) (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (*.f32 1/4 (pow.f32 u1 4))))))))
	15.1b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (.f32 2 (log.f32 (cbrt.f32 (-.f32 1 u1)))) (log.f32 (cbrt.f32 (-.f32 1 u1)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	4.1b	(.f32 (sqrt.f32 (neg.f32 (.f32 u1 (+.f32 -1 (.f32 u1 -1/2))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	14.4b	(.f32 (sqrt.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u1 u1))) (log.f32 (+.f32 u1 1))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	13.3b	(.f32 (.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (cbrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))) (cbrt.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	2.4b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (-.f32 (.f32 (pow.f32 u1 12) 1/64) (pow.f32 (-.f32 (.f32 u1 (.f32 u1 (-.f32 -1/2 (.f32 1/3 u1)))) u1) 3)))) (sqrt.f32 (+.f32 (.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1)) (-.f32 (.f32 (.f32 (pow.f32 u1 4) -1/4) (.f32 (pow.f32 u1 4) -1/4)) (.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))))
	13.3b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
▶	2.3b	(.f32 (.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (cos.f32 (log.f32 (pow.f32 (exp.f32 (.f32 u2 PI.f32)) 2)))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))))))
	13.7b	(.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (sqrt.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	13.7b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	13.9b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (-.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 PI.f32 4))) 1) (.f32 2 (.f32 (.f32 u2 u2) (pow.f32 PI.f32 2)))))

Compiler

Compiled 2507 to 1816 computations (27.6% saved)

localize108.0ms (1%)

Local error

Found 4 expressions with local error:

0.4b	(*.f32 u2 PI.f32)
0.4b	(*.f32 u2 PI.f32)
0.4b	(pow.f32 (exp.f32 (*.f32 u2 PI.f32)) 2)
12.7b	(log.f32 (pow.f32 (exp.f32 (*.f32 u2 PI.f32)) 2))

rewrite229.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

16×	`add-sqr-sqrt_binary32`
12×	`*-un-lft-identity_binary32`
12×	`add-cube-cbrt_binary32`
9×	`add-exp-log_binary32`
9×	`pow1_binary32`

Counts

4 → 75

Calls

4 calls:

3.0ms	(*.f32 u2 PI.f32)
3.0ms	(*.f32 u2 PI.f32)
3.0ms	(pow.f32 (exp.f32 (*.f32 u2 PI.f32)) 2)
2.0ms	(log.f32 (pow.f32 (exp.f32 (*.f32 u2 PI.f32)) 2))

Compiler

Compiled 3431 to 2125 computations (38.1% saved)

series88.0ms (0.8%)

Error

0.1b

Counts

4 → 15

Calls

4 calls:

26.0ms	(log.f32 (pow.f32 (exp.f32 (*.f32 u2 PI.f32)) 2))
19.0ms	(pow.f32 (exp.f32 (*.f32 u2 PI.f32)) 2)
13.0ms	(*.f32 u2 PI.f32)
13.0ms	(*.f32 u2 PI.f32)

Compiler

Compiled 1539 to 1134 computations (26.3% saved)

simplify122.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

480×	`associate-l_binary32`
418×	`distribute-rgt-in_binary32`
396×	`associate-r_binary32`
378×	`distribute-lft-in_binary32`
331×	`exp-prod_binary32`

Counts

90 → 48

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	960
1	180	823
2	493	823
3	1806	820
4	4275	820
5	4628	820
6	4995	820
7	4974	820

prune129.0ms (1.1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	47	19	66

Error

0.1b

Counts

66 → 19

Alt Table

Status	Error	Program
	3.3b	(.f32 (.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 PI.f32) u2))))
	13.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 PI.f32) u2))))
	2.3b	(.f32 (.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (cos.f32 (log.f32 (pow.f32 (exp.f32 u2) (.f32 2 PI.f32))))))
	13.7b	(.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (sqrt.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	2.4b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))) (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))))))
	8.2b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4)))))))
	4.2b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (log.f32 (pow.f32 (exp.f32 u1) (.f32 u1 (-.f32 -1/2 (.f32 1/3 u1))))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	2.3b	(.f32 (.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 (.f32 u2 PI.f32) 2)) (cbrt.f32 (.f32 (.f32 u2 PI.f32) 2))) (cbrt.f32 (.f32 (*.f32 u2 PI.f32) 2))))))
	2.6b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))) (cbrt.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))))) (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (*.f32 1/4 (pow.f32 u1 4))))))))
	15.1b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (.f32 2 (log.f32 (cbrt.f32 (-.f32 1 u1)))) (log.f32 (cbrt.f32 (-.f32 1 u1)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	4.1b	(.f32 (sqrt.f32 (neg.f32 (.f32 u1 (+.f32 -1 (.f32 u1 -1/2))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	14.4b	(.f32 (sqrt.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u1 u1))) (log.f32 (+.f32 u1 1))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	13.3b	(.f32 (.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (cbrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))))) (cbrt.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	2.4b	(/.f32 (.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (-.f32 (.f32 (pow.f32 u1 12) 1/64) (pow.f32 (-.f32 (.f32 u1 (.f32 u1 (-.f32 -1/2 (.f32 1/3 u1)))) u1) 3)))) (sqrt.f32 (+.f32 (.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1)) (-.f32 (.f32 (.f32 (pow.f32 u1 4) -1/4) (.f32 (pow.f32 u1 4) -1/4)) (.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))))
	13.3b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	2.3b	(.f32 (.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 1/3 u1) 1/2)) (+.f32 u1 (.f32 1/4 (pow.f32 u1 4))))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (cos.f32 (log.f32 (pow.f32 (exp.f32 (.f32 u2 PI.f32)) 2)))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))))))
	13.7b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	13.9b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (-.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 PI.f32 4))) 1) (.f32 2 (.f32 (.f32 u2 u2) (pow.f32 PI.f32 2)))))

Compiler

Compiled 2227 to 1521 computations (31.7% saved)

regimes5.4s (47.6%)

Accuracy

Total 0.3b remaining (69.2%)

Threshold costs 0.3b (69.2%)

Compiler

Compiled 79301 to 62971 computations (20.6% saved)

bsearch12.0ms (0.1%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

27×	`distribute-rgt-neg-in_binary32`
27×	`cancel-sign-sub-inv_binary32`
21×	`*-commutative_binary32`
20×	`distribute-lft-neg-in_binary32`
20×	`neg-sub0_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	167
1	71	167
2	102	161
3	129	161
4	161	161
5	184	161
6	204	161
7	220	161
8	224	161
9	215	161

end5.0ms (0%)

Compiler: Compiled 104 to 76 computations (26.9% saved)

sample2.9s (25.5%)

Algorithm

1×

intervals

Results

946.0ms	8000×	body	128	valid
249.0ms	8000×	pre	128	true
0.0ms	7×	pre	128	false

Compiler

Compiled 866 to 671 computations (22.5% saved)

Iter	Nodes	Cost
0	14	22
1	26	22
2	37	22
3	44	22
4	51	22
5	60	22
6	74	22
7	97	22
8	108	22
9	110	22
10	127	22
11	123	22
12	134	22
13	137	22
14	138	22
15	116	22

Iter	Nodes	Cost
0	42	167
1	71	167
2	102	161
3	129	161
4	161	161
5	184	161
6	204	161
7	220	161
8	224	161
9	215	161

Iter	Nodes	Cost
0	14	22
1	26	22
2	37	22
3	44	22
4	51	22
5	60	22
6	74	22
7	97	22
8	108	22
9	110	22
10	127	22
11	123	22
12	134	22
13	137	22
14	138	22
15	116	22

Iter	Nodes	Cost
0	42	167
1	71	167
2	102	161
3	129	161
4	161	161
5	184	161
6	204	161
7	220	161
8	224	161
9	215	161

Details

analyze420.0ms (3.7%)

sample61.0ms (0.5%)

simplify16.0ms (0.1%)

prune2.0ms (0%)

localize39.0ms (0.3%)

rewrite135.0ms (1.2%)

series92.0ms (0.8%)

simplify127.0ms (1.1%)

prune111.0ms (1%)

localize71.0ms (0.6%)

rewrite228.0ms (2%)

series145.0ms (1.3%)

simplify113.0ms (1%)

prune203.0ms (1.8%)

localize102.0ms (0.9%)

rewrite188.0ms (1.7%)

series57.0ms (0.5%)

simplify108.0ms (1%)

prune130.0ms (1.1%)

localize108.0ms (1%)

rewrite229.0ms (2%)

series88.0ms (0.8%)

simplify122.0ms (1.1%)

prune129.0ms (1.1%)

regimes5.4s (47.6%)

bsearch12.0ms (0.1%)

simplify12.0ms (0.1%)

end5.0ms (0%)

sample2.9s (25.5%)

Profiling

Iter	Nodes	Cost
0	14	22
1	26	22
2	37	22
3	44	22
4	51	22
5	60	22
6	74	22
7	97	22
8	108	22
9	110	22
10	127	22
11	123	22
12	134	22
13	137	22
14	138	22
15	116	22

Iter	Nodes	Cost
0	42	167
1	71	167
2	102	161
3	129	161
4	161	161
5	184	161
6	204	161
7	220	161
8	224	161
9	215	161