Details

analyze74.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
3.1%	3.1%	93.8%	2
3.1%	3.1%	93.8%	3
4.7%	1.6%	93.8%	4
4.7%	1.6%	93.8%	5
5.5%	0.8%	93.8%	6
5.5%	0.8%	93.8%	7
5.8%	0.4%	93.8%	8
5.8%	0.4%	93.8%	9
6%	0.2%	93.8%	10
6%	0.2%	93.8%	11
6.1%	0.1%	93.8%	12
6.1%	0.1%	93.8%	13
6.2%	0%	93.8%	14

Compiler

Compiled 36 to 30 computations (16.7% saved)

sample2.3s (35.1%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify126.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

909×	`cube-prod_binary64`
818×	`unswap-sqr_binary64`
698×	`fabs-mul_binary64`
671×	`sqr-pow_binary64`
541×	`cube-mult_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	24
1	38	24
2	63	24
3	101	24
4	203	24
5	528	24
6	667	24
7	856	24
8	1442	24
9	1481	24
10	1512	24
11	1576	24
12	1582	24
13	1854	24
14	2077	24
15	2498	24
16	3106	24
17	3604	24
18	4037	24
19	4445	24
20	4754	24
21	4859	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 70 to 60 computations (14.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.2b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

series307.0ms (4.7%)

Counts

4 → 52

Calls

4 calls:

158.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
116.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
30.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`

Counts

4 → 64

Calls

4 calls:

4.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
4.0ms	(.f64 (.f64 2 (PI.f64)) u2)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

simplify104.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

621×	`unswap-sqr_binary64`
393×	`cancel-sign-sub-inv_binary64`
381×	`*-commutative_binary64`
263×	`fma-neg_binary64`
249×	`sub-neg_binary64`

Counts

116 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	2057
1	326	1932
2	949	1852
3	1807	1800
4	3478	1800
5	4916	1800
6	4917	1800

prune126.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Error

Counts

105 → 8

Alt Table

Status	Error	Program
	0.7b	(expm1.f64 (log1p.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)))
	0.5b	(fma.f64 (exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (exp.f64 (+.f64 (log.f64 1/6) (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (.f64 1/6 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
▶	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (.f64 (.f64 (sqrt.f64 1/6) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (.f64 (sqrt.f64 1/6) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 1/6 1/6) 1/6) (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 (.f64 -2 (log.f64 u1)))) (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 2559 to 1952 computations (23.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (neg.f64 (log.f64 u1)))
✓	0.3b	(*.f64 u2 (PI.f64))
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
✓	0.5b	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))))

series353.0ms (5.4%)

Counts

4 → 68

Calls

4 calls:

170.0ms	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
158.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))))
22.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
2.0ms	(*.f64 u2 (PI.f64))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-prod_binary64`
18×	`associate-l_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`

Counts

4 → 86

Calls

4 calls:

8.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))))
3.0ms	(*.f64 u2 (PI.f64))
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.0ms	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)

simplify130.0ms (2%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-neg_binary64`
515×	`*-commutative_binary64`
379×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`
263×	`fma-def_binary64`

Counts

154 → 143

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	180	3395
1	401	3209
2	1225	3115
3	2639	3096
4	4926	3094
5	5120	3094

prune157.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	143	8	151

Error

Counts

151 → 8

Alt Table

Status	Error	Program
	0.5b	(fma.f64 1/6 (.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (log.f64 u1)))) (.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (log.f64 u1)))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (*.f64 u2 (PI.f64))))))) 1/2)
	0.7b	(expm1.f64 (log1p.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)))
	0.5b	(fma.f64 (exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (exp.f64 (+.f64 (log.f64 1/6) (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
▶	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (.f64 (.f64 (sqrt.f64 1/6) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (.f64 (sqrt.f64 1/6) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 1/6 1/6) 1/6) (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 (.f64 -2 (log.f64 u1)))) (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 3869 to 2400 computations (38% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.3b	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
✓	0.3b	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))

series63.0ms (1%)

Counts

2 → 24

Calls

2 calls:

32.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))
31.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64`
15×	`pow-prod-down_binary64`
12×	`associate-l_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`sqrt-pow1_binary64`

Counts

2 → 56

Calls

2 calls:

8.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
7.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-neg_binary64`
311×	`*-commutative_binary64`
240×	`neg-mul-1_binary64`
239×	`associate-*r/_binary64`
218×	`associate-*l/_binary64`

Counts

80 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1130
1	170	1084
2	470	1084
3	633	1076
4	841	1076
5	1846	1076
6	3632	1076
7	4942	1076

prune151.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	135	6	141

Error

Counts

141 → 6

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (exp.f64 (log.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (exp.f64 (+.f64 (log.f64 1/6) (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
▶	0.3b	(fma.f64 (sqrt.f64 (.f64 1/6 (.f64 1/6 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (.f64 (sqrt.f64 1/6) (exp.f64 (log.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 1/6 1/6) 1/6) (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 (.f64 -2 (log.f64 u1)))) (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 3367 to 2702 computations (19.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (.f64 1/6 (.f64 1/6 (*.f64 -2 (log.f64 u1)))))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 1/6 (.f64 1/6 (*.f64 -2 (log.f64 u1))))
✓	0.4b	(.f64 1/6 (.f64 -2 (log.f64 u1)))

series68.0ms (1%)

Counts

3 → 36

Calls

3 calls:

25.0ms	(sqrt.f64 (.f64 1/6 (.f64 1/6 (*.f64 -2 (log.f64 u1)))))
22.0ms	(.f64 1/6 (.f64 1/6 (*.f64 -2 (log.f64 u1))))
21.0ms	(.f64 1/6 (.f64 -2 (log.f64 u1)))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`distribute-lft-in_binary64`
48×	`distribute-rgt-in_binary64`
36×	`log-prod_binary64`
27×	`pow1_binary64`
17×	`*-un-lft-identity_binary64`

Counts

3 → 94

Calls

3 calls:

8.0ms	(sqrt.f64 (.f64 1/6 (.f64 1/6 (*.f64 -2 (log.f64 u1)))))
6.0ms	(.f64 1/6 (.f64 1/6 (*.f64 -2 (log.f64 u1))))
4.0ms	(.f64 1/6 (.f64 -2 (log.f64 u1)))

simplify102.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

608×	`distribute-rgt-neg-out_binary64`
572×	`distribute-lft-neg-out_binary64`
368×	`*-commutative_binary64`
366×	`fma-def_binary64`
181×	`unsub-neg_binary64`

Counts

130 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	1520
1	237	1212
2	717	1197
3	1060	1173
4	1974	1173
5	4750	1173
6	4985	1173
7	4774	1173

prune178.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	161	6	167

Error

Counts

167 → 6

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (exp.f64 (+.f64 (log.f64 1/6) (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.3b	(fma.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
✓	0.3b	(fma.f64 (sqrt.f64 (.f64 1/6 (.f64 1/6 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (.f64 (sqrt.f64 1/6) (exp.f64 (log.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 1/6 1/6) 1/6) (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 (.f64 -2 (log.f64 u1)))) (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 3731 to 2824 computations (24.3% saved)

regimes1.9s (29.9%)

Accuracy

Total 0.2b remaining (89.8%)

Threshold costs 0.2b (89.8%)

Counts

151 → 1

Compiler

Compiled 36612 to 31991 computations (12.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	16	21
2	16	21

end120.0ms (1.9%)

Compiler: Compiled 162 to 142 computations (12.3% saved)

Details

analyze74.0ms (1.1%)

sample2.3s (35.1%)

simplify126.0ms (1.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series307.0ms (4.7%)

rewrite13.0ms (0.2%)

simplify104.0ms (1.6%)

prune126.0ms (1.9%)

localize12.0ms (0.2%)

series353.0ms (5.4%)

rewrite17.0ms (0.3%)

simplify130.0ms (2%)

prune157.0ms (2.4%)

localize13.0ms (0.2%)

series63.0ms (1%)

rewrite17.0ms (0.3%)

simplify86.0ms (1.3%)

prune151.0ms (2.3%)

localize12.0ms (0.2%)

series68.0ms (1%)

rewrite25.0ms (0.4%)

simplify102.0ms (1.6%)

prune178.0ms (2.8%)

regimes1.9s (29.9%)

simplify2.0ms (0%)

end120.0ms (1.9%)

Profiling