Details

analyze229.0ms (3.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	68.7%	6.3%	5
25%	65.6%	9.5%	6
37.5%	39%	23.5%	7
37.5%	36.7%	25.9%	8
43.7%	20.7%	35.6%	9
43.7%	19.3%	37%	10
46.8%	10.6%	42.5%	11
46.8%	9.9%	43.3%	12
48.4%	5.4%	46.2%	13
48.4%	5%	46.6%	14

Compiler

Compiled 19 to 17 computations (10.5% saved)

sample53.0ms (0.8%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
1.0ms	11×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def_binary64`
7×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	26	23
2	40	21
3	49	21
4	56	21
5	63	21
6	74	21
7	73	21
8	62	21

prune3.0ms (0%)

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

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Compiler

Compiled 61 to 49 computations (19.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
✓	1.0b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
✓	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

series35.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

21.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
8.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
6.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 51

Calls

3 calls:

3.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
1.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
0.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))

simplify123.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

516×	`distribute-rgt-in_binary64`
515×	`fma-neg_binary64`
508×	`associate-/l/_binary64`
495×	`distribute-lft-in_binary64`
420×	`distribute-rgt-out_binary64`

Counts

123 → 97

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	105	2186
1	150	2070
2	246	2070
3	411	2070
4	874	2070
5	2199	2070
6	4684	2070
7	5109	2070

prune109.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	4	98

Error

1.0b

Counts

98 → 4

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) 3)))
▶	1.0b	(*.f64 2 (log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 2151 to 1235 computations (42.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
	0.0b	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
	1.0b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

series22.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

22.0ms

(log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log-pow_binary64`
3×	`log-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`exp-prod_binary64`

Counts

1 → 18

Calls

1 calls:

2.0ms

(log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

simplify127.0ms (2%)

Algorithm

1×	egg-herbie

Rules

813×	`log-prod_binary64`
451×	`exp-to-pow_binary64`
376×	`times-frac_binary64`
372×	`unswap-sqr_binary64`
368×	`log-pow_binary64`

Counts

42 → 34

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	936
1	76	878
2	110	878
3	149	878
4	243	878
5	504	878
6	1156	878
7	2811	878
8	4708	878
9	4941	878
10	4995	878
11	4970	878
12	4980	878

prune85.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	130	5	135

Error

0.0b

Counts

135 → 5

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (log.f64 (exp.f64 (cos.f64 (expm1.f64 (log1p.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))))))
▶	0.1b	(.f64 2 (+.f64 (.f64 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))) 2) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))))
	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) 3)))
✓	1.0b	(*.f64 2 (log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 3201 to 1955 computations (38.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))
✓	0.0b	(log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
✓	1.0b	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)
✓	1.0b	(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))

series3.3s (52%)

Counts

4 → 96

Calls

4 calls:

2.2s	(log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
1.1s	(cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))
23.0ms	(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
6.0ms	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-exp-log_binary64`

Counts

4 → 74

Calls

4 calls:

2.0ms	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)
2.0ms	(log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
2.0ms	(cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))
1.0ms	(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))

simplify137.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

521×	`associate-+l+_binary64`
345×	`associate-/l/_binary64`
280×	`distribute-rgt-out_binary64`
266×	`unswap-sqr_binary64`
250×	`associate-/l*_binary64`

Counts

170 → 129

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	3774
1	190	3619
2	289	3559
3	433	3520
4	857	3508
5	1881	3508
6	4804	3508

prune311.0ms (4.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	255	3	258
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	257	6	263

Error

Counts

263 → 6

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (+.f64 (.f64 (.f64 1/3 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 2) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))))
✓	0.1b	(.f64 2 (+.f64 (.f64 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))) 2) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))))
	1.6b	(.f64 2 (+.f64 (.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))) (cbrt.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))))) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))))) 2) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))))
▶	0.1b	(.f64 2 (+.f64 (.f64 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))) 2) (.f64 1/3 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h)))))))))
	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) 3)))
✓	1.0b	(*.f64 2 (log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 11076 to 7056 computations (36.3% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)
✓	1.0b	(*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))
	1.0b	(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
✓	1.0b	(cos.f64 (fma.f64 2/3 (PI.f64) (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))

series27.0ms (0.4%)

Counts

2 → 32

Calls

2 calls:

21.0ms	(cos.f64 (fma.f64 2/3 (PI.f64) (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))
5.0ms	(*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))
1.0ms	(cos.f64 (fma.f64 2/3 (PI.f64) (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))

simplify90.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-l_binary64`
644×	`unswap-sqr_binary64`
560×	`associate-/l*_binary64`
381×	`associate-r_binary64`
332×	`log-div_binary64`

Counts

62 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	1121
1	99	1044
2	149	1043
3	194	1043
4	241	1043
5	346	1043
6	602	1043
7	1371	1043
8	3345	1043
9	4661	1043
10	4834	1043

prune129.0ms (2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	105	6	111

Error

Counts

111 → 6

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (+.f64 (.f64 (.f64 1/3 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 2) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))))
✓	0.1b	(.f64 2 (+.f64 (.f64 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))) 2) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))))
	1.6b	(.f64 2 (+.f64 (.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))) (cbrt.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))))) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))))) 2) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))))
✓	0.1b	(.f64 2 (+.f64 (.f64 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))) 2) (.f64 1/3 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h)))))))))
	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) 3)))
✓	1.0b	(*.f64 2 (log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 4287 to 2673 computations (37.6% saved)

regimes287.0ms (4.5%)

Accuracy

Total 0.1b remaining (79.1%)

Threshold costs 0.1b (79.1%)

Counts

24 → 1

Compiler

Compiled 6814 to 5390 computations (20.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	53
1	35	53
2	39	53
3	42	53
4	43	53
5	43	53

end1.0ms (0%)

Compiler: Compiled 34 to 26 computations (23.5% saved)

sample1.2s (18.8%)

Algorithm

1×

intervals

Results

760.0ms	8000×	body	128	valid
49.0ms	579×	body	128	nan

Compiler

Compiled 260 to 202 computations (22.3% saved)

Details

analyze229.0ms (3.6%)

sample53.0ms (0.8%)

simplify12.0ms (0.2%)

prune3.0ms (0%)

localize10.0ms (0.2%)

series35.0ms (0.5%)

rewrite7.0ms (0.1%)

simplify123.0ms (1.9%)

prune109.0ms (1.7%)

localize13.0ms (0.2%)

series22.0ms (0.3%)

rewrite3.0ms (0%)

simplify127.0ms (2%)

prune85.0ms (1.3%)

localize17.0ms (0.3%)

series3.3s (52%)

rewrite10.0ms (0.2%)

simplify137.0ms (2.1%)

prune311.0ms (4.9%)

localize22.0ms (0.3%)

series27.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify90.0ms (1.4%)

prune129.0ms (2%)

regimes287.0ms (4.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.2s (18.8%)

Profiling