Details

analyze436.0ms (3.4%)

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)

sample2.7s (21%)

Results

2.4s	8256×	body	128	valid
170.0ms	553×	body	128	invalid

Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify15.0ms (0.1%)

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

prune6.0ms (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)

localize20.0ms (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)))

series94.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

59.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
23.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
12.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

rewrite26.0ms (0.2%)

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:

13.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
4.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
2.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

simplify237.0ms (1.8%)

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

prune205.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	3	98

Error

1.0b

Counts

98 → 3

Alt Table

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

Compiler

Compiled 2145 to 1221 computations (43.1% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))
✓	1.0b	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
✓	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))
✓	1.0b	(/.f64 1 (sqrt.f64 3))

series362.0ms (2.8%)

Counts

4 → 72

Calls

4 calls:

150.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))
112.0ms	(fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))
100.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
0.0ms	(/.f64 1 (sqrt.f64 3))

rewrite57.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
41×	`sqrt-prod_binary64`

Counts

4 → 152

Calls

4 calls:

22.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
10.0ms	(/.f64 1 (sqrt.f64 3))
1.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))
1.0ms	(fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))

simplify273.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-neg_binary64`
551×	`fma-def_binary64`
469×	`times-frac_binary64`
379×	`associate-/l*_binary64`
296×	`*-commutative_binary64`

Counts

224 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	4593
1	330	3862
2	933	3699
3	2132	3651
4	2660	3651
5	4263	3651
6	4937	3651
7	5174	3651

prune496.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	206	3	209

Error

1.0b

Counts

209 → 3

Alt Table

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

Compiler

Compiled 5616 to 3898 computations (30.6% saved)

localize26.0ms (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)))

series44.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

44.0ms

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

rewrite6.0ms (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:

4.0ms

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

simplify257.0ms (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

prune159.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	130	4	134

Error

Counts

134 → 4

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (-.f64 (log.f64 (exp.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (log.f64 (exp.f64 (.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))))
	1.6b	(.f64 2 (.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 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))))))
▶	0.0b	(.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))))))))

Compiler

Compiled 3251 to 1973 computations (39.3% saved)

localize30.0ms (0.2%)

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)))

series5.8s (45.3%)

Counts

4 → 96

Calls

4 calls:

3.9s	(log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
1.9s	(cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))
29.0ms	(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)

rewrite17.0ms (0.1%)

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:

4.0ms	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)
3.0ms	(log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
3.0ms	(cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))
2.0ms	(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))

simplify316.0ms (2.5%)

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

prune519.0ms (4.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	258	4	262

Error

Counts

262 → 4

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (-.f64 (log.f64 (exp.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (log.f64 (exp.f64 (.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 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 (.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))))))))
✓	0.0b	(.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))))))))

Compiler

Compiled 10839 to 6879 computations (36.5% saved)

regimes401.0ms (3.1%)

Accuracy

Total 0.1b remaining (79.9%)

Threshold costs 0.1b (79.9%)

Counts

26 → 1

Compiler

Compiled 5985 to 4695 computations (21.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	20	77
1	28	77
2	32	77
3	35	77
4	36	77
5	36	77

end277.0ms (2.2%)

Compiler: Compiled 215 to 161 computations (25.1% saved)

Details

analyze436.0ms (3.4%)

sample2.7s (21%)

simplify15.0ms (0.1%)

prune6.0ms (0%)

localize20.0ms (0.2%)

series94.0ms (0.7%)

rewrite26.0ms (0.2%)

simplify237.0ms (1.8%)

prune205.0ms (1.6%)

localize26.0ms (0.2%)

series362.0ms (2.8%)

rewrite57.0ms (0.4%)

simplify273.0ms (2.1%)

prune496.0ms (3.9%)

localize26.0ms (0.2%)

series44.0ms (0.3%)

rewrite6.0ms (0%)

simplify257.0ms (2%)

prune159.0ms (1.2%)

localize30.0ms (0.2%)

series5.8s (45.3%)

rewrite17.0ms (0.1%)

simplify316.0ms (2.5%)

prune519.0ms (4.1%)

regimes401.0ms (3.1%)

simplify7.0ms (0.1%)

end277.0ms (2.2%)

Profiling