Details

analyze425.0ms (5.5%)

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)

sample1.5s (18.9%)

Results

1.3s	8256×	body	128	valid
78.0ms	534×	body	128	invalid

Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify62.0ms (0.8%)

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 (0.1%)

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)

rewrite11.0ms (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:

6.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
2.0ms	(/.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))

simplify125.0ms (1.6%)

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

prune100.0ms (1.3%)

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 (log1p.f64 (expm1.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 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))))

Compiler

Compiled 2135 to 1211 computations (43.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series2.8s (35.9%)

Counts

4 → 80

Calls

4 calls:

1.2s	(cos.f64 (fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))))
1.1s	(fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))
504.0ms	(cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))
7.0ms	(exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`
4×	`exp-diff_binary64`

Counts

4 → 50

Calls

4 calls:

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

simplify186.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

591×	`unswap-sqr_binary64`
398×	`fma-def_binary64`
322×	`distribute-rgt-in_binary64`
312×	`distribute-lft-in_binary64`
311×	`log-prod_binary64`

Counts

130 → 84

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	89	2256
1	110	2155
2	175	2129
3	327	2050
4	821	2047
5	2630	2017
6	4129	2013
7	4800	2013
8	4948	2013
9	4989	2013
10	4835	2013

prune90.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	84	3	87

Error

1.0b

Counts

87 → 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 (log1p.f64 (expm1.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 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))))

Compiler

Compiled 1830 to 912 computations (50.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
✓	1.0b	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.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)))
✓	1.0b	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

series51.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
22.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
0.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

simplify236.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1392×	`sqr-pow_binary64`
724×	`unswap-sqr_binary64`
592×	`cube-prod_binary64`
500×	`fabs-mul_binary64`
470×	`pow-sqr_binary64`

Counts

70 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	1455
1	59	1377
2	74	1377
3	87	1377
4	100	1377
5	122	1377
6	170	1377
7	270	1377
8	614	1377
9	1210	1377
10	1349	1377
11	1612	1377
12	1917	1377
13	2211	1377
14	2613	1377
15	2967	1377
16	3150	1377
17	3407	1377
18	3546	1377
19	3625	1377
20	3705	1377
21	4463	1377
22	4855	1377

prune146.0ms (1.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	118	4	122

Error

1.0b

Counts

122 → 4

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 (log1p.f64 (expm1.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 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))))))
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))))

Compiler

Compiled 2858 to 1732 computations (39.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))))
✓	1.0b	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))
✓	1.0b	(log1p.f64 (expm1.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))))))
✓	1.0b	(*.f64 2/3 (PI.f64))

series1.1s (13.8%)

Counts

4 → 72

Calls

4 calls:

1.0s	(.f64 (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))))
27.0ms	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))
25.0ms	(log1p.f64 (expm1.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))))))
0.0ms	(*.f64 2/3 (PI.f64))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`pow1_binary64`

Counts

4 → 83

Calls

4 calls:

5.0ms	(.f64 (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))))
3.0ms	(*.f64 2/3 (PI.f64))
1.0ms	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))
0.0ms	(log1p.f64 (expm1.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))))))

simplify154.0ms (2%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
516×	`log-prod_binary64`
392×	`*-commutative_binary64`
348×	`sqr-pow_binary64`
333×	`associate-/l/_binary64`

Counts

155 → 112

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	3543
1	167	3487
2	340	3145
3	766	3097
4	1401	2962
5	2374	2962
6	4083	2962
7	4854	2962

prune228.0ms (3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	173	5	178

Error

0.0b

Counts

178 → 5

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

Compiler

Compiled 8365 to 4961 computations (40.7% saved)

regimes334.0ms (4.4%)

Accuracy

Total 0.0b remaining (72.7%)

Threshold costs 0.0b (72.7%)

Counts

31 → 1

Compiler

Compiled 9061 to 6394 computations (29.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
2×	`+-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	18	48
1	27	48
2	31	48
3	34	48
4	35	48
5	35	48

end132.0ms (1.7%)

Compiler: Compiled 212 to 156 computations (26.4% saved)

Details

analyze425.0ms (5.5%)

sample1.5s (18.9%)

simplify62.0ms (0.8%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series35.0ms (0.5%)

rewrite11.0ms (0.1%)

simplify125.0ms (1.6%)

prune100.0ms (1.3%)

localize18.0ms (0.2%)

series2.8s (35.9%)

rewrite5.0ms (0.1%)

simplify186.0ms (2.4%)

prune90.0ms (1.2%)

localize16.0ms (0.2%)

series51.0ms (0.7%)

rewrite1.0ms (0%)

simplify236.0ms (3.1%)

prune146.0ms (1.9%)

localize16.0ms (0.2%)

series1.1s (13.8%)

rewrite15.0ms (0.2%)

simplify154.0ms (2%)

prune228.0ms (3%)

regimes334.0ms (4.4%)

simplify3.0ms (0%)

end132.0ms (1.7%)

Profiling