Details

analyze181.0ms (3.1%)

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)

sample1.2s (20.9%)

Infinites

100% of outputs are infinite.

Results

1.1s	8256×	body	128	valid
69.0ms	590×	body	128	invalid

Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify10.0ms (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 (0.1%)

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

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)))

series34.0ms (0.6%)

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)

rewrite6.0ms (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:

2.0ms	(/.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))

simplify124.0ms (2.1%)

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

prune123.0ms (2.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	2	98

Error

1.0b

Counts

98 → 2

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 (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))))))

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 (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 2063 to 1167 computations (43.4% saved)

localize12.0ms (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))

series251.0ms (4.3%)

Counts

4 → 72

Calls

4 calls:

101.0ms	(fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))
89.0ms	(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)))))
60.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
0.0ms	(/.f64 1 (sqrt.f64 3))

rewrite39.0ms (0.7%)

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:

21.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
4.0ms	(/.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)))))
0.0ms	(fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))

simplify196.0ms (3.4%)

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

prune260.0ms (4.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	206	2	208

Error

1.0b

Counts

208 → 2

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 (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))))))

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 (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 5534 to 3844 computations (30.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series114.0ms (2%)

Counts

4 → 72

Calls

4 calls:

67.0ms	(pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3)
24.0ms	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))
22.0ms	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3))
0.0ms	(*.f64 2/3 (PI.f64))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`

Counts

4 → 78

Calls

4 calls:

3.0ms	(*.f64 2/3 (PI.f64))
3.0ms	(pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3))
1.0ms	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))

simplify144.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

740×	`sqr-pow_binary64`
574×	`fma-def_binary64`
453×	`*-commutative_binary64`
386×	`log-prod_binary64`
384×	`exp-prod_binary64`

Counts

150 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	112	3222
1	168	2982
2	370	2966
3	1274	2966
4	2317	2963
5	4114	2963
6	4941	2963

prune87.0ms (1.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	100	2	102

Error

Counts

102 → 2

Alt Table

Status	Error	Program
✓	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))))))
▶	0.0b	(.f64 2 (.f64 (cbrt.f64 (.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.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)))))))

Status

Error

Program

✓

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))))))

▶

0.0b

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

Compiler

Compiled 2472 to 1582 computations (36% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series1.3s (22.9%)

Counts

2 → 48

Calls

2 calls:

1.3s

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

34.0ms

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 41

Calls

2 calls:

3.0ms

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

2.0ms

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

simplify133.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

661×	`sqr-pow_binary64`
655×	`unswap-sqr_binary64`
614×	`distribute-rgt-in_binary64`
547×	`distribute-lft-in_binary64`
457×	`fma-def_binary64`

Counts

89 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	73	2203
1	110	1993
2	281	1965
3	1007	1933
4	2002	1930
5	3678	1930
6	4254	1930
7	5176	1930

prune199.0ms (3.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	162	2	164

Error

Counts

164 → 2

Alt Table

Status	Error	Program
✓	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))))))
✓	0.0b	(.f64 2 (.f64 (cbrt.f64 (.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.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)))))))

Status

Error

Program

✓

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))))))

✓

0.0b

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

Compiler

Compiled 7366 to 4166 computations (43.4% saved)

regimes1.2s (20.6%)

Accuracy

Total 0.0b remaining (64.5%)

Threshold costs 0.0b (64.5%)

Counts

118 → 1

Compiler

Compiled 26141 to 21449 computations (17.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	23	52
1	33	52
2	37	52
3	40	52
4	41	52
5	41	52

end86.0ms (1.5%)

Compiler: Compiled 128 to 96 computations (25% saved)

Details

analyze181.0ms (3.1%)

sample1.2s (20.9%)

simplify10.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series34.0ms (0.6%)

rewrite6.0ms (0.1%)

simplify124.0ms (2.1%)

prune123.0ms (2.1%)

localize12.0ms (0.2%)

series251.0ms (4.3%)

rewrite39.0ms (0.7%)

simplify196.0ms (3.4%)

prune260.0ms (4.5%)

localize16.0ms (0.3%)

series114.0ms (2%)

rewrite11.0ms (0.2%)

simplify144.0ms (2.5%)

prune87.0ms (1.5%)

localize17.0ms (0.3%)

series1.3s (22.9%)

rewrite8.0ms (0.1%)

simplify133.0ms (2.3%)

prune199.0ms (3.4%)

regimes1.2s (20.6%)

simplify4.0ms (0.1%)

end86.0ms (1.5%)

Profiling