Details

analyze237.0ms (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)

sample1.6s (24.9%)

Results

1.5s	8256×	body	128	valid
90.0ms	574×	body	128	invalid

Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify8.0ms (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

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

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)

localize9.0ms (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)))

series37.0ms (0.6%)

Counts

3 → 72

Calls

3 calls:

23.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
9.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
5.0ms	(/.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))

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

prune115.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Error

1.0b

Counts

98 → 5

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (.f64 (*.f64 (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.6b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (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 (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 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))))))

Compiler

Compiled 2235 to 1283 computations (42.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series60.0ms (0.9%)

Counts

4 → 96

Calls

4 calls:

24.0ms	(/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))
21.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h))))))
9.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))))
5.0ms	(/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h))))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
17×	`add-exp-log_binary64`

Counts

4 → 127

Calls

4 calls:

4.0ms	(/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h))))
2.0ms	(/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))
1.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h))))))
0.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))))

simplify223.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-def_binary64`
415×	`times-frac_binary64`
410×	`distribute-lft-out_binary64`
402×	`distribute-rgt-out_binary64`
350×	`fma-neg_binary64`

Counts

223 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	4210
1	212	3935
2	450	3916
3	931	3916
4	1586	3916
5	3047	3916
6	3475	3916
7	4739	3916
8	4876	3916

prune266.0ms (4.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	208	4	212

Error

1.0b

Counts

212 → 4

Alt Table

Status	Error	Program
	1.6b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (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 (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 (.f64 (/.f64 1 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h))))))))

Compiler

Compiled 5166 to 3046 computations (41% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series218.0ms (3.3%)

Counts

4 → 72

Calls

4 calls:

91.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h)))))))
66.0ms	(fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h))))))
61.0ms	(*.f64 (/.f64 1 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h)))))
0.0ms	(/.f64 1 (/.f64 (sqrt.f64 3) 1))

rewrite176.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

614×	`times-frac_binary64`
497×	`add-sqr-sqrt_binary64`
299×	`*-un-lft-identity_binary64`
251×	`add-exp-log_binary64`
203×	`add-cube-cbrt_binary64`

Counts

4 → 452

Calls

4 calls:

68.0ms	(*.f64 (/.f64 1 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h)))))
6.0ms	(/.f64 1 (/.f64 (sqrt.f64 3) 1))
1.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h)))))))
0.0ms	(fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h))))))

simplify393.0ms (6%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-def_binary64`
388×	`times-frac_binary64`
337×	`fma-neg_binary64`
332×	`associate-*l/_binary64`
304×	`associate-/l*_binary64`

Counts

524 → 550

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	233	13264
1	408	10974
2	1068	10821
3	2355	10748
4	2872	9400
5	4665	9400
6	4916	9400

prune903.0ms (13.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	549	1	550
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	549	5	554

Error

1.0b

Counts

554 → 5

Alt Table

Status	Error	Program
	1.6b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (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 (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 (.f64 (/.f64 1 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h))))))))
▶	1.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h))))))) (.f64 (sin.f64 (.f64 (PI.f64) 2/3)) (sin.f64 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h)))))))))

Compiler

Compiled 18252 to 13743 computations (24.7% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(sin.f64 (*.f64 (PI.f64) 2/3))
✓	1.0b	(*.f64 (PI.f64) 2/3)
	1.0b	(/.f64 1 (/.f64 (sqrt.f64 3) 1))
✓	1.6b	(cos.f64 (*.f64 (PI.f64) 2/3))

series0.0ms (0%)

Counts

3 → 0

Calls

3 calls:

0.0ms	(cos.f64 (*.f64 (PI.f64) 2/3))
0.0ms	(*.f64 (PI.f64) 2/3)
0.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 38

Calls

3 calls:

3.0ms	(*.f64 (PI.f64) 2/3)
1.0ms	(cos.f64 (*.f64 (PI.f64) 2/3))
1.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

603×	`unswap-sqr_binary64`
428×	`associate-*l/_binary64`
378×	`associate-*r/_binary64`
293×	`log-div_binary64`
277×	`*-commutative_binary64`

Counts

38 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	383
1	83	337
2	169	337
3	229	337
4	293	337
5	442	337
6	806	337
7	1343	337
8	3492	337
9	4632	337
10	4833	337
11	4757	337

prune415.0ms (6.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	325	1	326
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	328	3	331

Error

Counts

331 → 3

Alt Table

Status	Error	Program
	0.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (.f64 (cbrt.f64 (/.f64 1/3 (sqrt.f64 3))) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h))))))) (.f64 (sin.f64 (.f64 (PI.f64) 2/3)) (sin.f64 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h)))))))))
	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 (/.f64 (sqrt.f64 3) 1)) (/.f64 1 (/.f64 (sqrt.f64 3) (acos.f64 (/.f64 (neg.f64 g) h))))))))

Compiler

Compiled 18656 to 14670 computations (21.4% saved)

regimes1.4s (22%)

Accuracy

Total 0.0b remaining (63.2%)

Threshold costs 0.0b (63.2%)

Counts

140 → 1

Compiler

Compiled 40876 to 34884 computations (14.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	79
1	45	79
2	57	79
3	66	79
4	71	79
5	72	79
6	71	79

end116.0ms (1.8%)

Compiler: Compiled 190 to 162 computations (14.7% saved)

Details

analyze237.0ms (3.6%)

sample1.6s (24.9%)

simplify8.0ms (0.1%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series37.0ms (0.6%)

rewrite6.0ms (0.1%)

simplify123.0ms (1.9%)

prune115.0ms (1.8%)

localize11.0ms (0.2%)

series60.0ms (0.9%)

rewrite17.0ms (0.3%)

simplify223.0ms (3.4%)

prune266.0ms (4.1%)

localize15.0ms (0.2%)

series218.0ms (3.3%)

rewrite176.0ms (2.7%)

simplify393.0ms (6%)

prune903.0ms (13.8%)

localize23.0ms (0.3%)

series0.0ms (0%)

rewrite6.0ms (0.1%)

simplify86.0ms (1.3%)

prune415.0ms (6.3%)

regimes1.4s (22%)

simplify4.0ms (0.1%)

end116.0ms (1.8%)

Profiling