Details

analyze221.0ms (3.7%)

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)

sample1.4s (23.2%)

Results

1.3s	8256×	body	128	valid
80.0ms	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

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)

localize11.0ms (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)))

series33.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

19.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
7.0ms	(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)

rewrite5.0ms (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))

simplify127.0ms (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

prune127.0ms (2.1%)

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 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))))))
▶	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))))))

Compiler

Compiled 2235 to 1283 computations (42.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.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)))
✓	1.0b	(*.f64 (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
✓	1.0b	(cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
✓	1.0b	(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)))))

series1.5s (24.3%)

Counts

4 → 96

Calls

4 calls:

810.0ms	(*.f64 (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
573.0ms	(cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
46.0ms	(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)))))
33.0ms	(.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)))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`cbrt-prod_binary64`
79×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`

Counts

4 → 170

Calls

4 calls:

13.0ms	(*.f64 (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
11.0ms	(.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)))
2.0ms	(cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
1.0ms	(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)))))

simplify212.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

726×	`associate-/r/_binary64`
672×	`unswap-sqr_binary64`
581×	`associate-/r*_binary64`
217×	`*-commutative_binary64`
206×	`log-prod_binary64`

Counts

266 → 277

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	201	7001
1	313	6438
2	908	5987
3	1816	5857
4	4493	5741
5	4929	5741

prune532.0ms (8.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	367	0	367
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	367	5	372

Error

1.0b

Counts

372 → 5

Alt Table

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

Compiler

Compiled 14911 to 7812 computations (47.6% saved)

localize10.0ms (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))))))

series55.0ms (0.9%)

Counts

4 → 96

Calls

4 calls:

22.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h))))))
20.0ms	(/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))
7.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))))
6.0ms	(/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h))))

rewrite16.0ms (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)))))

simplify215.0ms (3.6%)

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

prune242.0ms (4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	207	5	212

Error

1.0b

Counts

212 → 5

Alt Table

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

Compiler

Compiled 5167 to 3037 computations (41.2% saved)

localize14.0ms (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)))

series20.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

20.0ms

(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)))))

simplify137.0ms (2.3%)

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

prune95.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	0	2	2
Picked	0	1	1
Done	1	1	2
Total	130	6	136

Error

0.0b

Counts

136 → 6

Alt Table

Status	Error	Program
	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))))))
	0.1b	(.f64 2 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))) (log.f64 (cbrt.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 (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 (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))))))

Compiler

Compiled 3196 to 1928 computations (39.7% saved)

regimes816.0ms (13.6%)

Accuracy

Total 0.1b remaining (85.7%)

Threshold costs 0.1b (85.7%)

Counts

75 → 1

Compiler

Compiled 21468 to 16862 computations (21.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	19	56
1	28	56
2	32	56
3	35	56
4	36	56
5	36	56

end190.0ms (3.2%)

Compiler: Compiled 260 to 192 computations (26.2% saved)

Details

analyze221.0ms (3.7%)

sample1.4s (23.2%)

simplify8.0ms (0.1%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series33.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify127.0ms (2.1%)

prune127.0ms (2.1%)

localize13.0ms (0.2%)

series1.5s (24.3%)

rewrite45.0ms (0.8%)

simplify212.0ms (3.5%)

prune532.0ms (8.9%)

localize10.0ms (0.2%)

series55.0ms (0.9%)

rewrite16.0ms (0.3%)

simplify215.0ms (3.6%)

prune242.0ms (4%)

localize14.0ms (0.2%)

series20.0ms (0.3%)

rewrite3.0ms (0%)

simplify137.0ms (2.3%)

prune95.0ms (1.6%)

regimes816.0ms (13.6%)

simplify3.0ms (0.1%)

end190.0ms (3.2%)

Profiling