Details

analyze269.0ms (4.6%)

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)

sample44.0ms (0.7%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
2.0ms	19×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify13.0ms (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 → 1

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

1.0b

Counts

2 → 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 45 to 39 computations (13.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
0.9b	(/.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)))

rewrite122.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

26×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`fma-udef_binary64`

Counts

3 → 120

Calls

3 calls:

14.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
11.0ms	(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))

Compiler

Compiled 2362 to 1335 computations (43.5% saved)

series56.0ms (0.9%)

Error

1.0b

Counts

3 → 18

Calls

3 calls:

25.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
15.0ms	(fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
14.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

Compiler

Compiled 631 to 553 computations (12.4% saved)

simplify131.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-def_binary64`
383×	`associate-/l*_binary64`
324×	`fma-neg_binary64`
278×	`associate-l_binary64`
211×	`cancel-sign-sub-inv_binary64`

Counts

138 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	2483
1	372	2385
2	945	2326
3	2315	2313
4	4825	2313
5	4899	2313

prune58.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	3	91

Error

0.0b

Counts

91 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 2 (.f64 (cbrt.f64 (*.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))) (cbrt.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
	1.0b	(*.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)))
	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))

Compiler

Compiled 1678 to 994 computations (40.8% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(cos.f64 (fma.f64 2/3 PI.f64 (/.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)))
1.0b	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
1.0b	(cbrt.f64 (*.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))

rewrite214.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

21×	`cos-sum_binary64`
21×	`fma-udef_binary64`
20×	`add-cube-cbrt_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`pow1_binary64`

Counts

4 → 141

Calls

4 calls:

14.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
14.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
13.0ms	(cbrt.f64 (*.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))
12.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))

Compiler

Compiled 5932 to 3326 computations (43.9% saved)

series161.0ms (2.7%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

68.0ms	(cbrt.f64 (*.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) (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)))
28.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
27.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))

Compiler

Compiled 2232 to 1544 computations (30.8% saved)

simplify261.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-neg_binary64`
603×	`unswap-sqr_binary64`
362×	`fma-def_binary64`
352×	`associate-l_binary64`
313×	`*-commutative_binary64`

Counts

165 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	4499
1	203	4174
2	481	4099
3	1083	4087
4	2000	4087
5	3565	4087
6	4840	4087
7	5019	4087

prune64.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	69	3	72

Error

0.0b

Counts

72 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (.f64 (cbrt.f64 (*.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))) (cbrt.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
	1.0b	(*.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)))
▶	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))

Compiler

Compiled 2717 to 1571 computations (42.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))
0.9b	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)
1.0b	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.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)))

rewrite144.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-cube-cbrt_binary64`
16×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`

Counts

4 → 148

Calls

4 calls:

16.0ms	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)
15.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
15.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))
9.0ms	(expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))

Compiler

Compiled 3069 to 1861 computations (39.4% saved)

series126.0ms (2.1%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

52.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))
31.0ms	(expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))
25.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
14.0ms	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)

Compiler

Compiled 1028 to 896 computations (12.8% saved)

simplify212.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

501×	`fma-def_binary64`
411×	`times-frac_binary64`
341×	`fma-neg_binary64`
289×	`associate-/l*_binary64`
233×	`*-commutative_binary64`

Counts

172 → 77

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	173	3277
1	351	3055
2	828	3003
3	1878	2976
4	3738	2968
5	4786	2968
6	4955	2968
7	4950	2968

prune44.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	77	3	80

Error

Counts

80 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (.f64 (cbrt.f64 (*.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))) (cbrt.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
▶	1.0b	(*.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)))
	1.0b	(.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (acos.f64 (neg.f64 (/.f64 g h)))) 2) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (cbrt.f64 (acos.f64 (neg.f64 (/.f64 g h)))) (cbrt.f64 3))))))))

Compiler

Compiled 1411 to 889 computations (37% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(/.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)))
1.0b	(pow.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)
1.0b	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3))

rewrite145.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

35×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
13×	`pow1_binary64`

Counts

4 → 163

Calls

4 calls:

15.0ms	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)
14.0ms	(pow.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)
12.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
10.0ms	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3))

Compiler

Compiled 3220 to 2000 computations (37.9% saved)

series109.0ms (1.8%)

Error

Counts

4 → 24

Calls

4 calls:

40.0ms	(pow.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)
26.0ms	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3))
25.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
14.0ms	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)

Compiler

Compiled 979 to 857 computations (12.5% saved)

simplify153.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

684×	`fma-def_binary64`
496×	`associate-l_binary64`
382×	`associate-r_binary64`
354×	`exp-prod_binary64`
311×	`log-prod_binary64`

Counts

187 → 94

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	175	3370
1	364	3016
2	938	2927
3	2866	2927
4	4531	2911
5	4950	2911

prune43.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

97 → 3

Alt Table

Status	Error	Program
	0.0b	(.f64 2 (.f64 (cbrt.f64 (*.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))) (cbrt.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
	1.0b	(*.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)))
	1.0b	(.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (acos.f64 (neg.f64 (/.f64 g h)))) 2) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (cbrt.f64 (acos.f64 (neg.f64 (/.f64 g h)))) (cbrt.f64 3))))))))

Compiler

Compiled 1412 to 899 computations (36.3% saved)

regimes2.2s (36.7%)

Accuracy

Total 0.0b remaining (65.8%)

Threshold costs 0.0b (65.8%)

Compiler

Compiled 43564 to 34209 computations (21.5% saved)

simplify6.0ms (0.1%)

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	22	48
1	31	48
2	35	48
3	38	48
4	39	48
5	39	48

end1.0ms (0%)

Compiler: Compiled 31 to 23 computations (25.8% saved)

sample1.3s (22.1%)

Algorithm

1×

intervals

Results

870.0ms	8000×	body	128	valid
56.0ms	554×	body	128	nan

Compiler

Compiled 145 to 111 computations (23.4% saved)

Details

analyze269.0ms (4.6%)

sample44.0ms (0.7%)

simplify13.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite122.0ms (2.1%)

series56.0ms (0.9%)

simplify131.0ms (2.2%)

prune58.0ms (1%)

localize18.0ms (0.3%)

rewrite214.0ms (3.6%)

series161.0ms (2.7%)

simplify261.0ms (4.4%)

prune64.0ms (1.1%)

localize14.0ms (0.2%)

rewrite144.0ms (2.4%)

series126.0ms (2.1%)

simplify212.0ms (3.6%)

prune44.0ms (0.7%)

localize14.0ms (0.2%)

rewrite145.0ms (2.5%)

series109.0ms (1.8%)

simplify153.0ms (2.6%)

prune43.0ms (0.7%)

regimes2.2s (36.7%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.3s (22.1%)

Profiling