Details

analyze2.3s (9%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	95.2%	4.8%	7
0%	94.4%	5.6%	8
0%	91.7%	8.3%	9
0%	91.1%	8.9%	10
0%	89.7%	10.3%	11
1.4%	88%	10.7%	12
1.4%	87.2%	11.4%	13
1.4%	87%	11.6%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample20.2s (79.7%)

Results

12.4s	4003×	body	8192	exit
3.7s	4202×	body	1024	valid
1.2s	507×	body	512	invalid
1.2s	2125×	body	512	valid
683.0ms	982×	body	1024	invalid
439.0ms	1024×	body	256	valid
260.0ms	205×	body	2048	valid
124.0ms	700×	body	128	valid
90.0ms	343×	body	128	invalid
66.0ms	229×	body	256	invalid

Compiler

Compiled 27 to 21 computations (22.2% saved)

simplify115.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

454×	`fma-def_binary64`
444×	`times-frac_binary64`
419×	`sub-neg_binary64`
365×	`distribute-rgt-neg-in_binary64`
340×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	23	18
2	49	18
3	106	18
4	225	17
5	449	17
6	962	17
7	1713	17
8	3588	17
9	4282	17
10	4773	17
11	4923	17
12	4957	17
13	4748	17

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

45.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.7b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 50 to 35 computations (30% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 re)
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	5.3b	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series27.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

23.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
2.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
2.0ms	(sin.f64 re)

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
27×	`prod-diff_binary64`
26×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 89

Calls

3 calls:

10.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
5.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
1.0ms	(sin.f64 re)

simplify110.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

628×	`fma-neg_binary64`
417×	`cancel-sign-sub-inv_binary64`
304×	`distribute-rgt-in_binary64`
285×	`associate-r_binary64`
279×	`associate-l_binary64`

Counts

125 → 141

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	239	2758
1	582	2452
2	2147	2237
3	4581	2232
4	4905	2232

prune85.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	2	142

Error

0.2b

Counts

142 → 2

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (sin.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
	45.7b	(.f64 (.f64 1/2 (sin.f64 re)) (log.f64 (/.f64 (exp.f64 (exp.f64 (neg.f64 im))) (exp.f64 (exp.f64 im)))))

Compiler

Compiled 3492 to 1254 computations (64.1% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 re)
✓	0.1b	(*.f64 1/6 (pow.f64 im 3))
✓	0.2b	(.f64 (sin.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))

series29.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

26.0ms	(.f64 (sin.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
3.0ms	(*.f64 1/6 (pow.f64 im 3))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
20×	`prod-diff_binary64`
15×	`associate-r_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 79

Calls

2 calls:

6.0ms	(.f64 (sin.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
6.0ms	(*.f64 1/6 (pow.f64 im 3))

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

901×	`fma-neg_binary64`
569×	`fma-def_binary64`
300×	`cancel-sign-sub-inv_binary64`
207×	`associate-r_binary64`
188×	`associate-l_binary64`

Counts

103 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	2115
1	444	1814
2	1449	1655
3	4457	1655
4	5060	1655

prune147.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	124	8	132
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	124	10	134

Error

0.0b

Counts

134 → 10

Alt Table

Status	Error	Program
	26.7b	(.f64 (sqrt.f64 (neg.f64 (.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))) (sqrt.f64 (neg.f64 (*.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))))
	45.7b	(.f64 (.f64 1/2 (sin.f64 re)) (log.f64 (/.f64 (exp.f64 (exp.f64 (neg.f64 im))) (exp.f64 (exp.f64 im)))))
✓	0.3b	(.f64 (sin.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
	21.6b	(/.f64 (.f64 (sin.f64 re) (fma.f64 im im (.f64 (pow.f64 im 6) -1/36))) (+.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3))))
	42.6b	(/.f64 (.f64 (sin.f64 re) (fma.f64 (pow.f64 (pow.f64 im 3) 3) -1/216 (pow.f64 (neg.f64 im) 3))) (+.f64 (.f64 (neg.f64 im) (neg.f64 im)) (+.f64 (.f64 (.f64 1/6 (pow.f64 im 3)) (.f64 1/6 (pow.f64 im 3))) (.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3))))))
	14.3b	(.f64 (log.f64 (exp.f64 (sin.f64 re))) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
	5.8b	(.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 re) (sin.f64 re)) (sin.f64 re))) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
▶	1.2b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im)) (neg.f64 (cbrt.f64 im)) (neg.f64 (.f64 (pow.f64 im 3) 1/6))) (sin.f64 re)) (.f64 (fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (*.f64 (pow.f64 im 3) 1/6)) (sin.f64 re)))
	28.7b	(.f64 (.f64 (sin.f64 re) (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (-.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3)))))
	32.1b	(.f64 (sqrt.f64 (sin.f64 re)) (.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (sqrt.f64 (sin.f64 re))))

Compiler

Compiled 3119 to 1989 computations (36.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im)) (neg.f64 (cbrt.f64 im)) (neg.f64 (.f64 (pow.f64 im 3) 1/6)))
✓	0.5b	(*.f64 (cbrt.f64 im) (cbrt.f64 im))
✓	0.7b	(cbrt.f64 im)
✓	17.5b	(fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (*.f64 (pow.f64 im 3) 1/6))

series135.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

50.0ms	(*.f64 (cbrt.f64 im) (cbrt.f64 im))
43.0ms	(fma.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im)) (neg.f64 (cbrt.f64 im)) (neg.f64 (.f64 (pow.f64 im 3) 1/6)))
34.0ms	(cbrt.f64 im)
8.0ms	(fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (*.f64 (pow.f64 im 3) 1/6))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 75

Calls

4 calls:

14.0ms	(*.f64 (cbrt.f64 im) (cbrt.f64 im))
1.0ms	(cbrt.f64 im)
0.0ms	(fma.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im)) (neg.f64 (cbrt.f64 im)) (neg.f64 (.f64 (pow.f64 im 3) 1/6)))
0.0ms	(fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (*.f64 (pow.f64 im 3) 1/6))

simplify69.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

613×	`exp-prod_binary64`
543×	`unswap-sqr_binary64`
529×	`fma-neg_binary64`
383×	`log-prod_binary64`
326×	`fma-def_binary64`

Counts

123 → 121

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	93	1201
1	158	952
2	503	822
3	1110	807
4	3202	795
5	4710	795

prune200.0ms (0.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	157	12	169

Error

0.0b

Counts

169 → 12

Alt Table

Status	Error	Program
	29.2b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) 3)) (sin.f64 re)) (.f64 (fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (*.f64 (pow.f64 im 3) 1/6)) (sin.f64 re)))
	21.6b	(/.f64 (.f64 (sin.f64 re) (fma.f64 im im (.f64 (pow.f64 im 6) -1/36))) (+.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3))))
▶	1.5b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 im) (.f64 (cbrt.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im))) (cbrt.f64 (cbrt.f64 im)))) (neg.f64 (cbrt.f64 im)) (neg.f64 (.f64 (pow.f64 im 3) 1/6))) (sin.f64 re)) (.f64 (fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (*.f64 (pow.f64 im 3) 1/6)) (sin.f64 re)))
	14.3b	(.f64 (log.f64 (exp.f64 (sin.f64 re))) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
	26.7b	(.f64 (sqrt.f64 (neg.f64 (.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))) (sqrt.f64 (neg.f64 (*.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))))
	45.7b	(.f64 (.f64 1/2 (sin.f64 re)) (log.f64 (/.f64 (exp.f64 (exp.f64 (neg.f64 im))) (exp.f64 (exp.f64 im)))))
✓	0.3b	(.f64 (sin.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
	42.6b	(/.f64 (.f64 (sin.f64 re) (fma.f64 (pow.f64 (pow.f64 im 3) 3) -1/216 (pow.f64 (neg.f64 im) 3))) (+.f64 (.f64 (neg.f64 im) (neg.f64 im)) (+.f64 (.f64 (.f64 1/6 (pow.f64 im 3)) (.f64 1/6 (pow.f64 im 3))) (.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3))))))
	5.8b	(.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 re) (sin.f64 re)) (sin.f64 re))) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
✓	1.2b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im)) (neg.f64 (cbrt.f64 im)) (neg.f64 (.f64 (pow.f64 im 3) 1/6))) (sin.f64 re)) (.f64 (fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (*.f64 (pow.f64 im 3) 1/6)) (sin.f64 re)))
	28.7b	(.f64 (.f64 (sin.f64 re) (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (-.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3)))))
	32.1b	(.f64 (sqrt.f64 (sin.f64 re)) (.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (sqrt.f64 (sin.f64 re))))

Compiler

Compiled 6345 to 3715 computations (41.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(cbrt.f64 (cbrt.f64 im))
	0.7b	(cbrt.f64 im)
✓	0.7b	(cbrt.f64 (*.f64 (cbrt.f64 im) (cbrt.f64 im)))
	17.5b	(fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (*.f64 (pow.f64 im 3) 1/6))

series607.0ms (2.4%)

Counts

2 → 24

Calls

2 calls:

324.0ms	(cbrt.f64 (*.f64 (cbrt.f64 im) (cbrt.f64 im)))
283.0ms	(cbrt.f64 (cbrt.f64 im))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

3.0ms	(cbrt.f64 (*.f64 (cbrt.f64 im) (cbrt.f64 im)))
1.0ms	(cbrt.f64 (cbrt.f64 im))

simplify105.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

692×	`sqr-pow_binary64`
622×	`fma-def_binary64`
551×	`unswap-sqr_binary64`
376×	`distribute-rgt-in_binary64`
313×	`*-commutative_binary64`

Counts

51 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	468
1	78	468
2	138	468
3	283	468
4	779	450
5	1271	450
6	1449	450
7	1730	450
8	2156	450
9	2689	450
10	3638	450
11	4799	450
12	4840	450

prune226.0ms (0.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	155	13	168

Error

0.0b

Counts

168 → 13

Alt Table

Status	Error	Program
	29.2b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) 3)) (sin.f64 re)) (.f64 (fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (*.f64 (pow.f64 im 3) 1/6)) (sin.f64 re)))
	21.6b	(/.f64 (.f64 (sin.f64 re) (fma.f64 im im (.f64 (pow.f64 im 6) -1/36))) (+.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3))))
✓	1.5b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 im) (.f64 (cbrt.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im))) (cbrt.f64 (cbrt.f64 im)))) (neg.f64 (cbrt.f64 im)) (neg.f64 (.f64 (pow.f64 im 3) 1/6))) (sin.f64 re)) (.f64 (fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (*.f64 (pow.f64 im 3) 1/6)) (sin.f64 re)))
	14.3b	(.f64 (log.f64 (exp.f64 (sin.f64 re))) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
	5.8b	(.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 re) (sin.f64 re)) (sin.f64 re))) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
	36.5b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 im) (.f64 (cbrt.f64 (.f64 (cbrt.f64 im) (.f64 (cbrt.f64 (pow.f64 im 2/3)) (cbrt.f64 (cbrt.f64 im))))) (cbrt.f64 (cbrt.f64 im)))) (neg.f64 (cbrt.f64 im)) (neg.f64 (.f64 (pow.f64 im 3) 1/6))) (sin.f64 re)) (.f64 (fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (.f64 (pow.f64 im 3) 1/6)) (sin.f64 re)))
	26.7b	(.f64 (sqrt.f64 (neg.f64 (.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))) (sqrt.f64 (neg.f64 (*.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))))
	45.7b	(.f64 (.f64 1/2 (sin.f64 re)) (log.f64 (/.f64 (exp.f64 (exp.f64 (neg.f64 im))) (exp.f64 (exp.f64 im)))))
✓	0.3b	(.f64 (sin.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
	42.6b	(/.f64 (.f64 (sin.f64 re) (fma.f64 (pow.f64 (pow.f64 im 3) 3) -1/216 (pow.f64 (neg.f64 im) 3))) (+.f64 (.f64 (neg.f64 im) (neg.f64 im)) (+.f64 (.f64 (.f64 1/6 (pow.f64 im 3)) (.f64 1/6 (pow.f64 im 3))) (.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3))))))
✓	1.2b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im)) (neg.f64 (cbrt.f64 im)) (neg.f64 (.f64 (pow.f64 im 3) 1/6))) (sin.f64 re)) (.f64 (fma.f64 (neg.f64 (pow.f64 im 3)) 1/6 (*.f64 (pow.f64 im 3) 1/6)) (sin.f64 re)))
	28.7b	(.f64 (.f64 (sin.f64 re) (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (-.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3)))))
	32.1b	(.f64 (sqrt.f64 (sin.f64 re)) (.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (sqrt.f64 (sin.f64 re))))

Compiler

Compiled 7336 to 3702 computations (49.5% saved)

regimes515.0ms (2%)

Accuracy

Total 0.5b remaining (54.8%)

Threshold costs 0.5b (54.8%)

Counts

71 → 1

Compiler

Compiled 11281 to 7631 computations (32.4% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	23	17
2	33	15
3	46	15
4	55	15
5	61	15
6	64	15
7	65	15
8	64	15

end287.0ms (1.1%)

Compiler: Compiled 375 to 267 computations (28.8% saved)

Details

analyze2.3s (9%)

sample20.2s (79.7%)

simplify115.0ms (0.5%)

prune3.0ms (0%)

localize9.0ms (0%)

series27.0ms (0.1%)

rewrite22.0ms (0.1%)

simplify110.0ms (0.4%)

prune85.0ms (0.3%)

localize9.0ms (0%)

series29.0ms (0.1%)

rewrite17.0ms (0.1%)

simplify91.0ms (0.4%)

prune147.0ms (0.6%)

localize18.0ms (0.1%)

series135.0ms (0.5%)

rewrite19.0ms (0.1%)

simplify69.0ms (0.3%)

prune200.0ms (0.8%)

localize21.0ms (0.1%)

series607.0ms (2.4%)

rewrite4.0ms (0%)

simplify105.0ms (0.4%)

prune226.0ms (0.9%)

regimes515.0ms (2%)

simplify5.0ms (0%)

end287.0ms (1.1%)

Profiling