Details

analyze571.0ms (4.8%)

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
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	40.6%	9.5%	7
50%	39%	11%	8
50%	33.6%	16.5%	9
50%	32.4%	17.7%	10
50%	29.5%	20.6%	11
50%	28.8%	21.3%	12
50%	27.3%	22.8%	13
50%	26.9%	23.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample4.9s (41.2%)

Results

1.5s	2083×	body	1024	valid
1.2s	1998×	body	1024	invalid
762.0ms	4671×	body	128	valid
431.0ms	983×	body	512	invalid
402.0ms	1015×	body	512	valid
142.0ms	482×	body	256	valid
126.0ms	737×	body	128	invalid
123.0ms	470×	body	256	invalid
8.0ms	5×	body	2048	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

778×	`unswap-sqr_binary64`
536×	`fma-def_binary64`
491×	`associate-/r*_binary64`
476×	`fabs-mul_binary64`
360×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	27	18
2	65	18
3	104	17
4	137	17
5	196	17
6	329	17
7	736	17
8	2242	17
9	2250	17
10	2619	17
11	4128	17
12	4563	17
13	5391	17

prune3.0ms (0%)

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 51 to 34 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
✓	0.0b	(/.f64 1/2 (exp.f64 im))
✓	0.2b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

series43.0ms (0.4%)

Counts

3 → 40

Calls

3 calls:

25.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
10.0ms	(/.f64 1/2 (exp.f64 im))
8.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 61

Calls

3 calls:

4.0ms	(/.f64 1/2 (exp.f64 im))
3.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
0.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-neg_binary64`
500×	`associate-l_binary64`
496×	`fma-def_binary64`
422×	`associate-r_binary64`
311×	`times-frac_binary64`

Counts

101 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	168	1824
1	395	1671
2	1184	1647
3	3869	1643
4	5027	1643

prune94.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	108	2	110

Error

0.2b

Counts

110 → 2

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
▶	0.7b	(+.f64 (.f64 1/720 (.f64 (sin.f64 re) (pow.f64 im 6))) (+.f64 (.f64 1/24 (.f64 (sin.f64 re) (pow.f64 im 4))) (+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))))

Status

Error

Program

✓

0.3b

(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

▶

0.7b

(+.f64 (*.f64 1/720 (*.f64 (sin.f64 re) (pow.f64 im 6))) (+.f64 (*.f64 1/24 (*.f64 (sin.f64 re) (pow.f64 im 4))) (+.f64 (sin.f64 re) (*.f64 1/2 (*.f64 (sin.f64 re) (pow.f64 im 2))))))

Compiler

Compiled 2066 to 1138 computations (44.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/720 (.f64 (sin.f64 re) (pow.f64 im 6)))
✓	0.1b	(.f64 1/24 (.f64 (sin.f64 re) (pow.f64 im 4)))
✓	0.1b	(*.f64 (sin.f64 re) (pow.f64 im 4))
✓	0.1b	(*.f64 (sin.f64 re) (pow.f64 im 2))

series75.0ms (0.6%)

Counts

4 → 16

Calls

4 calls:

26.0ms	(.f64 1/720 (.f64 (sin.f64 re) (pow.f64 im 6)))
20.0ms	(.f64 1/24 (.f64 (sin.f64 re) (pow.f64 im 4)))
15.0ms	(*.f64 (sin.f64 re) (pow.f64 im 4))
13.0ms	(*.f64 (sin.f64 re) (pow.f64 im 2))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
20×	`prod-exp_binary64`
18×	`add-cbrt-cube_binary64`
17×	`associate-r_binary64`

Counts

4 → 98

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 re) (pow.f64 im 2))
5.0ms	(.f64 1/720 (.f64 (sin.f64 re) (pow.f64 im 6)))
5.0ms	(.f64 1/24 (.f64 (sin.f64 re) (pow.f64 im 4)))
4.0ms	(*.f64 (sin.f64 re) (pow.f64 im 4))

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-neg_binary64`
577×	`unswap-sqr_binary64`
474×	`fma-def_binary64`
335×	`cancel-sign-sub-inv_binary64`
295×	`associate-r_binary64`

Counts

114 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	1892
1	510	1604
2	1689	1526
3	3416	1524
4	5147	1524

prune192.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	173	3	176

Error

0.2b

Counts

176 → 3

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓	0.7b	(+.f64 (.f64 1/720 (.f64 (sin.f64 re) (pow.f64 im 6))) (+.f64 (.f64 1/24 (.f64 (sin.f64 re) (pow.f64 im 4))) (+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))))
▶	4.2b	(+.f64 (exp.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re))))) (+.f64 (.f64 1/24 (.f64 (sin.f64 re) (pow.f64 im 4))) (+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))))

Compiler

Compiled 6369 to 4026 computations (36.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (sin.f64 re) (pow.f64 im 4))
	0.1b	(*.f64 (sin.f64 re) (pow.f64 im 2))
✓	0.3b	(exp.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re)))))
✓	55.9b	(log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re))))

series837.0ms (7%)

Counts

2 → 48

Calls

2 calls:

813.0ms	(log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re))))
24.0ms	(exp.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re)))))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`prod-exp_binary64`
5×	`exp-prod_binary64`
5×	`rem-log-exp_binary64`

Counts

2 → 33

Calls

2 calls:

5.0ms	(log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re))))
4.0ms	(exp.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re)))))

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-neg_binary64`
401×	`associate-r_binary64`
392×	`associate-l_binary64`
358×	`distribute-rgt-neg-in_binary64`
256×	`unswap-sqr_binary64`

Counts

81 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1274
1	221	1162
2	654	1134
3	2856	1134
4	5014	1134

prune256.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	167	3	170

Error

0.2b

Counts

170 → 3

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓	0.7b	(+.f64 (.f64 1/720 (.f64 (sin.f64 re) (pow.f64 im 6))) (+.f64 (.f64 1/24 (.f64 (sin.f64 re) (pow.f64 im 4))) (+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))))
▶	4.2b	(+.f64 (exp.f64 (.f64 (.f64 (cbrt.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re))))) (cbrt.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re)))))) (cbrt.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re))))))) (+.f64 (.f64 1/24 (.f64 (sin.f64 re) (pow.f64 im 4))) (+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))))

Compiler

Compiled 6456 to 4169 computations (35.4% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re))))) (cbrt.f64 (log.f64 (.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re))))))
✓	0.2b	(cbrt.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re)))))
✓	0.3b	(exp.f64 (.f64 (.f64 (cbrt.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re))))) (cbrt.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re)))))) (cbrt.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re)))))))
	55.9b	(log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re))))

series3.3s (27.7%)

Counts

3 → 72

Calls

3 calls:

1.7s

(*.f64 (cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re))))) (cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re))))))

1.6s

(cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re)))))

26.0ms

(exp.f64 (*.f64 (*.f64 (cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re))))) (cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re)))))) (cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re)))))))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`cbrt-prod_binary64`
37×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`log-pow_binary64`
16×	`*-un-lft-identity_binary64`

Counts

3 → 81

Calls

3 calls:

12.0ms

(*.f64 (cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re))))) (cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re))))))

3.0ms

(cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re)))))

2.0ms

(exp.f64 (*.f64 (*.f64 (cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re))))) (cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re)))))) (cbrt.f64 (log.f64 (*.f64 1/720 (*.f64 (pow.f64 im 6) (sin.f64 re)))))))

simplify141.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

450×	`unswap-sqr_binary64`
408×	`cancel-sign-sub-inv_binary64`
396×	`associate-r_binary64`
283×	`associate-l_binary64`
232×	`fma-def_binary64`

Counts

153 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	5181
1	792	4447
2	2995	4317
3	4897	4317
4	4954	4317

prune572.0ms (4.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	311	1	312
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	312	3	315

Error

0.2b

Counts

315 → 3

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
	4.2b	(+.f64 (exp.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (log.f64 (.f64 1/720 (.f64 (sin.f64 re) (pow.f64 im 6)))))) (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 (.f64 1/720 (.f64 (sin.f64 re) (pow.f64 im 6)))))) 4)) (cbrt.f64 (cbrt.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re))))))) (cbrt.f64 (log.f64 (.f64 1/720 (.f64 (pow.f64 im 6) (sin.f64 re))))))) (+.f64 (.f64 1/24 (.f64 (sin.f64 re) (pow.f64 im 4))) (+.f64 (sin.f64 re) (.f64 1/2 (*.f64 (sin.f64 re) (pow.f64 im 2))))))
✓	0.7b	(+.f64 (.f64 1/720 (.f64 (sin.f64 re) (pow.f64 im 6))) (+.f64 (.f64 1/24 (.f64 (sin.f64 re) (pow.f64 im 4))) (+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))))

Compiler

Compiled 21328 to 15092 computations (29.2% saved)

regimes362.0ms (3%)

Accuracy

Total 0.0b remaining (17.8%)

Threshold costs 0.0b (17.8%)

Counts

39 → 1

Compiler

Compiled 7830 to 5613 computations (28.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	15	24
2	15	24

end101.0ms (0.8%)

Compiler: Compiled 150 to 105 computations (30% saved)

Details

analyze571.0ms (4.8%)

sample4.9s (41.2%)

simplify76.0ms (0.6%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series43.0ms (0.4%)

rewrite10.0ms (0.1%)

simplify96.0ms (0.8%)

prune94.0ms (0.8%)

localize17.0ms (0.1%)

series75.0ms (0.6%)

rewrite25.0ms (0.2%)

simplify79.0ms (0.7%)

prune192.0ms (1.6%)

localize20.0ms (0.2%)

series837.0ms (7%)

rewrite11.0ms (0.1%)

simplify63.0ms (0.5%)

prune256.0ms (2.1%)

localize25.0ms (0.2%)

series3.3s (27.7%)

rewrite23.0ms (0.2%)

simplify141.0ms (1.2%)

prune572.0ms (4.8%)

regimes362.0ms (3%)

simplify2.0ms (0%)

end101.0ms (0.8%)

Profiling