Details

analyze1.8s (5.5%)

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
3.1%	96.8%	0.1%	7
3.1%	96.8%	0.1%	8
4.7%	95.2%	0.1%	9
4.7%	93.9%	1.5%	10
5.4%	93.1%	1.6%	11
5.4%	93%	1.6%	12
5.8%	92.6%	1.6%	13
5.8%	91.8%	2.4%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample19.9s (60.6%)

Results

15.6s	11296×	body	8192	exit
2.0s	3360×	body	1024	invalid
1.3s	8256×	body	128	valid
613.0ms	1655×	body	512	invalid
204.0ms	824×	body	256	invalid
51.0ms	369×	body	128	invalid
5.0ms	5×	body	2048	invalid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify87.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

656×	`unswap-sqr_binary64`
607×	`times-frac_binary64`
540×	`sqr-pow_binary64`
391×	`pow-sqr_binary64`
205×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	37	11
3	79	11
4	200	11
5	635	11
6	2301	11
7	2298	11
8	2410	11
9	2637	11
10	3067	11
11	3698	11
12	4907	11
13	4890	11

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))

Compiler

Compiled 37 to 22 computations (40.5% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))
✓	0.2b	(pow.f64 l (exp.f64 w))

series291.0ms (0.9%)

Counts

2 → 44

Calls

2 calls:

149.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))
141.0ms	(pow.f64 l (exp.f64 w))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`unpow-prod-down_binary64`
7×	`add-cube-cbrt_binary64`

Counts

2 → 48

Calls

2 calls:

6.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))
2.0ms	(pow.f64 l (exp.f64 w))

simplify68.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
739×	`fma-neg_binary64`
459×	`associate-+l+_binary64`
213×	`associate--l+_binary64`
162×	`cancel-sign-sub-inv_binary64`

Counts

92 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	1391
1	348	1242
2	1307	1192
3	4511	1192
4	5132	1192

prune59.0ms (0.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	4	86

Error

0.1b

Counts

86 → 4

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
	2.8b	(*.f64 (exp.f64 (neg.f64 w)) (expm1.f64 (log1p.f64 (pow.f64 l (exp.f64 w)))))
	11.9b	(+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (-.f64 (.f64 (.f64 l (.f64 w w)) (+.f64 (.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2)) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (.f64 w w))))))
	4.9b	(.f64 (exp.f64 (neg.f64 w)) (exp.f64 (.f64 (log.f64 l) (exp.f64 w))))

Compiler

Compiled 1611 to 544 computations (66.2% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 w))
✓	0.0b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
✓	0.2b	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
✓	0.2b	(pow.f64 l (sqrt.f64 (exp.f64 w)))

series1.7s (5.2%)

Counts

4 → 68

Calls

4 calls:

778.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
778.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
140.0ms	(pow.f64 l (sqrt.f64 (exp.f64 w)))
2.0ms	(sqrt.f64 (exp.f64 w))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`unpow-prod-down_binary64`
26×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`pow-unpow_binary64`

Counts

4 → 105

Calls

4 calls:

7.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
3.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
2.0ms	(pow.f64 l (sqrt.f64 (exp.f64 w)))
1.0ms	(sqrt.f64 (exp.f64 w))

simplify101.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-neg_binary64`
219×	`associate-r_binary64`
213×	`associate--l+_binary64`
204×	`unswap-sqr_binary64`
181×	`times-frac_binary64`

Counts

173 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	2917
1	535	2425
2	1911	2364
3	4284	2364
4	4978	2364

prune149.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	192	3	195
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	195	4	199

Error

0.0b

Counts

199 → 4

Alt Table

Status	Error	Program
	0.6b	(*.f64 (/.f64 (sqrt.f64 (pow.f64 l (exp.f64 w))) (exp.f64 w)) (sqrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))))
	11.9b	(+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (-.f64 (.f64 (.f64 l (.f64 w w)) (+.f64 (.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2)) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (.f64 w w))))))
▶	0.3b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w))))
	0.3b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))))

Compiler

Compiled 4269 to 1208 computations (71.7% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w))))
✓	0.2b	(pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w))))
✓	0.2b	(pow.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))
✓	0.2b	(pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w))))

series6.6s (20.2%)

Counts

4 → 96

Calls

4 calls:

2.3s	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w))))
2.3s	(pow.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))
1.4s	(pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w))))
514.0ms	(pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w))))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`unpow-prod-down_binary64`
34×	`add-sqr-sqrt_binary64`
24×	`pow-unpow_binary64`
23×	`pow-exp_binary64`
23×	`*-un-lft-identity_binary64`

Counts

4 → 135

Calls

4 calls:

11.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w))))
4.0ms	(pow.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))
3.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w))))
2.0ms	(pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w))))

simplify176.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

276×	`associate-r_binary64`
259×	`exp-prod_binary64`
255×	`unswap-sqr_binary64`
252×	`sqr-pow_binary64`
227×	`fma-neg_binary64`

Counts

231 → 220

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	5962
1	713	5712
2	2520	5250
3	4429	3816
4	4877	3816
5	4939	3816

prune147.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	220	4	224

Error

0.0b

Counts

224 → 4

Alt Table

Status	Error	Program
	1.3b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (*.f64 (cbrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w))))) (cbrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w)))))) (sqrt.f64 (exp.f64 w))) (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w))))) (sqrt.f64 (exp.f64 w)))))
	11.9b	(+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (-.f64 (.f64 (.f64 l (.f64 w w)) (+.f64 (.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2)) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (.f64 w w))))))
	0.6b	(*.f64 (/.f64 (sqrt.f64 (pow.f64 l (exp.f64 w))) (exp.f64 w)) (sqrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))))
▶	0.3b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))))

Compiler

Compiled 6492 to 1495 computations (77% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))
✓	0.2b	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w)))))
	0.2b	(pow.f64 l (sqrt.f64 (exp.f64 w)))
✓	0.2b	(log1p.f64 (sqrt.f64 (exp.f64 w)))

series950.0ms (2.9%)

Counts

3 → 48

Calls

3 calls:

748.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w)))))
199.0ms	(log1p.f64 (sqrt.f64 (exp.f64 w)))
3.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`unpow-prod-down_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 48

Calls

3 calls:

2.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w)))))
0.0ms	(log1p.f64 (sqrt.f64 (exp.f64 w)))
0.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))

simplify60.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

733×	`distribute-rgt-out_binary64`
486×	`fma-def_binary64`
457×	`associate-l_binary64`
358×	`associate-r_binary64`
307×	`unswap-sqr_binary64`

Counts

96 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1252
1	313	1131
2	825	1006
3	3005	1002
4	5469	1002

prune103.0ms (0.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	129	4	133

Error

0.0b

Counts

133 → 4

Alt Table

Status	Error	Program
	1.3b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (*.f64 (cbrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w))))) (cbrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w)))))) (sqrt.f64 (exp.f64 w))) (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (exp.f64 w))))) (sqrt.f64 (exp.f64 w)))))
	11.9b	(+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (-.f64 (.f64 (.f64 l (.f64 w w)) (+.f64 (.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2)) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (.f64 w w))))))
	0.6b	(*.f64 (/.f64 (sqrt.f64 (pow.f64 l (exp.f64 w))) (exp.f64 w)) (sqrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))))
	0.7b	(.f64 (exp.f64 (neg.f64 w)) (.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))) (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w)))))))

Compiler

Compiled 2937 to 853 computations (71% saved)

regimes418.0ms (1.3%)

Accuracy

Total 0.2b remaining (56.7%)

Threshold costs 0.2b (56.7%)

Counts

155 → 1

Compiler

Compiled 9041 to 5665 computations (37.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	16	24
2	18	24
3	19	24
4	19	24

end76.0ms (0.2%)

Compiler: Compiled 172 to 78 computations (54.7% saved)

Details

analyze1.8s (5.5%)

sample19.9s (60.6%)

simplify87.0ms (0.3%)

prune3.0ms (0%)

localize6.0ms (0%)

series291.0ms (0.9%)

rewrite10.0ms (0%)

simplify68.0ms (0.2%)

prune59.0ms (0.2%)

localize8.0ms (0%)

series1.7s (5.2%)

rewrite18.0ms (0.1%)

simplify101.0ms (0.3%)

prune149.0ms (0.5%)

localize10.0ms (0%)

series6.6s (20.2%)

rewrite28.0ms (0.1%)

simplify176.0ms (0.5%)

prune147.0ms (0.4%)

localize11.0ms (0%)

series950.0ms (2.9%)

rewrite5.0ms (0%)

simplify60.0ms (0.2%)

prune103.0ms (0.3%)

regimes418.0ms (1.3%)

simplify2.0ms (0%)

end76.0ms (0.2%)

Profiling