Details

analyze1.1s (5.1%)

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
12.5%	87.4%	0.1%	5
12.5%	78%	9.5%	6
20.3%	68.7%	11%	7
21.1%	62.4%	16.5%	8
25.4%	57%	17.7%	9
26%	52.1%	22%	10
28.3%	49%	22.7%	11
28.6%	47.2%	24.2%	12
29.8%	45.6%	24.7%	13
29.9%	43.9%	26.2%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample15.4s (74.2%)

Results

11.4s	4790×	body	8192	exit
1.9s	3176×	body	1024	invalid
1.2s	8256×	body	128	valid
580.0ms	1627×	body	512	invalid
192.0ms	825×	body	256	invalid
89.0ms	635×	body	128	invalid
3.0ms	1×	body	8192	invalid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify92.0ms (0.4%)

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

3 alts after pruning (3 fresh and 0 done)

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

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
	0.3b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))

Compiler

Compiled 55 to 32 computations (41.8% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
✓	0.3b	(pow.f64 l (exp.f64 w))

series313.0ms (1.5%)

Counts

2 → 40

Calls

2 calls:

162.0ms	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
151.0ms	(pow.f64 l (exp.f64 w))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
15×	`unpow-prod-down_binary64`

Counts

2 → 66

Calls

2 calls:

5.0ms	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
2.0ms	(pow.f64 l (exp.f64 w))

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

847×	`fma-def_binary64`
696×	`associate-l_binary64`
359×	`fma-neg_binary64`
322×	`times-frac_binary64`
234×	`associate-/l*_binary64`

Counts

106 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	1790
1	375	1705
2	1326	1665
3	4894	1665
4	5116	1665

prune70.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	90	3	93

Error

0.0b

Counts

93 → 3

Alt Table

Status	Error	Program
	14.7b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)
▶	2.4b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))
	14.5b	(-.f64 (fma.f64 1/6 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 3))) (+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (.f64 (.f64 l (.f64 w w)) (+.f64 (.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2)))) (fma.f64 l (.f64 (pow.f64 w 3) 1/6) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (*.f64 w w))))))

Compiler

Compiled 1740 to 586 computations (66.3% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
	0.3b	(pow.f64 l (exp.f64 w))
✓	2.3b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))

series161.0ms (0.8%)

Counts

1 → 24

Calls

1 calls:

161.0ms

(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

467×	`fma-def_binary64`
334×	`associate-l_binary64`
275×	`associate-+l+_binary64`
267×	`associate-r_binary64`
230×	`distribute-rgt-out--_binary64`

Counts

35 → 28

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	575
1	203	538
2	685	519
3	3220	505
4	4913	505
5	4957	505

prune67.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Error

Counts

122 → 4

Alt Table

Status	Error	Program
▶	2.9b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w)))))) (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))))
	14.7b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)
✓	2.4b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))
	14.5b	(-.f64 (fma.f64 1/6 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 3))) (+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (.f64 (.f64 l (.f64 w w)) (+.f64 (.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2)))) (fma.f64 l (.f64 (pow.f64 w 3) 1/6) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (*.f64 w w))))))

Compiler

Compiled 2494 to 922 computations (63% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 l (exp.f64 w))
✓	0.4b	(*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))))
✓	0.5b	(cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w)))))
	2.3b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))

series2.3s (11.2%)

Counts

2 → 48

Calls

2 calls:

1.4s

(*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))))

876.0ms

(cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w)))))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 55

Calls

2 calls:

4.0ms

(*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))))

1.0ms

(cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w)))))

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

675×	`associate-+l+_binary64`
320×	`associate--l+_binary64`
289×	`cancel-sign-sub-inv_binary64`
281×	`unswap-sqr_binary64`
224×	`associate-r_binary64`

Counts

103 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2742
1	486	2404
2	1788	2131
3	4909	2131
4	4967	2131

prune157.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	351	0	351
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	351	4	355

Error

Counts

355 → 4

Alt Table

Status	Error	Program
✓	2.9b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w)))))) (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))))
	14.7b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)
✓	2.4b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))
▶	14.5b	(-.f64 (fma.f64 1/6 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 3))) (+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (.f64 (.f64 l (.f64 w w)) (+.f64 (.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2)))) (fma.f64 l (.f64 (pow.f64 w 3) 1/6) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (*.f64 w w))))))

Compiler

Compiled 14967 to 2983 computations (80.1% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.4b	(*.f64 l (pow.f64 w 3))
✓	4.8b	(fma.f64 1/6 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 3))) (+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (.f64 (.f64 l (.f64 w w)) (+.f64 (*.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2))))
✓	5.0b	(fma.f64 l (.f64 (pow.f64 w 3) 1/6) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (.f64 w w)))))
✓	10.4b	(.f64 l (.f64 w w))

series260.0ms (1.3%)

Counts

4 → 60

Calls

4 calls:

204.0ms	(fma.f64 1/6 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 3))) (+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (.f64 (.f64 l (.f64 w w)) (+.f64 (*.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2))))
36.0ms	(fma.f64 l (.f64 (pow.f64 w 3) 1/6) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (.f64 w w)))))
11.0ms	(*.f64 l (pow.f64 w 3))
9.0ms	(.f64 l (.f64 w w))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-r_binary64`
11×	`add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 74

Calls

4 calls:

6.0ms	(*.f64 l (pow.f64 w 3))
4.0ms	(.f64 l (.f64 w w))
0.0ms	(fma.f64 l (.f64 (pow.f64 w 3) 1/6) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (.f64 w w)))))
0.0ms	(fma.f64 1/6 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 3))) (+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (.f64 (.f64 l (.f64 w w)) (+.f64 (*.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2))))

simplify105.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

411×	`distribute-rgt-in_binary64`
342×	`associate-r_binary64`
330×	`exp-prod_binary64`
320×	`associate-l_binary64`
284×	`unswap-sqr_binary64`

Counts

134 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	3896
1	606	3425
2	2291	3323
3	4712	3281
4	5167	3281

prune140.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	124	3	127

Error

Counts

127 → 3

Alt Table

Status	Error	Program
	14.5b	(-.f64 (.f64 l (+.f64 (+.f64 (.f64 1/6 (.f64 (pow.f64 w 3) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 3)))) (.f64 (.f64 w w) (fma.f64 1/2 (pow.f64 (log.f64 l) 2) 1/2))) (fma.f64 w (log.f64 l) 1))) (fma.f64 l (.f64 (pow.f64 w 3) 1/6) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (*.f64 w w))))))
✓	2.9b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w)))))) (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))))
✓	2.4b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))

Compiler

Compiled 7799 to 3559 computations (54.4% saved)

regimes204.0ms (1%)

Accuracy

Total 0.1b remaining (59.6%)

Threshold costs 0.1b (59.6%)

Counts

63 → 1

Compiler

Compiled 5504 to 3271 computations (40.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	12	11
2	10	11

end68.0ms (0.3%)

Compiler: Compiled 117 to 61 computations (47.9% saved)

Details

analyze1.1s (5.1%)

sample15.4s (74.2%)

simplify92.0ms (0.4%)

prune3.0ms (0%)

localize5.0ms (0%)

series313.0ms (1.5%)

rewrite10.0ms (0.1%)

simplify81.0ms (0.4%)

prune70.0ms (0.3%)

localize7.0ms (0%)

series161.0ms (0.8%)

rewrite1.0ms (0%)

simplify71.0ms (0.3%)

prune67.0ms (0.3%)

localize9.0ms (0%)

series2.3s (11.2%)

rewrite10.0ms (0%)

simplify91.0ms (0.4%)

prune157.0ms (0.8%)

localize29.0ms (0.1%)

series260.0ms (1.3%)

rewrite14.0ms (0.1%)

simplify105.0ms (0.5%)

prune140.0ms (0.7%)

regimes204.0ms (1%)

simplify2.0ms (0%)

end68.0ms (0.3%)

Profiling