Details

analyze1.4s (3.7%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	50%	0.1%	7
50%	50%	0.1%	8
50%	50%	0.1%	9
50%	48.6%	1.5%	10
50%	48.5%	1.6%	11
50%	48.5%	1.6%	12
50%	48.4%	1.6%	13
50%	47.7%	2.4%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample20.3s (55.8%)

Results

15.5s	5904×	body	8192	exit
2.0s	2426×	body	1024	invalid
1.7s	8256×	body	128	valid
581.0ms	1202×	body	512	invalid
269.0ms	588×	body	256	invalid
66.0ms	285×	body	128	invalid
16.0ms	3×	body	8192	invalid
10.0ms	7×	body	2048	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify167.0ms (0.5%)

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

prune5.0ms (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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
▶	0.5b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))

Compiler

Compiled 55 to 32 computations (41.8% saved)

localize13.0ms (0%)

Local error

Found 2 expressions with local error:

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

series465.0ms (1.3%)

Counts

2 → 44

Calls

2 calls:

248.0ms	(pow.f64 l (exp.f64 w))
217.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))

rewrite20.0ms (0.1%)

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:

13.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))
3.0ms	(pow.f64 l (exp.f64 w))

simplify116.0ms (0.3%)

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

prune120.0ms (0.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Error

0.0b

Counts

87 → 5

Alt Table

Status	Error	Program
	28.9b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)
	22.8b	(-.f64 (+.f64 (.f64 1/2 (.f64 l (pow.f64 w 2))) (+.f64 (.f64 1/6 (.f64 (log.f64 l) (.f64 l (pow.f64 w 3)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 (log.f64 l) 3) (.f64 l (pow.f64 w 3)))) (+.f64 (.f64 (log.f64 l) (.f64 l w)) (+.f64 l (.f64 1/2 (.f64 (pow.f64 (log.f64 l) 2) (.f64 l (pow.f64 w 2))))))))) (+.f64 (.f64 1/6 (.f64 l (pow.f64 w 3))) (+.f64 (.f64 1/2 (.f64 (log.f64 l) (.f64 l (pow.f64 w 2)))) (*.f64 l w))))
	3.5b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))
	3.2b	(exp.f64 (-.f64 (*.f64 (log.f64 l) (exp.f64 w)) w))
▶	0.5b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))

Compiler

Compiled 1713 to 612 computations (64.3% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

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

series2.8s (7.7%)

Counts

4 → 68

Calls

4 calls:

1.3s	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
1.2s	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
220.0ms	(pow.f64 l (sqrt.f64 (exp.f64 w)))
3.0ms	(sqrt.f64 (exp.f64 w))

rewrite34.0ms (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:

11.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
9.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
3.0ms	(pow.f64 l (sqrt.f64 (exp.f64 w)))
2.0ms	(sqrt.f64 (exp.f64 w))

simplify157.0ms (0.4%)

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 → 167

Iterations

Useful iterations: 2 (0.0ms)

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

prune237.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	193	5	198

Error

0.0b

Counts

198 → 5

Alt Table

Status	Error	Program
	28.9b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)
▶	0.5b	(.f64 (.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (cbrt.f64 (exp.f64 (neg.f64 w)))) (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))))
	3.5b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))
	22.9b	(-.f64 (+.f64 (.f64 (.f64 1/6 (.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 1/6 (.f64 l (pow.f64 w 3)) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (.f64 w w))))))
	3.2b	(exp.f64 (-.f64 (*.f64 (log.f64 l) (exp.f64 w)) w))

Compiler

Compiled 4245 to 1235 computations (70.9% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
✓	0.2b	(*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (cbrt.f64 (exp.f64 (neg.f64 w)))) (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))))
✓	0.3b	(cbrt.f64 (exp.f64 (neg.f64 w)))

series3.4s (9.2%)

Counts

3 → 60

Calls

3 calls:

1.8s

(*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))

1.2s

(*.f64 (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (cbrt.f64 (exp.f64 (neg.f64 w)))) (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))))

274.0ms

(cbrt.f64 (exp.f64 (neg.f64 w)))

rewrite61.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`cbrt-div_binary64`
47×	`add-exp-log_binary64`
34×	`associate-*l/_binary64`
33×	`prod-exp_binary64`
29×	`exp-neg_binary64`

Counts

3 → 116

Calls

3 calls:

21.0ms

(*.f64 (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (cbrt.f64 (exp.f64 (neg.f64 w)))) (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))))

12.0ms

(*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))

3.0ms

(cbrt.f64 (exp.f64 (neg.f64 w)))

simplify210.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

356×	`associate--l+_binary64`
296×	`cancel-sign-sub-inv_binary64`
281×	`associate-r_binary64`
260×	`associate-l_binary64`
216×	`exp-prod_binary64`

Counts

176 → 186

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	256	4182
1	563	3679
2	2002	3010
3	4307	2949
4	4957	2921
5	4963	2921

prune453.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	293	1	294
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	294	5	299

Error

0.0b

Counts

299 → 5

Alt Table

Status	Error	Program
▶	0.7b	(.f64 (.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (cbrt.f64 (exp.f64 (neg.f64 w)))) (.f64 (.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))))
	28.9b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)
	3.5b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))
	22.9b	(-.f64 (+.f64 (.f64 (.f64 1/6 (.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 1/6 (.f64 l (pow.f64 w 3)) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (.f64 w w))))))
	3.2b	(exp.f64 (-.f64 (*.f64 (log.f64 l) (exp.f64 w)) w))

Compiler

Compiled 9277 to 2087 computations (77.5% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w))))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (cbrt.f64 (exp.f64 (neg.f64 w)))) (.f64 (.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w))))
	0.3b	(cbrt.f64 (exp.f64 (neg.f64 w)))

series5.2s (14.3%)

Counts

3 → 72

Calls

3 calls:

1.9s

(*.f64 (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w))))

1.8s

(*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w))))

1.5s

(*.f64 (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (cbrt.f64 (exp.f64 (neg.f64 w)))) (*.f64 (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))))

rewrite121.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-exp-log_binary64`
105×	`prod-exp_binary64`
58×	`cbrt-div_binary64`
56×	`associate-*l/_binary64`
36×	`unpow-prod-down_binary64`

Counts

3 → 161

Calls

3 calls:

31.0ms

(*.f64 (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (cbrt.f64 (exp.f64 (neg.f64 w)))) (*.f64 (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))))

21.0ms

(*.f64 (*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w))))

15.0ms

(*.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w))))

simplify363.0ms (1%)

Algorithm

1×	egg-herbie

Rules

739×	`associate-r_binary64`
659×	`associate-l_binary64`
429×	`fma-def_binary64`
358×	`*-commutative_binary64`
356×	`associate-+r+_binary64`

Counts

233 → 233

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	466	10352
1	1222	8509
2	4754	8507
3	4984	8507

prune459.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	328	1	329
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	329	5	334

Error

0.0b

Counts

334 → 5

Alt Table

Status	Error	Program
	0.7b	(.f64 (.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (cbrt.f64 (exp.f64 (neg.f64 w))))) (cbrt.f64 (cbrt.f64 (exp.f64 (neg.f64 w)))))) (.f64 (.f64 (cbrt.f64 (exp.f64 (neg.f64 w))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))) (pow.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (exp.f64 w)))))
	22.9b	(-.f64 (+.f64 (.f64 (.f64 1/6 (.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 1/6 (.f64 l (pow.f64 w 3)) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (.f64 w w))))))
	28.9b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)
	3.5b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))
	3.2b	(exp.f64 (-.f64 (*.f64 (log.f64 l) (exp.f64 w)) w))

Compiler

Compiled 15945 to 2994 computations (81.2% saved)

regimes164.0ms (0.5%)

Accuracy

Total 0.3b remaining (82.5%)

Threshold costs 0.3b (82.5%)

Counts

38 → 1

Compiler

Compiled 3263 to 1771 computations (45.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-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	8	13
1	13	13
2	15	13
3	16	13
4	16	13

end157.0ms (0.4%)

Compiler: Compiled 162 to 90 computations (44.4% saved)

Details

analyze1.4s (3.7%)

sample20.3s (55.8%)

simplify167.0ms (0.5%)

prune5.0ms (0%)

localize13.0ms (0%)

series465.0ms (1.3%)

rewrite20.0ms (0.1%)

simplify116.0ms (0.3%)

prune120.0ms (0.3%)

localize17.0ms (0%)

series2.8s (7.7%)

rewrite34.0ms (0.1%)

simplify157.0ms (0.4%)

prune237.0ms (0.7%)

localize17.0ms (0%)

series3.4s (9.2%)

rewrite61.0ms (0.2%)

simplify210.0ms (0.6%)

prune453.0ms (1.2%)

localize38.0ms (0.1%)

series5.2s (14.3%)

rewrite121.0ms (0.3%)

simplify363.0ms (1%)

prune459.0ms (1.3%)

regimes164.0ms (0.5%)

simplify3.0ms (0%)

end157.0ms (0.4%)

Profiling