Details

analyze1.3s (6.5%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
31.2%	68.7%	0.1%	5
31.2%	59.3%	9.5%	6
34.3%	54.6%	11%	7
34.3%	49.2%	16.5%	8
35.9%	46.4%	17.7%	9
35.9%	42.1%	22%	10
36.7%	40.6%	22.7%	11
36.7%	39.1%	24.2%	12
37.1%	38.3%	24.7%	13
37.1%	36.7%	26.2%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample596.0ms (2.9%)

Algorithm

1×

intervals

Results

423.0ms	158×	body	8192	exit
37.0ms	89×	body	1024	nan
18.0ms	256×	body	128	valid
9.0ms	42×	body	512	nan
4.0ms	25×	body	256	nan
1.0ms	12×	body	128	nan
0.0ms	6×	body	128	invalid
0.0ms	3×	body	128	overflowed

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify92.0ms (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

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

0.2b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 35 to 18 computations (48.6% 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))
✓	0.2b	(pow.f64 l (exp.f64 w))

series428.0ms (2.1%)

Counts

2 → 40

Calls

2 calls:

249.0ms	(pow.f64 l (exp.f64 w))
179.0ms	(/.f64 (pow.f64 l (exp.f64 w)) (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:

4.0ms	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
2.0ms	(pow.f64 l (exp.f64 w))

simplify92.0ms (0.5%)

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

prune143.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	4	92

Error

0.0b

Counts

92 → 4

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
	9.2b	(/.f64 (+.f64 l (fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (log.f64 (sqrt.f64 l)))) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (.f64 l (+.f64 (.f64 (log.f64 l) w) (.f64 1/6 (*.f64 (pow.f64 (log.f64 l) 3) (pow.f64 w 3)))))))) (exp.f64 w))
▶	4.7b	(/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))
	12.1b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)

Compiler

Compiled 1737 to 583 computations (66.4% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))
✓	0.1b	(log.f64 (pow.f64 l (exp.f64 w)))
	0.2b	(pow.f64 l (exp.f64 w))
✓	4.7b	(exp.f64 (log.f64 (pow.f64 l (exp.f64 w))))

series1.1s (5.2%)

Counts

3 → 68

Calls

3 calls:

737.0ms	(log.f64 (pow.f64 l (exp.f64 w)))
158.0ms	(/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))
156.0ms	(exp.f64 (log.f64 (pow.f64 l (exp.f64 w))))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`log-prod_binary64`
35×	`exp-sum_binary64`
33×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`

Counts

3 → 99

Calls

3 calls:

7.0ms	(/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))
2.0ms	(exp.f64 (log.f64 (pow.f64 l (exp.f64 w))))
2.0ms	(log.f64 (pow.f64 l (exp.f64 w)))

simplify110.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

933×	`fma-def_binary64`
542×	`associate-l_binary64`
344×	`fma-neg_binary64`
242×	`div-exp_binary64`
171×	`associate-/l*_binary64`

Counts

167 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	2657
1	452	2515
2	1398	2468
3	4358	2468
4	5278	2468

prune101.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	213	4	217

Error

0.0b

Counts

217 → 4

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
	9.2b	(/.f64 (+.f64 l (fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (log.f64 (sqrt.f64 l)))) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (.f64 l (+.f64 (.f64 (log.f64 l) w) (.f64 1/6 (*.f64 (pow.f64 (log.f64 l) 3) (pow.f64 w 3)))))))) (exp.f64 w))
▶	4.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))) (cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w)))) (cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))))
	12.1b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)

Compiler

Compiled 4059 to 1215 computations (70.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 l (exp.f64 w))
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))) (cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))))
✓	0.5b	(cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w)))
	4.7b	(exp.f64 (log.f64 (pow.f64 l (exp.f64 w))))

series2.5s (12.4%)

Counts

2 → 48

Calls

2 calls:

1.6s

(*.f64 (cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))) (cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))))

959.0ms

(cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w)))

rewrite95.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

230×	`cbrt-prod_binary64`
214×	`add-sqr-sqrt_binary64`
198×	`times-frac_binary64`
141×	`exp-sum_binary64`
141×	`log-prod_binary64`

Counts

2 → 215

Calls

2 calls:

31.0ms

(*.f64 (cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))) (cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))))

5.0ms

(cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w)))

simplify274.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

727×	`times-frac_binary64`
458×	`fma-neg_binary64`
361×	`associate-r_binary64`
305×	`associate-l_binary64`
295×	`cancel-sign-sub-inv_binary64`

Counts

263 → 359

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	447	10065
1	766	9598
2	2667	9295
3	3972	9268
4	5835	9268

prune339.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	740	1	741
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	741	4	745

Error

Counts

745 → 4

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
▶	9.2b	(/.f64 (+.f64 l (fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (log.f64 (sqrt.f64 l)))) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (.f64 l (+.f64 (.f64 (log.f64 l) w) (.f64 1/6 (*.f64 (pow.f64 (log.f64 l) 3) (pow.f64 w 3)))))))) (exp.f64 w))
	27.0b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))) 6) 1/3) (cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))))
	12.1b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)

Compiler

Compiled 33373 to 5515 computations (83.5% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.7b	(/.f64 (+.f64 l (fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (log.f64 (sqrt.f64 l)))) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (.f64 l (+.f64 (.f64 (log.f64 l) w) (.f64 1/6 (*.f64 (pow.f64 (log.f64 l) 3) (pow.f64 w 3)))))))) (exp.f64 w))
✓	5.8b	(fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (log.f64 (sqrt.f64 l)))) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (.f64 l (+.f64 (.f64 (log.f64 l) w) (.f64 1/6 (*.f64 (pow.f64 (log.f64 l) 3) (pow.f64 w 3)))))))
✓	7.1b	(*.f64 l (pow.f64 w 3))
✓	8.6b	(.f64 l (.f64 w w))

series397.0ms (2%)

Counts

4 → 48

Calls

4 calls:

206.0ms	(/.f64 (+.f64 l (fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (log.f64 (sqrt.f64 l)))) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (.f64 l (+.f64 (.f64 (log.f64 l) w) (.f64 1/6 (*.f64 (pow.f64 (log.f64 l) 3) (pow.f64 w 3)))))))) (exp.f64 w))
168.0ms	(fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (log.f64 (sqrt.f64 l)))) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (.f64 l (+.f64 (.f64 (log.f64 l) w) (.f64 1/6 (*.f64 (pow.f64 (log.f64 l) 3) (pow.f64 w 3)))))))
14.0ms	(*.f64 l (pow.f64 w 3))
8.0ms	(.f64 l (.f64 w w))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`
13×	`associate-r_binary64`

Counts

4 → 99

Calls

4 calls:

5.0ms	(/.f64 (+.f64 l (fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (log.f64 (sqrt.f64 l)))) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (.f64 l (+.f64 (.f64 (log.f64 l) w) (.f64 1/6 (*.f64 (pow.f64 (log.f64 l) 3) (pow.f64 w 3)))))))) (exp.f64 w))
5.0ms	(*.f64 l (pow.f64 w 3))
4.0ms	(.f64 l (.f64 w w))
0.0ms	(fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (log.f64 (sqrt.f64 l)))) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (.f64 l (+.f64 (.f64 (log.f64 l) w) (.f64 1/6 (*.f64 (pow.f64 (log.f64 l) 3) (pow.f64 w 3)))))))

simplify177.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

343×	`distribute-rgt-in_binary64`
326×	`distribute-lft-in_binary64`
311×	`associate-/l*_binary64`
247×	`associate-r_binary64`
244×	`associate-l_binary64`

Counts

147 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	7346
1	612	6734
2	2141	6489
3	4971	6489
4	5041	6489

prune226.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	161	4	165

Error

Counts

165 → 4

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
✓	9.2b	(/.f64 (+.f64 l (fma.f64 (.f64 l (pow.f64 w 3)) (.f64 (log.f64 l) (+.f64 1/6 (log.f64 (sqrt.f64 l)))) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (.f64 l (+.f64 (.f64 (log.f64 l) w) (.f64 1/6 (*.f64 (pow.f64 (log.f64 l) 3) (pow.f64 w 3)))))))) (exp.f64 w))
	27.0b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))) 6) 1/3) (cbrt.f64 (/.f64 (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))) (exp.f64 w))))
	12.1b	(fma.f64 w (-.f64 (*.f64 l (log.f64 l)) l) l)

Compiler

Compiled 11056 to 5123 computations (53.7% saved)

regimes104.0ms (0.5%)

Accuracy

Total 0.2b remaining (66.7%)

Threshold costs 0.2b (66.7%)

Counts

30 → 1

Compiler

Compiled 2435 to 1384 computations (43.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	6	11

end0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

sample12.1s (59.7%)

Algorithm

1×

intervals

Results

9.1s	4702×	body	8192	exit
1.2s	3219×	body	1024	nan
527.0ms	8000×	body	128	valid
319.0ms	1496×	body	512	nan
99.0ms	796×	body	256	nan
20.0ms	340×	body	128	nan
12.0ms	140×	body	128	overflowed
8.0ms	3×	body	8192	nan
8.0ms	107×	body	128	invalid
3.0ms	2×	body	4096	nan
2.0ms	4×	body	2048	nan

Compiler

Compiled 119 to 72 computations (39.5% saved)

Details

analyze1.3s (6.5%)

sample596.0ms (2.9%)

simplify92.0ms (0.5%)

prune3.0ms (0%)

localize5.0ms (0%)

series428.0ms (2.1%)

rewrite10.0ms (0.1%)

simplify92.0ms (0.5%)

prune143.0ms (0.7%)

localize8.0ms (0%)

series1.1s (5.2%)

rewrite18.0ms (0.1%)

simplify110.0ms (0.5%)

prune101.0ms (0.5%)

localize12.0ms (0.1%)

series2.5s (12.4%)

rewrite95.0ms (0.5%)

simplify274.0ms (1.4%)

prune339.0ms (1.7%)

localize31.0ms (0.2%)

series397.0ms (2%)

rewrite25.0ms (0.1%)

simplify177.0ms (0.9%)

prune226.0ms (1.1%)

regimes104.0ms (0.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample12.1s (59.7%)

Profiling