Details

analyze1.2s (5.8%)

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
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)

sample15.0s (74%)

Results

11.0s	4892×	body	8192	exit
1.9s	3285×	body	1024	invalid
1.2s	8256×	body	128	valid
571.0ms	1677×	body	512	invalid
178.0ms	856×	body	256	invalid
81.0ms	603×	body	128	invalid
9.0ms	4×	body	4096	invalid
6.0ms	2×	body	8192	invalid
4.0ms	4×	body	2048	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify86.0ms (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

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

0.2b

Counts

3 → 2

Alt Table

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

series237.0ms (1.2%)

Counts

2 → 44

Calls

2 calls:

119.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))
117.0ms	(pow.f64 l (exp.f64 w))

rewrite9.0ms (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)))
1.0ms	(pow.f64 l (exp.f64 w))

simplify63.0ms (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

prune70.0ms (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

0.1b

Counts

87 → 5

Alt Table

Status	Error	Program
	9.1b	(.f64 (exp.f64 (neg.f64 w)) (+.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 (.f64 1/6 (pow.f64 (log.f64 l) 3)) (pow.f64 w 3))))))))
	7.9b	(.f64 (exp.f64 (neg.f64 w)) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (fma.f64 (log.f64 l) (*.f64 l w) l)))
	4.6b	(exp.f64 (-.f64 (*.f64 (log.f64 l) (exp.f64 w)) w))
▶	2.6b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))
	4.6b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))

Compiler

Compiled 1687 to 590 computations (65% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
	0.2b	(pow.f64 l (exp.f64 w))
✓	2.4b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))

series252.0ms (1.2%)

Counts

2 → 44

Calls

2 calls:

127.0ms	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
124.0ms	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

4.0ms	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))

simplify95.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

475×	`fma-def_binary64`
405×	`associate-l_binary64`
332×	`associate-r_binary64`
281×	`associate-+l+_binary64`
213×	`associate--l+_binary64`

Counts

102 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	1929
1	321	1826
2	997	1788
3	4460	1788
4	4983	1788
5	4977	1788

prune70.0ms (0.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	102	5	107

Error

0.1b

Counts

107 → 5

Alt Table

Status	Error	Program
	9.1b	(.f64 (exp.f64 (neg.f64 w)) (+.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 (.f64 1/6 (pow.f64 (log.f64 l) 3)) (pow.f64 w 3))))))))
▶	2.7b	(*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))))
	7.9b	(.f64 (exp.f64 (neg.f64 w)) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (fma.f64 (log.f64 l) (*.f64 l w) l)))
	4.6b	(exp.f64 (-.f64 (*.f64 (log.f64 l) (exp.f64 w)) w))
	4.6b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))

Compiler

Compiled 2141 to 812 computations (62.1% saved)

localize8.0ms (0%)

Local error

Found 4 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))
✓	0.4b	(*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (sqrt.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))))

series127.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

127.0ms

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

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
16×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 53

Calls

1 calls:

5.0ms

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

simplify87.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

474×	`associate-l_binary64`
469×	`fma-def_binary64`
354×	`associate-r_binary64`
328×	`unswap-sqr_binary64`
278×	`associate-+l+_binary64`

Counts

77 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1425
1	252	1241
2	835	1162
3	3678	1125
4	4881	1125
5	4988	1125

prune179.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	274	3	277
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	275	7	282

Error

0.1b

Counts

282 → 7

Alt Table

Status	Error	Program
	2.8b	(.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 l (.f64 (cbrt.f64 (exp.f64 w)) (cbrt.f64 (exp.f64 w)))) (cbrt.f64 (exp.f64 w))) (exp.f64 w))))))
	4.6b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))
	9.1b	(.f64 (exp.f64 (neg.f64 w)) (+.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 (.f64 1/6 (pow.f64 (log.f64 l) 3)) (pow.f64 w 3))))))))
	4.2b	(*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (sqrt.f64 (expm1.f64 (log1p.f64 (exp.f64 (-.f64 (log.f64 (pow.f64 l (exp.f64 w))) w))))))
	7.9b	(.f64 (exp.f64 (neg.f64 w)) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (fma.f64 (log.f64 l) (*.f64 l w) l)))
	4.6b	(exp.f64 (-.f64 (*.f64 (log.f64 l) (exp.f64 w)) w))
▶	2.7b	(*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (exp.f64 w))))))

Compiler

Compiled 8469 to 1965 computations (76.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
✓	0.4b	(*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (exp.f64 w))))))
	2.4b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))
✓	2.4b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (exp.f64 w))))

series1.8s (8.9%)

Counts

3 → 68

Calls

3 calls:

680.0ms

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

563.0ms

(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))

555.0ms

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

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
10×	`unpow-prod-down_binary64`

Counts

3 → 72

Calls

3 calls:

5.0ms

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

3.0ms

(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))

0.0ms

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

simplify109.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-def_binary64`
588×	`associate-l_binary64`
463×	`associate-r_binary64`
213×	`associate--l+_binary64`
140×	`exp-prod_binary64`

Counts

140 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	3025
1	415	2294
2	1182	2178
3	4495	2178
4	4985	2178
5	5040	2178

prune113.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	143	8	151

Error

0.0b

Counts

151 → 8

Alt Table

Status	Error	Program
	2.8b	(.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 l (.f64 (cbrt.f64 (exp.f64 w)) (cbrt.f64 (exp.f64 w)))) (cbrt.f64 (exp.f64 w))) (exp.f64 w))))))
	4.6b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))
	9.1b	(.f64 (exp.f64 (neg.f64 w)) (+.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 (.f64 1/6 (pow.f64 (log.f64 l) 3)) (pow.f64 w 3))))))))
	4.2b	(*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (sqrt.f64 (expm1.f64 (log1p.f64 (exp.f64 (-.f64 (log.f64 (pow.f64 l (exp.f64 w))) w))))))
	7.9b	(.f64 (exp.f64 (neg.f64 w)) (fma.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l)))) (fma.f64 (log.f64 l) (*.f64 l w) l)))
	4.3b	(.f64 (sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 l) (exp.f64 w))) (exp.f64 w))) (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (exp.f64 w))))))
	4.6b	(exp.f64 (-.f64 (*.f64 (log.f64 l) (exp.f64 w)) w))
	2.7b	(*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))) (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (fabs.f64 (cbrt.f64 (exp.f64 w)))) (sqrt.f64 (cbrt.f64 (exp.f64 w)))) (exp.f64 w))))))

Compiler

Compiled 5116 to 1123 computations (78% saved)

regimes605.0ms (3%)

Accuracy

Total 0.2b remaining (65.5%)

Threshold costs 0.2b (65.5%)

Counts

184 → 1

Compiler

Compiled 11360 to 6472 computations (43% 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	11	21
1	18	21
2	20	21
3	21	21
4	20	21

end138.0ms (0.7%)

Compiler: Compiled 250 to 152 computations (39.2% saved)

Details

analyze1.2s (5.8%)

sample15.0s (74%)

simplify86.0ms (0.4%)

prune5.0ms (0%)

localize5.0ms (0%)

series237.0ms (1.2%)

rewrite9.0ms (0%)

simplify63.0ms (0.3%)

prune70.0ms (0.3%)

localize6.0ms (0%)

series252.0ms (1.2%)

rewrite7.0ms (0%)

simplify95.0ms (0.5%)

prune70.0ms (0.3%)

localize8.0ms (0%)

series127.0ms (0.6%)

rewrite10.0ms (0%)

simplify87.0ms (0.4%)

prune179.0ms (0.9%)

localize16.0ms (0.1%)

series1.8s (8.9%)

rewrite12.0ms (0.1%)

simplify109.0ms (0.5%)

prune113.0ms (0.6%)

regimes605.0ms (3%)

simplify2.0ms (0%)

end138.0ms (0.7%)

Profiling