Details

analyze418.0ms (6%)

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
25%	74.9%	0.1%	5
43.7%	56.2%	0.1%	6
53.1%	42.1%	4.8%	7
59.3%	35.9%	4.8%	8
62.4%	30.4%	7.1%	9
64.8%	28.1%	7.1%	10
66%	25.8%	8.3%	11
66.9%	24.8%	8.3%	12
67.4%	23.7%	8.9%	13
67.9%	23.3%	8.9%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample4.6s (66.5%)

Results

2.5s	2510×	body	8192	exit
1.7s	7634×	body	128	valid
133.0ms	208×	body	1024	valid
102.0ms	266×	body	512	valid
38.0ms	148×	body	256	valid
13.0ms	77×	body	128	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify103.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
741×	`fabs-mul_binary64`
531×	`fabs-div_binary64`
469×	`swap-sqr_binary64`
420×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	28	11
3	45	11
4	59	11
5	89	11
6	120	11
7	148	11
8	188	11
9	201	11
10	231	11
11	257	11
12	336	11
13	544	11
14	967	11
15	2930	11
16	3463	11
17	3600	11
18	3896	11
19	4820	11
20	4969	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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 36 to 22 computations (38.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.7b	(log1p.f64 (exp.f64 x))

series267.0ms (3.8%)

Counts

2 → 36

Calls

2 calls:

187.0ms	(log1p.f64 (exp.f64 x))
79.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`fma-neg_binary64`

Counts

2 → 32

Calls

2 calls:

2.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
0.0ms	(log1p.f64 (exp.f64 x))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

620×	`cancel-sign-sub-inv_binary64`
339×	`unswap-sqr_binary64`
285×	`*-commutative_binary64`
285×	`unsub-neg_binary64`
252×	`distribute-rgt-in_binary64`

Counts

68 → 56

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	73	789
1	167	742
2	426	710
3	1507	707
4	3171	707
5	4588	701
6	4872	701

prune29.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	3	57

Error

0.2b

Counts

57 → 3

Alt Table

Status	Error	Program
▶	10.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	26.0b	(log.f64 (/.f64 (+.f64 1 (exp.f64 x)) (exp.f64 (*.f64 x y))))

Compiler

Compiled 797 to 296 computations (62.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

series10.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(fma.f64 x (-.f64 1/2 y) (log.f64 2))

rewrite5.0ms (0.1%)

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 → 10

Calls

1 calls:

4.0ms

(fma.f64 x (-.f64 1/2 y) (log.f64 2))

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-neg_binary64`
478×	`neg-sub0_binary64`
433×	`neg-mul-1_binary64`
375×	`*-commutative_binary64`
362×	`distribute-rgt-in_binary64`

Counts

34 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	459
1	52	346
2	104	346
3	328	346
4	1670	346
5	2981	346
6	4467	346
7	4969	346

prune18.0ms (0.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	21	4	25

Error

0.2b

Counts

25 → 4

Alt Table

Status	Error	Program
✓	10.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	20.2b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
	27.1b	(log.f64 (.f64 2 (exp.f64 (.f64 x (-.f64 1/2 y)))))

Compiler

Compiled 298 to 225 computations (24.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.1b	(.f64 (.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
✓	0.7b	(*.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
✓	16.6b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (fma.f64 x (-.f64 1/2 y) (log.f64 2))))

series55.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

29.0ms

(*.f64 (*.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

15.0ms

(*.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

10.0ms

(cbrt.f64 (*.f64 (*.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (fma.f64 x (-.f64 1/2 y) (log.f64 2))))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 74

Calls

3 calls:

4.0ms

(*.f64 (*.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

3.0ms

(cbrt.f64 (*.f64 (*.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (fma.f64 x (-.f64 1/2 y) (log.f64 2))))

3.0ms

(*.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

424×	`distribute-rgt-in_binary64`
391×	`distribute-lft-in_binary64`
239×	`fma-neg_binary64`
188×	`associate-r_binary64`
187×	`fma-def_binary64`

Counts

146 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	5226
1	505	4009
2	1948	3583
3	5174	3583

prune186.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	215	5	220

Error

0.2b

Counts

220 → 5

Alt Table

Status	Error	Program
✓	10.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
	23.5b	(cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) 3) 3)))
▶	21.6b	(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) 6)) (cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) 3))))
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	27.1b	(log.f64 (.f64 2 (exp.f64 (.f64 x (-.f64 1/2 y)))))

Compiler

Compiled 6332 to 4861 computations (23.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.1b	(cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) 3)))
✓	1.1b	(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
✓	13.6b	(cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) 6))
✓	16.6b	(cbrt.f64 (pow.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) 3))

series239.0ms (3.4%)

Counts

4 → 96

Calls

4 calls:

130.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) 6))
48.0ms	(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
47.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) 3)))
13.0ms	(cbrt.f64 (pow.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) 3))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`cbrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64`

Counts

4 → 81

Calls

4 calls:

2.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) 3)))
2.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) 6))
1.0ms	(cbrt.f64 (pow.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) 3))
1.0ms	(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

simplify157.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

734×	`times-frac_binary64`
596×	`fma-def_binary64`
506×	`associate-/l*_binary64`
239×	`*-commutative_binary64`
136×	`+-commutative_binary64`

Counts

177 → 206

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	691	11445
1	2324	10693
2	5358	10693

prune292.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	206	5	211

Error

0.2b

Counts

211 → 5

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	62.9b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 1/3 (/.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x))) (/.f64 (-.f64 1/2 y) (/.f64 (log.f64 2) x))) (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x)))) 6)) (cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) 3))))
✓	10.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
	26.4b	(.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) 6)) (cbrt.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) 6))) (cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)) 3))))
	27.1b	(log.f64 (.f64 2 (exp.f64 (.f64 x (-.f64 1/2 y)))))

Compiler

Compiled 13797 to 11185 computations (18.9% saved)

regimes150.0ms (2.1%)

Accuracy

Total 0.2b remaining (58.3%)

Threshold costs 0.2b (58.3%)

Counts

40 → 1

Compiler

Compiled 2751 to 2219 computations (19.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	23	11
3	29	11
4	33	11
5	34	11
6	34	11

end105.0ms (1.5%)

Compiler: Compiled 134 to 106 computations (20.9% saved)

Details

analyze418.0ms (6%)

sample4.6s (66.5%)

simplify103.0ms (1.5%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series267.0ms (3.8%)

rewrite4.0ms (0.1%)

simplify77.0ms (1.1%)

prune29.0ms (0.4%)

localize5.0ms (0.1%)

series10.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify67.0ms (1%)

prune18.0ms (0.3%)

localize8.0ms (0.1%)

series55.0ms (0.8%)

rewrite16.0ms (0.2%)

simplify93.0ms (1.3%)

prune186.0ms (2.7%)

localize13.0ms (0.2%)

series239.0ms (3.4%)

rewrite15.0ms (0.2%)

simplify157.0ms (2.2%)

prune292.0ms (4.2%)

regimes150.0ms (2.1%)

simplify2.0ms (0%)

end105.0ms (1.5%)

Profiling