Details

analyze407.0ms (6.4%)

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)

sample4.0s (63.5%)

Results

2.6s	2685×	body	8192	exit
1.0s	7570×	body	128	valid
161.0ms	248×	body	1024	valid
106.0ms	260×	body	512	valid
44.0ms	174×	body	256	valid
11.0ms	85×	body	128	invalid
5.0ms	4×	body	2048	valid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify37.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

369×	`times-frac_binary64`
363×	`associate-l_binary64`
285×	`associate-/l/_binary64`
280×	`associate-/l*_binary64`
262×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	30	11
3	47	11
4	66	11
5	100	11
6	154	11
7	205	11
8	273	11
9	352	11
10	414	11
11	440	11
12	519	11
13	747	11
14	1549	11
15	4642	11

Stop Event

1×	node limit

Counts

1 → 2

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

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(-.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))
✓	0.5b	(log1p.f64 (exp.f64 x))

series204.0ms (3.2%)

Counts

2 → 36

Calls

2 calls:

144.0ms	(log1p.f64 (exp.f64 x))
60.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

rewrite54.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

733×	`expm1-log1p-u_binary64`
732×	`log1p-expm1-u_binary64`
659×	`prod-diff_binary64`
111×	`egg-rr`
76×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	147	16
2	1998	16

Stop Event

1×	node limit

Counts

2 → 111

Calls

2 calls:

50.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
50.0ms	(log1p.f64 (exp.f64 x))

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

537×	`fma-def_binary64`
237×	`distribute-lft-out_binary64`
196×	`sub-neg_binary64`
194×	`*-commutative_binary64`
188×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	356
1	81	350
2	201	337
3	652	321
4	2594	321
5	4861	321

Stop Event

1×	node limit

Counts

147 → 130

prune74.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	126	5	131

Error

0.2b

Counts

131 → 5

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	17.9b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (.f64 (.f64 x y) (+.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)))))
	12.2b	(/.f64 1 (/.f64 (+.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (pow.f64 (.f64 x y) 2))))
▶	2.1b	(.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2))
	15.6b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

Compiler

Compiled 2968 to 926 computations (68.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2)
	0.5b	(log1p.f64 (exp.f64 x))
✓	0.7b	(.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2))
✓	1.1b	(cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

series140.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

63.0ms

(*.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2))

46.0ms

(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2)

30.0ms

(cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

rewrite67.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`prod-diff_binary64`
244×	`fma-def_binary64`
186×	`egg-rr`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	229	40
2	2625	40

Stop Event

1×	node limit

Counts

3 → 186

Calls

3 calls:

63.0ms

(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2)

63.0ms

(*.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2))

62.0ms

(cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Rules

414×	`associate-r_binary64`
318×	`fma-def_binary64`
285×	`associate-l_binary64`
242×	`times-frac_binary64`
210×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	354	4010
1	1230	3922

Stop Event

1×	node limit

Counts

258 → 294

prune301.0ms (4.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	414	3	417
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	416	6	422

Error

0.2b

Counts

422 → 6

Alt Table

Status	Error	Program
✓	2.1b	(.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2))
▶	12.2b	(/.f64 1 (/.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (pow.f64 (*.f64 x y) 2))))
	16.8b	(.f64 (pow.f64 (pow.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)) 1/6) 2) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2))
	15.6b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.5b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	17.9b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 (.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) 2)))

Compiler

Compiled 15713 to 7339 computations (53.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 x y) 2)
	0.5b	(log1p.f64 (exp.f64 x))
✓	0.6b	(pow.f64 (log1p.f64 (exp.f64 x)) 2)
✓	11.0b	(/.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (pow.f64 (*.f64 x y) 2)))

series163.0ms (2.6%)

Counts

3 → 60

Calls

3 calls:

133.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 2)
22.0ms	(/.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (pow.f64 (*.f64 x y) 2)))
8.0ms	(pow.f64 (*.f64 x y) 2)

rewrite55.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

958×	`prod-diff_binary64`
123×	`add-sqr-sqrt_binary64`
123×	`expm1-log1p-u_binary64`
122×	`log1p-expm1-u_binary64`
118×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	257	43
2	3339	43

Stop Event

1×	node limit

Counts

3 → 77

Calls

3 calls:

53.0ms	(pow.f64 (*.f64 x y) 2)
53.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 2)
53.0ms	(/.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (pow.f64 (*.f64 x y) 2)))

simplify37.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

689×	`fma-def_binary64`
656×	`associate-/l*_binary64`
476×	`associate-/r*_binary64`
228×	`associate-l_binary64`
172×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	1519
1	339	1481
2	1371	1428

Stop Event

1×	node limit

Counts

137 → 110

prune136.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	161	5	166

Error

0.2b

Counts

166 → 5

Alt Table

Status	Error	Program
	16.8b	(.f64 (pow.f64 (pow.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)) 1/6) 2) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2))
	15.6b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.5b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	2.1b	(.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2))
▶	15.0b	(/.f64 1 (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (pow.f64 (*.f64 x y) 2))))))

Compiler

Compiled 4572 to 2388 computations (47.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (pow.f64 (*.f64 x y) 2)))))
	0.5b	(log1p.f64 (exp.f64 x))
	0.6b	(pow.f64 (log1p.f64 (exp.f64 x)) 2)
	11.0b	(/.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (pow.f64 (*.f64 x y) 2)))

series24.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

24.0ms

(expm1.f64 (log1p.f64 (/.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (pow.f64 (*.f64 x y) 2)))))

rewrite55.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

315×	`fma-def_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
217×	`log-pow_binary64`
180×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	278	28
2	3546	28

Stop Event

1×	node limit

Counts

1 → 51

Calls

1 calls:

53.0ms

(expm1.f64 (log1p.f64 (/.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (pow.f64 (*.f64 x y) 2)))))

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

621×	`associate-/l*_binary64`
476×	`associate-/r*_binary64`
473×	`fma-def_binary64`
233×	`associate-r_binary64`
202×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	1123
1	300	1097
2	1218	1053

Stop Event

1×	node limit

Counts

75 → 74

prune162.0ms (2.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	208	5	213

Error

0.2b

Counts

213 → 5

Alt Table

Status	Error	Program
	16.8b	(.f64 (pow.f64 (pow.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)) 1/6) 2) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2))
	15.6b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.5b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	2.1b	(.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))) 2))
✓	15.0b	(/.f64 1 (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (pow.f64 (*.f64 x y) 2))))))

Compiler

Compiled 6662 to 3742 computations (43.8% saved)

regimes130.0ms (2.1%)

Accuracy

Total 0.2b remaining (51.4%)

Threshold costs 0.2b (51.4%)

Counts

42 → 1

Compiler

Compiled 2332 to 1554 computations (33.4% 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	25	11
3	31	11
4	35	11
5	36	11

Stop Event

1×

saturated

end81.0ms (1.3%)

Compiler: Compiled 105 to 65 computations (38.1% saved)

Details

analyze407.0ms (6.4%)

sample4.0s (63.5%)

simplify37.0ms (0.6%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series204.0ms (3.2%)

rewrite54.0ms (0.9%)

simplify39.0ms (0.6%)

prune74.0ms (1.2%)

localize9.0ms (0.1%)

series140.0ms (2.2%)

rewrite67.0ms (1.1%)

simplify61.0ms (1%)

prune301.0ms (4.8%)

localize15.0ms (0.2%)

series163.0ms (2.6%)

rewrite55.0ms (0.9%)

simplify37.0ms (0.6%)

prune136.0ms (2.2%)

localize16.0ms (0.3%)

series24.0ms (0.4%)

rewrite55.0ms (0.9%)

simplify33.0ms (0.5%)

prune162.0ms (2.6%)

regimes130.0ms (2.1%)

simplify2.0ms (0%)

end81.0ms (1.3%)

Profiling