Details

analyze317.0ms (5.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
50%	50%	0.1%	5
62.4%	37.5%	0.1%	6
62.4%	37.5%	0.1%	7
68.7%	31.2%	0.1%	8
68.7%	31.2%	0.1%	9
71.8%	28.1%	0.1%	10
71.8%	28.1%	0.1%	11
73.4%	26.5%	0.1%	12
73.4%	26.5%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample3.0s (50%)

Infinites

1.1% of outputs are infinite.

Results

1.5s	3864×	body	8192	exit
640.0ms	6777×	body	128	valid
374.0ms	3933×	body	128	invalid
187.0ms	719×	body	512	valid
110.0ms	729×	body	256	valid
12.0ms	31×	body	1024	valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

568×	`neg-mul-1_binary64`
503×	`fma-def_binary64`
491×	`fma-neg_binary64`
484×	`div-sub_binary64`
416×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	22	23
2	58	23
3	152	21
4	338	18
5	1090	18
6	2902	18
7	3695	18
8	4706	18
9	4881	18

prune3.0ms (0.1%)

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

11.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.0b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
▶	11.0b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 94 to 48 computations (48.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (exp.f64 wj))
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	3.0b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series46.0ms (0.8%)

Counts

3 → 52

Calls

3 calls:

18.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
14.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
14.0ms	(/.f64 x (exp.f64 wj))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

3 → 100

Calls

3 calls:

14.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
10.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
3.0ms	(/.f64 x (exp.f64 wj))

simplify115.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-neg_binary64`
444×	`fma-def_binary64`
331×	`distribute-rgt-in_binary64`
292×	`associate--l+_binary64`
278×	`distribute-lft-in_binary64`

Counts

152 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3154
1	583	3016
2	1604	2995
3	4798	2993
4	5298	2993

prune102.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	152	4	156

Error

0.0b

Counts

156 → 4

Alt Table

Status	Error	Program
	11.0b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))
✓	11.0b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
▶	2.9b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
	37.8b	(cbrt.f64 (.f64 (.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

Compiler

Compiled 3312 to 1437 computations (56.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
✓	0.0b	(fma.f64 5/2 (.f64 wj wj) (.f64 wj -2))
✓	0.0b	(.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2)))

series33.0ms (0.6%)

Counts

3 → 60

Calls

3 calls:

16.0ms	(.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2)))
14.0ms	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
3.0ms	(fma.f64 5/2 (.f64 wj wj) (.f64 wj -2))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`fma-udef_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 51

Calls

3 calls:

3.0ms	(.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2)))
2.0ms	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
0.0ms	(fma.f64 5/2 (.f64 wj wj) (.f64 wj -2))

simplify92.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-neg_binary64`
474×	`fma-def_binary64`
393×	`associate-l_binary64`
371×	`distribute-rgt-in_binary64`
350×	`associate-r_binary64`

Counts

111 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	1943
1	246	1662
2	774	1456
3	3401	1456
4	4684	1456
5	4952	1456

prune99.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Error

0.0b

Counts

114 → 4

Alt Table

Status	Error	Program
▶	11.0b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))
✓	11.0b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	2.9b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
	37.8b	(cbrt.f64 (.f64 (.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

Compiler

Compiled 2330 to 1156 computations (50.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (exp.f64 wj))
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1))
✓	0.0b	(*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1))
✓	3.0b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))

series173.0ms (2.9%)

Counts

3 → 72

Calls

3 calls:

99.0ms

(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))

44.0ms

(*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1))

31.0ms

(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1))

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
54×	`add-cube-cbrt_binary64`
44×	`times-frac_binary64`
36×	`prod-diff_binary64`

Counts

3 → 163

Calls

3 calls:

13.0ms

(*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1))

10.0ms

(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1))

9.0ms

(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))

simplify138.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

590×	`associate-/l*_binary64`
274×	`cancel-sign-sub-inv_binary64`
250×	`sub-neg_binary64`
224×	`fma-neg_binary64`
148×	`fma-def_binary64`

Counts

235 → 288

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	7066
1	820	6306
2	2849	5658
3	5122	5658

prune238.0ms (4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	326	1	327
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	326	5	331

Error

0.0b

Counts

331 → 5

Alt Table

Status	Error	Program
	38.5b	(exp.f64 (log.f64 (+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))))
✓	11.0b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))
✓	11.0b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	2.9b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
▶	37.8b	(cbrt.f64 (.f64 (.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

Compiler

Compiled 9876 to 4740 computations (52% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
✓	0.1b	(.f64 (.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
	3.0b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	28.0b	(cbrt.f64 (.f64 (.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

series87.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

42.0ms

(*.f64 (*.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

25.0ms

(*.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

20.0ms

(cbrt.f64 (*.f64 (*.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

rewrite148.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`flip-+_binary64`
60×	`frac-times_binary64`
60×	`flip3-+_binary64`
30×	`associate-*l/_binary64`
29×	`pow1_binary64`

Counts

3 → 140

Calls

3 calls:

48.0ms

(*.f64 (*.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

42.0ms

(cbrt.f64 (*.f64 (*.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

27.0ms

(*.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

simplify238.0ms (4%)

Algorithm

1×	egg-herbie

Rules

362×	`associate-r_binary64`
360×	`associate-l_binary64`
333×	`fma-neg_binary64`
325×	`fma-def_binary64`
258×	`distribute-rgt-in_binary64`

Counts

212 → 244

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	374	15205
1	1151	12420
2	4663	12416
3	4967	12416

prune314.0ms (5.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	370	0	370
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	370	5	375

Error

0.0b

Counts

375 → 5

Alt Table

Status	Error	Program
	38.5b	(exp.f64 (log.f64 (+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))))
✓	11.0b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))
✓	11.0b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	2.9b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
✓	37.8b	(cbrt.f64 (.f64 (.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

Compiler

Compiled 21385 to 9236 computations (56.8% saved)

regimes476.0ms (8%)

Accuracy

Total 0.4b remaining (53.8%)

Threshold costs 0.4b (53.8%)

Counts

99 → 3

Compiler

Compiled 5235 to 3366 computations (35.7% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 18 to 8 computations (55.6% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

26×	`+-commutative_binary64`
23×	`sub-neg_binary64`
23×	`neg-sub0_binary64`
23×	`neg-mul-1_binary64`
20×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	121
1	58	121
2	71	121
3	82	121
4	103	121
5	117	121
6	138	121
7	164	121
8	190	121
9	210	121
10	220	121
11	224	121
12	225	121
13	221	121

end109.0ms (1.8%)

Compiler: Compiled 276 to 139 computations (49.6% saved)

Iter	Nodes	Cost
0	38	121
1	58	121
2	71	121
3	82	121
4	103	121
5	117	121
6	138	121
7	164	121
8	190	121
9	210	121
10	220	121
11	224	121
12	225	121
13	221	121

Iter	Nodes	Cost
0	38	121
1	58	121
2	71	121
3	82	121
4	103	121
5	117	121
6	138	121
7	164	121
8	190	121
9	210	121
10	220	121
11	224	121
12	225	121
13	221	121

Details

analyze317.0ms (5.4%)

sample3.0s (50%)

simplify78.0ms (1.3%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series46.0ms (0.8%)

rewrite34.0ms (0.6%)

simplify115.0ms (1.9%)

prune102.0ms (1.7%)

localize9.0ms (0.1%)

series33.0ms (0.6%)

rewrite7.0ms (0.1%)

simplify92.0ms (1.6%)

prune99.0ms (1.7%)

localize10.0ms (0.2%)

series173.0ms (2.9%)

rewrite52.0ms (0.9%)

simplify138.0ms (2.3%)

prune238.0ms (4%)

localize14.0ms (0.2%)

series87.0ms (1.5%)

rewrite148.0ms (2.5%)

simplify238.0ms (4%)

prune314.0ms (5.3%)

regimes476.0ms (8%)

bsearch3.0ms (0.1%)

simplify12.0ms (0.2%)

end109.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	38	121
1	58	121
2	71	121
3	82	121
4	103	121
5	117	121
6	138	121
7	164	121
8	190	121
9	210	121
10	220	121
11	224	121
12	225	121
13	221	121