Details

analyze463.0ms (7.8%)

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
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample144.0ms (2.4%)

Algorithm

1×

intervals

Results

27.0ms	103×	body	8192	exit
13.0ms	214×	body	128	valid
5.0ms	20×	body	256	valid
3.0ms	22×	body	512	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 39 to 19 computations (51.3% saved)

simplify80.0ms (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

14.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.2b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	14.7b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 94 to 48 computations (48.9% saved)

localize10.0ms (0.2%)

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))
✓	6.1b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series85.0ms (1.4%)

Counts

3 → 52

Calls

3 calls:

50.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
19.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
16.0ms	(/.f64 x (exp.f64 wj))

rewrite39.0ms (0.7%)

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:

15.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
13.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
3.0ms	(/.f64 x (exp.f64 wj))

simplify116.0ms (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

prune148.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	152	4	156

Error

0.0b

Counts

156 → 4

Alt Table

Status	Error	Program
	14.5b	(fma.f64 (*.f64 (cbrt.f64 wj) (cbrt.f64 wj)) (cbrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
▶	2.3b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
	14.2b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))
	14.2b	(+.f64 wj (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (pow.f64 wj 3) 1)) (+.f64 (.f64 wj wj) (-.f64 (.f64 1 1) (.f64 wj 1)))))

Compiler

Compiled 3332 to 1464 computations (56.1% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
✓	0.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
✓	0.1b	(*.f64 8/3 (pow.f64 wj 3))
✓	7.9b	(.f64 x (.f64 wj wj))

series65.0ms (1.1%)

Counts

4 → 72

Calls

4 calls:

32.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
21.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
8.0ms	(.f64 x (.f64 wj wj))
3.0ms	(*.f64 8/3 (pow.f64 wj 3))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-r_binary64`

Counts

4 → 96

Calls

4 calls:

6.0ms	(.f64 x (.f64 wj wj))
5.0ms	(*.f64 8/3 (pow.f64 wj 3))
3.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
0.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))

simplify123.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-def_binary64`
521×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
479×	`fma-neg_binary64`
401×	`cancel-sign-sub-inv_binary64`

Counts

168 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3853
1	409	3376
2	1438	3085
3	4985	3004
4	5189	3004

prune240.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	172	5	177

Error

0.0b

Counts

177 → 5

Alt Table

Status	Error	Program
✓	2.3b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
	53.9b	(fma.f64 wj wj (.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))))
	14.5b	(fma.f64 (*.f64 (cbrt.f64 wj) (cbrt.f64 wj)) (cbrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
▶	14.2b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))
	14.2b	(+.f64 wj (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (pow.f64 wj 3) 1)) (+.f64 (.f64 wj wj) (-.f64 (.f64 1 1) (.f64 wj 1)))))

Compiler

Compiled 6338 to 3476 computations (45.2% saved)

localize13.0ms (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))
✓	6.1b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))

series225.0ms (3.8%)

Counts

3 → 72

Calls

3 calls:

112.0ms

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

69.0ms

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

44.0ms

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

rewrite55.0ms (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:

18.0ms

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

12.0ms

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

6.0ms

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

simplify158.0ms (2.6%)

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

prune332.0ms (5.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	326	1	327
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	328	4	332

Error

0.0b

Counts

332 → 4

Alt Table

Status	Error	Program
✓	2.3b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
	53.9b	(fma.f64 wj wj (.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))))
	14.5b	(fma.f64 (*.f64 (cbrt.f64 wj) (cbrt.f64 wj)) (cbrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
▶	14.2b	(+.f64 wj (/.f64 (.f64 (fma.f64 wj wj -1) (-.f64 (/.f64 x (exp.f64 wj)) wj)) (.f64 (fma.f64 wj wj -1) (+.f64 wj 1))))

Compiler

Compiled 9855 to 4734 computations (52% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 wj wj -1) (-.f64 (/.f64 x (exp.f64 wj)) wj))
✓	0.0b	(*.f64 (fma.f64 wj wj -1) (+.f64 wj 1))
✓	0.0b	(/.f64 (.f64 (fma.f64 wj wj -1) (-.f64 (/.f64 x (exp.f64 wj)) wj)) (.f64 (fma.f64 wj wj -1) (+.f64 wj 1)))
✓	6.1b	(+.f64 wj (/.f64 (.f64 (fma.f64 wj wj -1) (-.f64 (/.f64 x (exp.f64 wj)) wj)) (.f64 (fma.f64 wj wj -1) (+.f64 wj 1))))

series56.0ms (0.9%)

Counts

4 → 84

Calls

4 calls:

19.0ms	(+.f64 wj (/.f64 (.f64 (fma.f64 wj wj -1) (-.f64 (/.f64 x (exp.f64 wj)) wj)) (.f64 (fma.f64 wj wj -1) (+.f64 wj 1))))
17.0ms	(*.f64 (fma.f64 wj wj -1) (-.f64 (/.f64 x (exp.f64 wj)) wj))
17.0ms	(/.f64 (.f64 (fma.f64 wj wj -1) (-.f64 (/.f64 x (exp.f64 wj)) wj)) (.f64 (fma.f64 wj wj -1) (+.f64 wj 1)))
3.0ms	(*.f64 (fma.f64 wj wj -1) (+.f64 wj 1))

rewrite62.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
78×	`prod-diff_binary64`
56×	`times-frac_binary64`

Counts

4 → 180

Calls

4 calls:

16.0ms	(/.f64 (.f64 (fma.f64 wj wj -1) (-.f64 (/.f64 x (exp.f64 wj)) wj)) (.f64 (fma.f64 wj wj -1) (+.f64 wj 1)))
11.0ms	(*.f64 (fma.f64 wj wj -1) (-.f64 (/.f64 x (exp.f64 wj)) wj))
6.0ms	(*.f64 (fma.f64 wj wj -1) (+.f64 wj 1))
6.0ms	(+.f64 wj (/.f64 (.f64 (fma.f64 wj wj -1) (-.f64 (/.f64 x (exp.f64 wj)) wj)) (.f64 (fma.f64 wj wj -1) (+.f64 wj 1))))

simplify189.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-neg_binary64`
330×	`associate-l_binary64`
290×	`associate-r_binary64`
232×	`*-commutative_binary64`
202×	`times-frac_binary64`

Counts

264 → 299

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	400	6738
1	841	6205
2	3855	6074
3	4972	6063
4	4977	6063

prune228.0ms (3.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	299	0	299
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	299	4	303

Error

0.0b

Counts

303 → 4

Alt Table

Status	Error	Program
✓	2.3b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
	53.9b	(fma.f64 wj wj (.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))))
	14.5b	(fma.f64 (*.f64 (cbrt.f64 wj) (cbrt.f64 wj)) (cbrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	14.2b	(+.f64 wj (/.f64 (.f64 (fma.f64 wj wj -1) (-.f64 (/.f64 x (exp.f64 wj)) wj)) (.f64 (fma.f64 wj wj -1) (+.f64 wj 1))))

Compiler

Compiled 10252 to 4422 computations (56.9% saved)

regimes972.0ms (16.3%)

Accuracy

Total 0.1b remaining (44.6%)

Threshold costs 0.1b (44.6%)

Counts

193 → 3

Compiler

Compiled 11127 to 7248 computations (34.9% saved)

bsearch42.0ms (0.7%)

Steps

Iters	Range		Point
7	4.8517694905582416e-12	1.0009000468275882e-9	9.727382200534923e-10
8	-0.04487936118332952	-1.6688445438210008e-6	-4.62645130249213e-6

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`*-commutative_binary64`
6×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	99
1	55	99
2	65	99
3	71	99
4	74	99
5	73	99

end1.0ms (0%)

Compiler: Compiled 70 to 44 computations (37.1% saved)

sample2.1s (34.6%)

Algorithm

1×

intervals

Results

1.0s	3835×	body	8192	exit
319.0ms	6553×	body	128	valid
106.0ms	710×	body	512	valid
68.0ms	711×	body	256	valid
6.0ms	26×	body	1024	valid
5.0ms	72×	body	128	invalid
0.0ms	9×	body	128	overflowed

Compiler

Compiled 181 to 110 computations (39.2% saved)

Details

analyze463.0ms (7.8%)

sample144.0ms (2.4%)

simplify80.0ms (1.3%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series85.0ms (1.4%)

rewrite39.0ms (0.7%)

simplify116.0ms (1.9%)

prune148.0ms (2.5%)

localize16.0ms (0.3%)

series65.0ms (1.1%)

rewrite22.0ms (0.4%)

simplify123.0ms (2.1%)

prune240.0ms (4%)

localize13.0ms (0.2%)

series225.0ms (3.8%)

rewrite55.0ms (0.9%)

simplify158.0ms (2.6%)

prune332.0ms (5.6%)

localize12.0ms (0.2%)

series56.0ms (0.9%)

rewrite62.0ms (1%)

simplify189.0ms (3.2%)

prune228.0ms (3.8%)

regimes972.0ms (16.3%)

bsearch42.0ms (0.7%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample2.1s (34.6%)

Profiling