Details

analyze511.0ms (9.1%)

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)

sample61.0ms (1.1%)

Algorithm

1×

intervals

Results

30.0ms	117×	body	8192	exit
10.0ms	206×	body	128	valid
4.0ms	29×	body	512	valid
2.0ms	21×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 39 to 19 computations (51.3% saved)

simplify88.0ms (1.6%)

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

prune4.0ms (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

14.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.4b	(+.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)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	0.3b	(/.f64 x (exp.f64 wj))
✓	4.5b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite37.0ms (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:

13.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
11.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
3.0ms	(/.f64 x (exp.f64 wj))

series89.0ms (1.6%)

Counts

3 → 52

Calls

3 calls:

32.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
28.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
28.0ms	(/.f64 x (exp.f64 wj))

simplify124.0ms (2.2%)

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 → 233

Iterations

Useful iterations: 3 (0.0ms)

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

prune116.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	229	4	233
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	230	5	235

Error

0.0b

Counts

235 → 5

Alt Table

Status	Error	Program
	44.8b	(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
	7.2b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
▶	1.5b	(-.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)))
✓	14.4b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	14.4b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))

Compiler

Compiled 3293 to 1447 computations (56.1% saved)

localize14.0ms (0.2%)

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)))
✓	0.2b	(*.f64 8/3 (pow.f64 wj 3))
✓	5.5b	(.f64 x (.f64 wj wj))

rewrite19.0ms (0.3%)

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:

5.0ms	(*.f64 8/3 (pow.f64 wj 3))
4.0ms	(.f64 x (.f64 wj wj))
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))

series147.0ms (2.6%)

Counts

4 → 72

Calls

4 calls:

54.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
53.0ms	(-.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)))
25.0ms	(.f64 x (.f64 wj wj))
14.0ms	(*.f64 8/3 (pow.f64 wj 3))

simplify149.0ms (2.7%)

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 → 323

Iterations

Useful iterations: 3 (0.0ms)

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

prune224.0ms (4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	323	5	328

Error

0.0b

Counts

328 → 5

Alt Table

Status	Error	Program
	44.8b	(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
▶	7.2b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
✓	1.5b	(-.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)))
✓	14.4b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	14.4b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))

Compiler

Compiled 6330 to 3457 computations (45.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj))
✓	0.0b	(*.f64 (exp.f64 wj) wj)
✓	0.3b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 65

Calls

3 calls:

5.0ms	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
4.0ms	(+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj))
4.0ms	(*.f64 (exp.f64 wj) wj)

series57.0ms (1%)

Counts

3 → 22

Calls

3 calls:

46.0ms	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
7.0ms	(*.f64 (exp.f64 wj) wj)
4.0ms	(+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj))

simplify99.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

785×	`times-frac_binary64`
488×	`fma-neg_binary64`
456×	`cancel-sign-sub-inv_binary64`
412×	`fma-def_binary64`
308×	`associate-l_binary64`

Counts

87 → 158

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1458
1	337	1367
2	954	1338
3	3010	1323
4	4869	1323
5	4897	1323

prune109.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	158	5	163

Error

0.0b

Counts

163 → 5

Alt Table

Status	Error	Program
	44.8b	(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
✓	7.2b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
✓	1.5b	(-.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)))
✓	14.4b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
▶	14.4b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))

Compiler

Compiled 2380 to 705 computations (70.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))
	0.3b	(/.f64 x (exp.f64 wj))
✓	4.5b	(+.f64 wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (fma.f64 wj wj -1)) (-.f64 wj 1)))

rewrite57.0ms (1%)

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:

20.0ms

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

9.0ms

(/.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)))

series192.0ms (3.4%)

Counts

3 → 72

Calls

3 calls:

103.0ms

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

50.0ms

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

38.0ms

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

simplify177.0ms (3.2%)

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 → 423

Iterations

Useful iterations: 2 (0.0ms)

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

prune283.0ms (5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	466	1	467
Fresh	1	0	1
Picked	1	0	1
Done	0	3	3
Total	468	4	472

Error

0.0b

Counts

472 → 4

Alt Table

Status	Error	Program
	55.5b	(-.f64 (+.f64 wj (/.f64 wj (fma.f64 wj wj -1))) (*.f64 (/.f64 wj (fma.f64 wj wj -1)) wj))
✓	14.4b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	7.2b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
✓	1.5b	(-.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)))

Compiler

Compiled 9756 to 4679 computations (52% saved)

regimes630.0ms (11.2%)

Accuracy

Total 1.2b remaining (93.8%)

Threshold costs 0b (0%)

Compiler

Compiled 9414 to 5979 computations (36.5% saved)

bsearch10.0ms (0.2%)

Steps

Iters	Range		Point
1	-7.900006550436292e+43	-4.7780973850309204e+39	-6.143922385183966e+41

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	55
1	37	55
2	44	55
3	48	55
4	50	55
5	49	55

end1.0ms (0%)

Compiler: Compiled 40 to 26 computations (35% saved)

sample2.4s (42.2%)

Algorithm

1×

intervals

Results

1.3s	3933×	body	8192	exit
332.0ms	6572×	body	128	valid
105.0ms	689×	body	512	valid
69.0ms	710×	body	256	valid
6.0ms	29×	body	1024	valid
4.0ms	79×	body	128	invalid
1.0ms	19×	body	128	overflowed

Compiler

Compiled 132 to 80 computations (39.4% saved)

Details

analyze511.0ms (9.1%)

sample61.0ms (1.1%)

simplify88.0ms (1.6%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

rewrite37.0ms (0.7%)

series89.0ms (1.6%)

simplify124.0ms (2.2%)

prune116.0ms (2.1%)

localize14.0ms (0.2%)

rewrite19.0ms (0.3%)

series147.0ms (2.6%)

simplify149.0ms (2.7%)

prune224.0ms (4%)

localize8.0ms (0.1%)

rewrite16.0ms (0.3%)

series57.0ms (1%)

simplify99.0ms (1.8%)

prune109.0ms (1.9%)

localize11.0ms (0.2%)

rewrite57.0ms (1%)

series192.0ms (3.4%)

simplify177.0ms (3.2%)

prune283.0ms (5%)

regimes630.0ms (11.2%)

bsearch10.0ms (0.2%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.4s (42.2%)

Profiling