Details

analyze515.0ms (18.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample34.0ms (1.2%)

Algorithm

1×

intervals

Results

15.0ms	95×	body	1024	valid
4.0ms	95×	body	128	valid
4.0ms	40×	body	512	valid
2.0ms	11×	body	2048	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	11	11
2	12	11
3	10	11

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

41.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	41.8b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Compiler

Compiled 16 to 10 computations (37.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.6b	(-.f64 (exp.f64 x) 1)

rewrite99.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

41.7b

Rules

35×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

2 → 63

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 822 to 421 computations (48.8% saved)

series22.0ms (0.8%)

Error

0.2b

Counts

2 → 12

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 248 to 175 computations (29.4% saved)

simplify158.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

459×	`div-sub_binary64`
349×	`associate-/l*_binary64`
317×	`associate-r_binary64`
264×	`unsub-neg_binary64`
262×	`associate-/l/_binary64`

Counts

75 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	1272
1	205	1207
2	542	1199
3	1375	1198
4	3524	1198
5	4891	1198
6	4994	1198
7	4987	1198
8	4887	1198

prune19.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	4	45

Error

0.0b

Counts

45 → 4

Alt Table

Status	Error	Program
✓	41.8b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
	20.3b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))
	41.5b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
▶	15.0b	(/.f64 (exp.f64 x) (+.f64 x (+.f64 (.f64 1/24 (pow.f64 x 4)) (.f64 x (.f64 x (+.f64 1/2 (.f64 x 1/6)))))))

Compiler

Compiled 441 to 256 computations (42% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.1b	(*.f64 1/24 (pow.f64 x 4))
0.3b	(*.f64 x 1/6)
11.0b	(+.f64 (.f64 1/24 (pow.f64 x 4)) (.f64 x (.f64 x (+.f64 1/2 (.f64 x 1/6)))))

rewrite84.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

20×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
13×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 80

Calls

4 calls:

6.0ms	(*.f64 1/24 (pow.f64 x 4))
5.0ms	(+.f64 (.f64 1/24 (pow.f64 x 4)) (.f64 x (.f64 x (+.f64 1/2 (.f64 x 1/6)))))
4.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
3.0ms	(*.f64 x 1/6)

Compiler

Compiled 2068 to 1421 computations (31.3% saved)

series60.0ms (2.1%)

Error

0.0b

Counts

4 → 17

Calls

4 calls:

31.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
9.0ms	(+.f64 (.f64 1/24 (pow.f64 x 4)) (.f64 x (.f64 x (+.f64 1/2 (.f64 x 1/6)))))
6.0ms	(*.f64 1/24 (pow.f64 x 4))
5.0ms	(*.f64 x 1/6)

Compiler

Compiled 730 to 525 computations (28.1% saved)

simplify120.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

602×	`distribute-rgt-in_binary64`
586×	`distribute-lft-in_binary64`
351×	`*-commutative_binary64`
323×	`cancel-sign-sub-inv_binary64`
306×	`neg-mul-1_binary64`

Counts

97 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	1307
1	347	1208
2	1097	1190
3	3396	1190
4	4834	1190
5	4813	1190
6	5067	1190

prune33.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	55	4	59

Error

0.0b

Counts

59 → 4

Alt Table

Status	Error	Program
✓	41.8b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
▶	20.3b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))
	41.5b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
✓	15.0b	(/.f64 (exp.f64 x) (+.f64 x (+.f64 (.f64 1/24 (pow.f64 x 4)) (.f64 x (.f64 x (+.f64 1/2 (.f64 x 1/6)))))))

Compiler

Compiled 1018 to 666 computations (34.6% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 x) (*.f64 x 1/12))
0.0b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))
0.1b	(*.f64 (pow.f64 x 3) 1/720)
0.3b	(*.f64 x 1/12)

rewrite80.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
15×	`add-log-exp_binary64`
11×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64`

Counts

4 → 75

Calls

4 calls:

9.0ms	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))
5.0ms	(+.f64 (/.f64 1 x) (*.f64 x 1/12))
4.0ms	(*.f64 (pow.f64 x 3) 1/720)
3.0ms	(*.f64 x 1/12)

Compiler

Compiled 1533 to 1234 computations (19.5% saved)

series39.0ms (1.4%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

11.0ms	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))
9.0ms	(*.f64 (pow.f64 x 3) 1/720)
8.0ms	(+.f64 (/.f64 1 x) (*.f64 x 1/12))
5.0ms	(*.f64 x 1/12)

Compiler

Compiled 558 to 453 computations (18.8% saved)

simplify100.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

344×	`distribute-rgt-in_binary64`
342×	`times-frac_binary64`
334×	`distribute-lft-in_binary64`
198×	`exp-prod_binary64`
180×	`associate-+l+_binary64`

Counts

99 → 72

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	1360
1	318	1282
2	1267	1267
3	4316	1243
4	4865	1243
5	4861	1243

prune37.0ms (1.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	71	5	76

Error

0.0b

Counts

76 → 5

Alt Table

Status	Error	Program
✓	41.8b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
✓	20.3b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))
▶	41.5b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
✓	15.0b	(/.f64 (exp.f64 x) (+.f64 x (+.f64 (.f64 1/24 (pow.f64 x 4)) (.f64 x (.f64 x (+.f64 1/2 (.f64 x 1/6)))))))
	44.8b	(exp.f64 (log.f64 (-.f64 (+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) 1/2)) (.f64 1/720 (pow.f64 x 3)))))

Compiler

Compiled 1070 to 855 computations (20.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
2.6b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite37.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

2 → 62

Calls

2 calls:

5.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
3.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 872 to 542 computations (37.8% saved)

series19.0ms (0.7%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

7.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
5.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 249 to 206 computations (17.3% saved)

simplify111.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

441×	`times-frac_binary64`
423×	`unsub-neg_binary64`
360×	`div-sub_binary64`
354×	`cancel-sign-sub-inv_binary64`
251×	`associate-/l*_binary64`

Counts

74 → 50

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	94	1151
1	199	1072
2	433	1062
3	1291	1059
4	3574	1041
5	4953	1041
6	4877	1041

prune17.0ms (0.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	50	5	55

Error

0.0b

Counts

55 → 5

Alt Table

Status	Error	Program
	41.5b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
	15.0b	(/.f64 (exp.f64 x) (+.f64 x (+.f64 (.f64 1/24 (pow.f64 x 4)) (.f64 x (.f64 x (+.f64 1/2 (.f64 x 1/6)))))))
	44.8b	(exp.f64 (log.f64 (-.f64 (+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) 1/2)) (.f64 1/720 (pow.f64 x 3)))))
	20.3b	(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))) (.f64 (pow.f64 x 3) 1/720))
	60.9b	(/.f64 1 (/.f64 (-.f64 1 (pow.f64 (exp.f64 x) -2)) (+.f64 1 (exp.f64 (neg.f64 x)))))

Compiler

Compiled 413 to 289 computations (30% saved)

regimes153.0ms (5.4%)

Accuracy

Total 1.1b remaining (99.3%)

Threshold costs 0b (0%)

Compiler

Compiled 3036 to 2114 computations (30.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	15	21
2	15	21

end1.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

sample1.0s (36.6%)

Algorithm

1×

intervals

Results

421.0ms	2595×	body	1024	valid
122.0ms	1341×	body	512	valid
97.0ms	3101×	body	128	valid
60.0ms	308×	body	2048	valid
44.0ms	655×	body	256	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 103 to 80 computations (22.3% saved)

Details

analyze515.0ms (18.3%)

sample34.0ms (1.2%)

simplify11.0ms (0.4%)

prune1.0ms (0%)

localize4.0ms (0.1%)

rewrite99.0ms (3.5%)

series22.0ms (0.8%)

simplify158.0ms (5.6%)

prune19.0ms (0.7%)

localize12.0ms (0.4%)

rewrite84.0ms (3%)

series60.0ms (2.1%)

simplify120.0ms (4.3%)

prune33.0ms (1.2%)

localize11.0ms (0.4%)

rewrite80.0ms (2.8%)

series39.0ms (1.4%)

simplify100.0ms (3.6%)

prune37.0ms (1.3%)

localize5.0ms (0.2%)

rewrite37.0ms (1.3%)

series19.0ms (0.7%)

simplify111.0ms (3.9%)

prune17.0ms (0.6%)

regimes153.0ms (5.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.0s (36.6%)

Profiling