Details

analyze172.0ms (5.1%)

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
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	240×	body	128	valid
3.0ms	6×	body	1024	valid
1.0ms	6×	body	512	valid
1.0ms	4×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 25 to 19 computations (24% saved)

simplify104.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

892×	`prod-exp_binary64`
741×	`fabs-mul_binary64`
531×	`fabs-div_binary64`
469×	`swap-sqr_binary64`
379×	`times-frac_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	18	14
2	27	14
3	39	14
4	50	14
5	70	14
6	92	14
7	112	14
8	146	14
9	150	14
10	158	14
11	178	14
12	253	14
13	461	14
14	873	14
15	2790	14
16	3179	14
17	3256	14
18	3475	14
19	3469	14
20	5201	14

prune2.0ms (0.1%)

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

1.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	1.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))

Compiler

Compiled 22 to 16 computations (27.3% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
0.0b	(+.f64 1 (exp.f64 x))
1.2b	(log.f64 (+.f64 1 (exp.f64 x)))

rewrite72.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

11×	`*-un-lft-identity_binary64`
8×	`log-prod_binary64`
6×	`add-log-exp_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`pow1_binary64` `log-div_binary64` `add-exp-log_binary64` `associate--l+_binary64`

Counts

3 → 45

Calls

3 calls:

6.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
4.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
3.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 708 to 393 computations (44.5% saved)

series258.0ms (7.6%)

Error

0.9b

Counts

3 → 26

Calls

3 calls:

226.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
13.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
6.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 550 to 400 computations (27.3% saved)

simplify165.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

657×	`cancel-sign-sub-inv_binary64`
350×	`sub-neg_binary64`
330×	`unsub-neg_binary64`
302×	`unswap-sqr_binary64`
266×	`distribute-rgt-in_binary64` `*-commutative_binary64`

Counts

71 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	1019
1	241	970
2	562	948
3	1448	942
4	3189	942
5	4558	942
6	4964	942
7	4998	942
8	4999	942
9	4872	942

prune63.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	44	5	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	5	50

Error

0.8b

Counts

50 → 5

Alt Table

Status	Error	Program
	12.5b	(+.f64 (log.f64 2) (*.f64 x (-.f64 1/2 y)))
▶	1.3b	(-.f64 (-.f64 (log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))) (*.f64 x y))
	12.8b	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 1/2 (.f64 x x))))) (*.f64 x y))
	15.1b	(/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 x) 1)) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log.f64 (+.f64 (exp.f64 x) 1)) (+.f64 (log.f64 (+.f64 (exp.f64 x) 1)) (.f64 x y)))))
	1.8b	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)))) (*.f64 x y))

Compiler

Compiled 892 to 538 computations (39.7% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 3)
1.0b	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
3.8b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
4.2b	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))

rewrite143.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

21×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`log-prod_binary64`
7×	`pow1_binary64`

Counts

4 → 77

Calls

4 calls:

9.0ms	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))
7.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
6.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
3.0ms	(pow.f64 (exp.f64 x) 3)

Compiler

Compiled 2018 to 1236 computations (38.8% saved)

series100.0ms (3%)

Error

0.8b

Counts

4 → 24

Calls

4 calls:

24.0ms	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))
21.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
12.0ms	(pow.f64 (exp.f64 x) 3)
11.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))

Compiler

Compiled 1256 to 895 computations (28.7% saved)

simplify134.0ms (4%)

Algorithm

1×	egg-herbie

Rules

493×	`exp-prod_binary64`
466×	`log-prod_binary64`
346×	`difference-of-squares_binary64`
292×	`cancel-sign-sub-inv_binary64`
256×	`cube-prod_binary64`

Counts

101 → 65

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	185	1539
1	376	1412
2	1004	1377
3	2717	1377
4	3688	1371
5	4550	1371
6	4913	1371

prune83.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	65	5	70

Error

0.8b

Counts

70 → 5

Alt Table

Status	Error	Program
	12.5b	(+.f64 (log.f64 2) (*.f64 x (-.f64 1/2 y)))
✓	1.3b	(-.f64 (-.f64 (log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))) (*.f64 x y))
	12.8b	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 1/2 (.f64 x x))))) (*.f64 x y))
	15.1b	(/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 x) 1)) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log.f64 (+.f64 (exp.f64 x) 1)) (+.f64 (log.f64 (+.f64 (exp.f64 x) 1)) (.f64 x y)))))
▶	1.8b	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)))) (*.f64 x y))

Compiler

Compiled 1482 to 925 computations (37.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(+.f64 (exp.f64 x) 1)
1.9b	(log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)))
1.9b	(log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)))

rewrite84.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

16×	`*-un-lft-identity_binary64`
14×	`log-prod_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64` `add-log-exp_binary64`
6×	`log-pow_binary64` `add-exp-log_binary64`
4×	`flip3-+_binary64` `sqrt-div_binary64` `log-div_binary64` `flip-+_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64`

Counts

4 → 64

Calls

4 calls:

5.0ms	(log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)))
5.0ms	(log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)))
4.0ms	(+.f64 (exp.f64 x) 1)
4.0ms	(+.f64 (exp.f64 x) 1)

Compiler

Compiled 1345 to 854 computations (36.5% saved)

series84.0ms (2.5%)

Error

0.8b

Counts

4 → 24

Calls

4 calls:

24.0ms	(log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)))
22.0ms	(log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)))
10.0ms	(+.f64 (exp.f64 x) 1)
8.0ms	(+.f64 (exp.f64 x) 1)

Compiler

Compiled 1287 to 1020 computations (20.7% saved)

simplify134.0ms (4%)

Algorithm

1×	egg-herbie

Rules

873×	`associate-/l*_binary64`
526×	`cancel-sign-sub-inv_binary64`
422×	`associate-/l/_binary64`
167×	`associate-/r/_binary64`
157×	`associate-+l+_binary64`

Counts

88 → 38

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1438
1	216	1262
2	514	1156
3	1730	1138
4	4557	1138
5	4947	1138
6	4982	1138
7	4912	1138

prune46.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	39	4	43

Error

0.8b

Counts

43 → 4

Alt Table

Status	Error	Program
▶	12.5b	(+.f64 (log.f64 2) (*.f64 x (-.f64 1/2 y)))
✓	1.3b	(-.f64 (-.f64 (log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))) (*.f64 x y))
	15.1b	(/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 x) 1)) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log.f64 (+.f64 (exp.f64 x) 1)) (+.f64 (log.f64 (+.f64 (exp.f64 x) 1)) (.f64 x y)))))
	13.6b	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (log.f64 (sqrt.f64 (+.f64 x (+.f64 2 (.f64 1/2 (.f64 x x))))))) (*.f64 x y))

Compiler

Compiled 957 to 626 computations (34.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 x (-.f64 1/2 y))
0.0b	(+.f64 (log.f64 2) (*.f64 x (-.f64 1/2 y)))

rewrite81.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

13×	`add-sqr-sqrt_binary64`
12×	`cancel-sign-sub-inv_binary64`
11×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`distribute-rgt-in_binary64` `associate-+r+_binary64` `distribute-lft-in_binary64`

Counts

2 → 52

Calls

2 calls:

7.0ms	(*.f64 x (-.f64 1/2 y))
5.0ms	(+.f64 (log.f64 2) (*.f64 x (-.f64 1/2 y)))

Compiler

Compiled 751 to 527 computations (29.8% saved)

series61.0ms (1.8%)

Error

0.8b

Counts

2 → 21

Calls

2 calls:

34.0ms	(+.f64 (log.f64 2) (*.f64 x (-.f64 1/2 y)))
18.0ms	(*.f64 x (-.f64 1/2 y))

Compiler

Compiled 425 to 320 computations (24.7% saved)

simplify89.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

516×	`neg-mul-1_binary64`
425×	`associate-+l+_binary64`
411×	`associate-l_binary64`
363×	`associate-r_binary64`
306×	`cancel-sign-sub-inv_binary64`

Counts

73 → 48

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	106	825
1	249	779
2	646	779
3	2302	779
4	4629	779
5	5345	779

prune37.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	46	6	52

Error

0.8b

Counts

52 → 6

Alt Table

Status	Error	Program
	7.0b	(+.f64 (log.f64 2) (neg.f64 (*.f64 x y)))
	1.3b	(-.f64 (-.f64 (log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))) (*.f64 x y))
	15.1b	(/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 x) 1)) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log.f64 (+.f64 (exp.f64 x) 1)) (+.f64 (log.f64 (+.f64 (exp.f64 x) 1)) (.f64 x y)))))
	13.6b	(-.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (log.f64 (sqrt.f64 (+.f64 x (+.f64 2 (.f64 1/2 (.f64 x x))))))) (*.f64 x y))
	12.9b	(+.f64 (log.f64 2) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 1/2 y) (cbrt.f64 x))))
	21.7b	(cbrt.f64 (pow.f64 (+.f64 (log.f64 2) (*.f64 x (-.f64 1/2 y))) 3))

Compiler

Compiled 447 to 321 computations (28.2% saved)

regimes470.0ms (13.9%)

Accuracy

Total 0.3b remaining (52.6%)

Threshold costs 0.3b (52.6%)

Compiler

Compiled 5914 to 4441 computations (24.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	31	35
2	46	35
3	56	35
4	62	35
5	63	35
6	62	35

end1.0ms (0%)

Compiler: Compiled 24 to 17 computations (29.2% saved)

sample928.0ms (27.4%)

Algorithm

1×

intervals

Results

361.0ms	7396×	body	128	valid
88.0ms	223×	body	1024	valid
54.0ms	243×	body	512	valid
17.0ms	138×	body	256	valid
2.0ms	36×	body	128	invalid
0.0ms	7×	body	128	overflowed

Compiler

Compiled 164 to 115 computations (29.9% saved)

Details

analyze172.0ms (5.1%)

sample24.0ms (0.7%)

simplify104.0ms (3.1%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

rewrite72.0ms (2.1%)

series258.0ms (7.6%)

simplify165.0ms (4.9%)

prune63.0ms (1.9%)

localize15.0ms (0.4%)

rewrite143.0ms (4.2%)

series100.0ms (3%)

simplify134.0ms (4%)

prune83.0ms (2.4%)

localize9.0ms (0.3%)

rewrite84.0ms (2.5%)

series84.0ms (2.5%)

simplify134.0ms (4%)

prune46.0ms (1.3%)

localize6.0ms (0.2%)

rewrite81.0ms (2.4%)

series61.0ms (1.8%)

simplify89.0ms (2.6%)

prune37.0ms (1.1%)

regimes470.0ms (13.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample928.0ms (27.4%)

Profiling