Details

analyze100.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample97.0ms (1.9%)

Algorithm

1×

intervals

Results

72.0ms	147×	body	2048	valid
13.0ms	63×	body	1024	valid
3.0ms	23×	body	512	valid
1.0ms	11×	body	256	valid
0.0ms	12×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

801×	`associate-/l*_binary64`
548×	`unswap-sqr_binary64`
536×	`div-sub_binary64`
451×	`associate-/r*_binary64`
284×	`cancel-sign-sub-inv_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	35	13
3	57	13
4	102	13
5	198	13
6	389	13
7	738	13
8	1255	13
9	3975	13
10	4882	13
11	4992	13
12	4809	13

prune2.0ms (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

25.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	25.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
4.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite74.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

25.3b

Rules

11×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64`
6×	`add-sqr-sqrt_binary64` `cancel-sign-sub-inv_binary64`
4×	`add-cube-cbrt_binary64` `frac-add_binary64` `associate-+l+_binary64`
3×	`flip3--_binary64` `flip--_binary64`

Counts

2 → 39

Calls

2 calls:

8.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
8.0ms	(-.f64 (exp.f64 x) 2)

Compiler

Compiled 634 to 334 computations (47.3% saved)

series29.0ms (0.6%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

9.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
6.0ms	(-.f64 (exp.f64 x) 2)

Compiler

Compiled 292 to 218 computations (25.3% saved)

simplify94.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

904×	`times-frac_binary64`
613×	`associate-+r+_binary64`
319×	`*-commutative_binary64`
214×	`unsub-neg_binary64`
199×	`+-commutative_binary64`

Counts

51 → 36

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	810
1	251	764
2	599	744
3	1684	726
4	3254	726
5	4961	726
6	4845	726

prune30.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	34	2	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	2	37

Error

0.0b

Counts

37 → 2

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))) (.f64 1/20160 (pow.f64 x 8)))
	25.7b	(/.f64 (+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (.f64 (exp.f64 x) -3)) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))

Status

Error

Program

▶

0.2b

(+.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) (*.f64 1/20160 (pow.f64 x 8)))

25.7b

(/.f64 (+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (*.f64 (exp.f64 x) -3)) (*.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))

Compiler

Compiled 455 to 252 computations (44.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))
0.0b	(*.f64 1/20160 (pow.f64 x 8))
0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite140.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

28×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
19×	`add-exp-log_binary64`
13×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
12×	`unpow-prod-down_binary64`

Counts

4 → 88

Calls

4 calls:

8.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))
5.0ms	(*.f64 1/12 (pow.f64 x 4))
5.0ms	(*.f64 1/360 (pow.f64 x 6))
5.0ms	(*.f64 1/20160 (pow.f64 x 8))

Compiler

Compiled 2364 to 1747 computations (26.1% saved)

series72.0ms (1.4%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

32.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))
12.0ms	(*.f64 1/20160 (pow.f64 x 8))
10.0ms	(*.f64 1/360 (pow.f64 x 6))
10.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 709 to 561 computations (20.9% saved)

simplify110.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

696×	`unswap-sqr_binary64`
455×	`*-commutative_binary64`
381×	`log-prod_binary64`
294×	`cancel-sign-sub-inv_binary64`
270×	`distribute-rgt-in_binary64`

Counts

106 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	1445
1	348	1364
2	1089	1284
3	2472	1270
4	4765	1270
5	5164	1270

prune63.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	65	3	68

Error

Counts

68 → 3

Alt Table

Status	Error	Program
	54.6b	(+.f64 (/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) 3)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (-.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (.f64 x x))))) (*.f64 1/20160 (pow.f64 x 8)))
✓	0.2b	(+.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))) (.f64 1/20160 (pow.f64 x 8)))
▶	25.7b	(/.f64 (+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (.f64 (exp.f64 x) -3)) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))

Compiler

Compiled 1273 to 932 computations (26.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)))
0.0b	(*.f64 (exp.f64 x) -3)
0.1b	(pow.f64 (exp.f64 x) 3)
3.5b	(+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (*.f64 (exp.f64 x) -3))

rewrite98.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
7×	`associate-r_binary64`

Counts

4 → 80

Calls

4 calls:

8.0ms	(+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (*.f64 (exp.f64 x) -3))
7.0ms	(*.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)))
5.0ms	(*.f64 (exp.f64 x) -3)
3.0ms	(pow.f64 (exp.f64 x) 3)

Compiler

Compiled 1845 to 1104 computations (40.2% saved)

series68.0ms (1.3%)

Error

Counts

4 → 24

Calls

4 calls:

15.0ms	(+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (*.f64 (exp.f64 x) -3))
11.0ms	(pow.f64 (exp.f64 x) 3)
10.0ms	(*.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)))
8.0ms	(*.f64 (exp.f64 x) -3)

Compiler

Compiled 1135 to 792 computations (30.2% saved)

simplify88.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

743×	`distribute-rgt-in_binary64`
422×	`unswap-sqr_binary64`
294×	`exp-prod_binary64`
252×	`log-prod_binary64`
241×	`associate-l_binary64`

Counts

104 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	1363
1	432	1272
2	1761	1226
3	4258	1226
4	4942	1226

prune49.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	65	3	68

Error

Counts

68 → 3

Alt Table

Status	Error	Program
▶	54.6b	(+.f64 (/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) 3)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (-.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (.f64 x x))))) (*.f64 1/20160 (pow.f64 x 8)))
✓	0.2b	(+.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))) (.f64 1/20160 (pow.f64 x 8)))
✓	25.7b	(/.f64 (+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (.f64 (exp.f64 x) -3)) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))

Compiler

Compiled 1192 to 761 computations (36.2% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/12 (pow.f64 x 4))
0.1b	(*.f64 1/12 (pow.f64 x 4))
0.1b	(*.f64 1/12 (pow.f64 x 4))
53.7b	(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) 3)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (-.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (.f64 x x)))))

rewrite266.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

37×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64` `associate-r_binary64`
12×	`add-cbrt-cube_binary64` `times-frac_binary64` `unpow-prod-down_binary64`

Counts

4 → 110

Calls

4 calls:

17.0ms	(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) 3)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (-.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (.f64 x x)))))
8.0ms	(*.f64 1/12 (pow.f64 x 4))
5.0ms	(*.f64 1/12 (pow.f64 x 4))
5.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 7188 to 5663 computations (21.2% saved)

series131.0ms (2.6%)

Error

Counts

4 → 18

Calls

4 calls:

80.0ms	(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) 3)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (-.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (.f64 x x)))))
16.0ms	(*.f64 1/12 (pow.f64 x 4))
15.0ms	(*.f64 1/12 (pow.f64 x 4))
14.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 1355 to 1093 computations (19.3% saved)

simplify116.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

699×	`distribute-rgt-in_binary64`
691×	`distribute-lft-in_binary64`
625×	`associate-l_binary64`
529×	`associate-r_binary64`
68×	`cancel-sign-sub-inv_binary64`

Counts

128 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	4909
1	304	4579
2	941	4504
3	5053	4504

prune74.0ms (1.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	63	3	66

Error

Counts

66 → 3

Alt Table

Status	Error	Program
	54.6b	(+.f64 (/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) 3)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (-.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))) (.f64 x x))))) (*.f64 1/20160 (pow.f64 x 8)))
	0.2b	(+.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))) (.f64 1/20160 (pow.f64 x 8)))
	25.7b	(/.f64 (+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (.f64 (exp.f64 x) -3)) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))

Compiler

Compiled 2354 to 1820 computations (22.7% saved)

regimes154.0ms (3%)

Accuracy

Total 0.5b remaining (91.6%)

Threshold costs 0.5b (91.6%)

Compiler

Compiled 2485 to 1786 computations (28.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64` `+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	59
1	26	59
2	26	59

end1.0ms (0%)

Compiler: Compiled 40 to 30 computations (25% saved)

sample3.1s (60.5%)

Algorithm

1×

intervals

Results

2.1s	4210×	body	2048	valid
435.0ms	1957×	body	1024	valid
117.0ms	1022×	body	512	valid
33.0ms	476×	body	256	valid
12.0ms	335×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 149 to 114 computations (23.5% saved)

Details

analyze100.0ms (2%)

sample97.0ms (1.9%)

simplify87.0ms (1.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite74.0ms (1.5%)

series29.0ms (0.6%)

simplify94.0ms (1.9%)

prune30.0ms (0.6%)

localize13.0ms (0.3%)

rewrite140.0ms (2.8%)

series72.0ms (1.4%)

simplify110.0ms (2.2%)

prune63.0ms (1.2%)

localize13.0ms (0.3%)

rewrite98.0ms (1.9%)

series68.0ms (1.3%)

simplify88.0ms (1.7%)

prune49.0ms (1%)

localize21.0ms (0.4%)

rewrite266.0ms (5.3%)

series131.0ms (2.6%)

simplify116.0ms (2.3%)

prune74.0ms (1.5%)

regimes154.0ms (3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample3.1s (60.5%)

Profiling