Details

analyze316.0ms

Algorithm

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

sample28.0ms

Algorithm

intervals

Results

10.0ms	55×	body	1280	valid
7.0ms	65×	body	640	valid
2.0ms	95×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	19×	body	160	valid

simplify90.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4999	7
1	4999	7

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.7b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.7b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1.0))
5.1b	(-.f64 (exp.f64 x) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`add-exp-log_binary64` `associate-/l*_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 50

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1.0))
5.0ms	(-.f64 (exp.f64 x) 1.0)

series12.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1.0))
3.0ms	(-.f64 (exp.f64 x) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5019	574

prune67.0ms

Filtered

41 candidates to 56 candidates (-36.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	5	57

Merged error: 0.0b

Counts

57 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (*.f64 x 1/6))
0.0b	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (*.f64 x 1/6)))))
0.1b	(.f64 (.f64 x x) (+.f64 1/2 (*.f64 x 1/6)))
0.3b	(*.f64 x 1/6)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`
11×	`pow1_binary64`
9×	`times-frac_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`associate-r/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `-commutative_binary64`
1×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 81

Calls

4 calls:

3.0ms	(+.f64 1/2 (*.f64 x 1/6))
9.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (*.f64 x 1/6)))))
8.0ms	(.f64 (.f64 x x) (+.f64 1/2 (*.f64 x 1/6)))
4.0ms	(*.f64 x 1/6)

series32.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 1/2 (*.f64 x 1/6))
7.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (*.f64 x 1/6)))))
13.0ms	(.f64 (.f64 x x) (+.f64 1/2 (*.f64 x 1/6)))
3.0ms	(*.f64 x 1/6)

simplify63.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4909	1111
1	4909	1111

prune87.0ms

Filtered

65 candidates to 93 candidates (-43.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Merged error: 0.0b

Counts

98 → 5

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (*.f64 x 1/12) (/.f64 1 x))
0.0b	(+.f64 1/2 (+.f64 (*.f64 x 1/12) (/.f64 1 x)))
0.3b	(*.f64 x 1/12)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`sum-log_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

3 → 43

Calls

3 calls:

7.0ms	(+.f64 (*.f64 x 1/12) (/.f64 1 x))
9.0ms	(+.f64 1/2 (+.f64 (*.f64 x 1/12) (/.f64 1 x)))
4.0ms	(*.f64 x 1/12)

series17.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(+.f64 (*.f64 x 1/12) (/.f64 1 x))
3.0ms	(+.f64 1/2 (+.f64 (*.f64 x 1/12) (/.f64 1 x)))
3.0ms	(*.f64 x 1/12)

simplify54.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4846	420
1	4846	420

prune54.0ms

Filtered

34 candidates to 52 candidates (-52.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	50	7	57

Merged error: 0.0b

Counts

57 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 x x) (+.f64 (*.f64 x 1/6) 1/2))
0.1b	(pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 (*.f64 x 1/6) 1/2)))) 3)
0.3b	(*.f64 x 1/6)
24.7b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 (*.f64 x 1/6) 1/2)))) 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
36×	`times-frac_binary64` `cbrt-prod_binary64`
30×	`unpow-prod-down_binary64` `cube-prod_binary64`
14×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
12×	`pow1_binary64`
8×	`associate-/r/_binary64`
6×	`associate-r_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `div-inv_binary64`
3×	`pow-unpow_binary64`
2×	`associate-r/_binary64` `sqr-pow_binary64` `cube-div_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64` `unpow3_binary64` `-commutative_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64`

Counts

4 → 137

Calls

4 calls:

11.0ms	(.f64 (.f64 x x) (+.f64 (*.f64 x 1/6) 1/2))
8.0ms	(pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 (*.f64 x 1/6) 1/2)))) 3)
4.0ms	(*.f64 x 1/6)
8.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 (*.f64 x 1/6) 1/2)))) 3))

series37.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(.f64 (.f64 x x) (+.f64 (*.f64 x 1/6) 1/2))
13.0ms	(pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 (*.f64 x 1/6) 1/2)))) 3)
3.0ms	(*.f64 x 1/6)
8.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 (*.f64 x 1/6) 1/2)))) 3))

simplify46.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5033	2802

prune98.0ms

Filtered

76 candidates to 149 candidates (-96.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	149	7	156

Merged error: 0.0b

Counts

156 → 7

regimes98.0ms

Accuracy

97.2% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 21.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	39
1	37	39

end0.0ms

sample844.0ms

Algorithm

intervals

Results

397.0ms	2300×	body	1280	valid
181.0ms	1640×	body	640	valid
63.0ms	2814×	body	80	valid
61.0ms	819×	body	320	valid
21.0ms	427×	body	160	valid
0.0ms	2×	body	1280	invalid

Details

analyze316.0ms

sample28.0ms

simplify90.0ms

prune5.0ms

localize4.0ms

rewrite14.0ms

series12.0ms

simplify65.0ms

prune67.0ms

localize9.0ms

rewrite27.0ms

series32.0ms

simplify63.0ms

prune87.0ms

localize6.0ms

rewrite22.0ms

series17.0ms

simplify54.0ms

prune54.0ms

localize12.0ms

rewrite37.0ms

series37.0ms

simplify46.0ms

prune98.0ms

regimes98.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample844.0ms

Profiling