Details

analyze256.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample64.0ms

Algorithm

intervals

Results

29.0ms	77×	body	1024	valid
14.0ms	35×	body	2048	valid
7.0ms	37×	body	512	valid
4.0ms	87×	body	128	valid
2.0ms	17×	body	256	valid
2.0ms	3×	body	4096	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	10	14

prune1.0ms

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: 50.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

1.6b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.4b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.0b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`flip3-+_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 42

Calls

3 calls:

7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
7.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series191.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
97.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
37.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify83.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4839	862
1	4839	862

prune243.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0.0b

Counts

52 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
19.4b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
13×	`add-exp-log_binary64`
10×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `unpow-prod-down_binary64`
7×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
6×	`prod-exp_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
3×	`pow1_binary64`
2×	`pow-to-exp_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

3 → 69

Calls

3 calls:

8.0ms	(*.f64 3/40 (pow.f64 x 5))
7.0ms	(*.f64 (pow.f64 x 3) 1/6)
7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

series175.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(*.f64 3/40 (pow.f64 x 5))
50.0ms	(*.f64 (pow.f64 x 3) 1/6)
60.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

simplify66.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5029	1008

prune61.0ms

Filtered

50 candidates to 78 candidates (-56.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Merged error: 0.0b

Counts

82 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 1/2 x))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.3b	(/.f64 1/8 (pow.f64 x 3))
10.2b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
15×	`add-log-exp_binary64`
12×	`associate-/r*_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
10×	`add-exp-log_binary64`
9×	`distribute-lft-out_binary64`
6×	`log-prod_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `sum-log_binary64`
4×	`sqr-pow_binary64` `distribute-lft-out--_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`diff-log_binary64` `log-div_binary64` `+-commutative_binary64` `associate-+r+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-+r-_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-exp_binary64` `associate--l+_binary64`

Counts

4 → 113

Calls

4 calls:

7.0ms	(+.f64 x (/.f64 1/2 x))
27.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
26.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

series224.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+.f64 x (/.f64 1/2 x))
44.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
46.0ms	(/.f64 1/8 (pow.f64 x 3))
77.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4890	2077
1	4890	2077

prune88.0ms

Filtered

73 candidates to 125 candidates (-71.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	125	4	129

Merged error: 0.0b

Counts

129 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.3b	(/.f64 1/8 (pow.f64 x 3))
12.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
15.9b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
71×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
11×	`log-prod_binary64`
10×	`sqr-pow_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-sub_binary64`
5×	`pow1_binary64` `log-div_binary64`
4×	`distribute-lft-out_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sum-log_binary64`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/.f64 1/16 (pow.f64 x 5))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
44.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
46.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

series245.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/.f64 1/16 (pow.f64 x 5))
48.0ms	(/.f64 1/8 (pow.f64 x 3))
81.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
50.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify80.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4864	3605
1	4864	3605

prune163.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	171	4	175

Merged error: 0.0b

Counts

175 → 4

regimes66.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch34.0ms

Steps

Iters	Range		Point
9	0.8118807294673237	251290.20220650133	0.9637304954849593
8	-794.0745720962416	-0.017150286319278833	-1.0435202563005457

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms

sample1.9s

Algorithm

intervals

Results

945.0ms	2533×	body	1024	valid
397.0ms	1213×	body	2048	valid
239.0ms	1164×	body	512	valid
105.0ms	2402×	body	128	valid
72.0ms	631×	body	256	valid
27.0ms	57×	body	4096	valid

Details

analyze256.0ms

sample64.0ms

simplify8.0ms

prune1.0ms

localize7.0ms

rewrite21.0ms

series191.0ms

simplify83.0ms

prune243.0ms

localize9.0ms

rewrite27.0ms

series175.0ms

simplify66.0ms

prune61.0ms

localize10.0ms

rewrite79.0ms

series224.0ms

simplify67.0ms

prune88.0ms

localize13.0ms

rewrite119.0ms

series245.0ms

simplify80.0ms

prune163.0ms

regimes66.0ms

bsearch34.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling