Details

analyze276.0ms

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

sample76.0ms

Algorithm

intervals

Results

41.0ms	81×	body	1280	valid
15.0ms	50×	body	640	valid
6.0ms	18×	body	2560	valid
4.0ms	19×	body	320	valid
3.0ms	77×	body	80	valid
1.0ms	11×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

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: 53.4b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

1.0b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
1.4b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
15.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite18.0ms

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:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series82.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
23.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
16.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify92.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4835	862
1	4835	862

prune62.0ms

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: 0b

Counts

52 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (pow.f64 x 5) 3/40)
0.1b	(*.f64 (pow.f64 x 3) 1/6)
19.3b	(-.f64 (+.f64 x (.f64 (pow.f64 x 5) 3/40)) (.f64 (pow.f64 x 3) 1/6))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`associate-l_binary64`
13×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `unpow-prod-down_binary64`
7×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
6×	`associate-r_binary64` `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:

5.0ms	(*.f64 (pow.f64 x 5) 3/40)
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
7.0ms	(-.f64 (+.f64 x (.f64 (pow.f64 x 5) 3/40)) (.f64 (pow.f64 x 3) 1/6))

series83.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(*.f64 (pow.f64 x 5) 3/40)
24.0ms	(*.f64 (pow.f64 x 3) 1/6)
28.0ms	(-.f64 (+.f64 x (.f64 (pow.f64 x 5) 3/40)) (.f64 (pow.f64 x 3) 1/6))

simplify85.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5090	1009

prune61.0ms

Filtered

51 candidates to 78 candidates (-52.9%)

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: 0b

Counts

82 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.3b	(/.f64 1/8 (pow.f64 x 3))
12.6b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
18×	`add-log-exp_binary64`
13×	`unpow-prod-down_binary64` `cube-prod_binary64`
12×	`associate-/r*_binary64`
10×	`add-exp-log_binary64`
9×	`distribute-lft-out_binary64`
6×	`log-prod_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `sum-log_binary64`
4×	`diff-log_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `log-div_binary64` `associate-+r+_binary64` `frac-sub_binary64` `associate--l+_binary64`
1×	`pow-to-exp_binary64` `associate-+r-_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 123

Calls

4 calls:

24.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
19.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
21.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
22.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
25.0ms	(/.f64 1/8 (pow.f64 x 3))
41.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5445	2608

prune96.0ms

Filtered

80 candidates to 135 candidates (-68.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	135	4	139

Merged error: 0b

Counts

139 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/16 (pow.f64 x 5))
0.3b	(/.f64 1/8 (pow.f64 x 3))
14.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
22.7b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite88.0ms

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))
5.0ms	(/.f64 1/8 (pow.f64 x 3))
36.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
36.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/.f64 1/16 (pow.f64 x 5))
26.0ms	(/.f64 1/8 (pow.f64 x 3))
42.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
27.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify100.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4879	3605
1	4879	3605

prune169.0ms

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: 0b

Counts

175 → 4

regimes20.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.7b

bsearch38.0ms

Steps

Iters	Range		Point
10	2.2229764251778617e-08	137969.22337435448	0.9538825683643378
9	-120.97131362631039	-1.637996403267889e-07	-1.058807815338858

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2372×	body	1280	valid
450.0ms	1575×	body	640	valid
266.0ms	785×	body	2560	valid
130.0ms	767×	body	320	valid
88.0ms	2109×	body	80	valid
41.0ms	392×	body	160	valid

Details

analyze276.0ms

sample76.0ms

simplify12.0ms

prune5.0ms

localize6.0ms

rewrite18.0ms

series82.0ms

simplify92.0ms

prune62.0ms

localize9.0ms

rewrite19.0ms

series83.0ms

simplify85.0ms

prune61.0ms

localize10.0ms

rewrite75.0ms

series114.0ms

simplify67.0ms

prune96.0ms

localize14.0ms

rewrite88.0ms

series130.0ms

simplify100.0ms

prune169.0ms

regimes20.0ms

bsearch38.0ms

simplify5.0ms

end0.0ms

sample2.2s

Profiling