Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample25.0ms

Algorithm

intervals

Results

8.0ms	53×	body	1280	valid
6.0ms	52×	body	640	valid
4.0ms	127×	body	80	valid
1.0ms	16×	body	320	valid
0.0ms	8×	body	160	valid

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	682	19
1	682	19

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: 30.2b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
1.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
20×	`distribute-lft-out_binary64`
18×	`distribute-lft-out--_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64` `difference-of-sqr-1_binary64`
4×	`associate-/r/_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-sub_binary64`

Counts

3 → 113

Calls

3 calls:

9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))
35.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series62.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
12.0ms	(/.f64 x (+.f64 x 1))
40.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify94.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4950	2299
1	4950	2299

prune132.0ms

Filtered

77 candidates to 122 candidates (-58.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	4	123

Merged error: 0.0b

Counts

123 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
0.0b	(/.f64 x (+.f64 x 1))
0.0b	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
1.8b	(-.f64 (/.f64 x (+.f64 x 1)) (log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity_binary64`
76×	`add-sqr-sqrt_binary64`
69×	`times-frac_binary64`
68×	`exp-prod_binary64`
39×	`add-cube-cbrt_binary64`
36×	`log-pow_binary64`
18×	`distribute-lft-out_binary64` `difference-of-squares_binary64`
10×	`distribute-lft-out--_binary64`
8×	`difference-of-sqr-1_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `log-prod_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
4×	`associate-/r*_binary64`
3×	`associate--r+_binary64` `flip3--_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 139

Calls

4 calls:

11.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
5.0ms	(/.f64 x (+.f64 x 1))
12.0ms	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
43.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
11.0ms	(/.f64 x (+.f64 x 1))
16.0ms	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
36.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (log.f64 (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))

simplify122.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4921	2330
1	4921	2330

prune124.0ms

Filtered

102 candidates to 151 candidates (-48.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	151	4	155

Merged error: 0.0b

Counts

155 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.3b	(/.f64 -1 (*.f64 x x))
0.6b	(/.f64 3 (pow.f64 x 3))
6.0b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64` `times-frac_binary64`
39×	`add-sqr-sqrt_binary64`
35×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-/r*_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
9×	`unpow3_binary64`
6×	`distribute-lft-out_binary64` `associate-/l*_binary64`
5×	`div-exp_binary64`
4×	`pow1_binary64` `distribute-rgt-out_binary64` `sqr-pow_binary64` `div-inv_binary64` `cube-mult_binary64`
3×	`cbrt-undiv_binary64` `frac-sub_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `distribute-rgt1-in_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 128

Calls

4 calls:

26.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
4.0ms	(/.f64 -1 (*.f64 x x))
5.0ms	(/.f64 3 (pow.f64 x 3))
39.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
17.0ms	(/.f64 -1 (*.f64 x x))
25.0ms	(/.f64 3 (pow.f64 x 3))
17.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify60.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5346	2247

prune103.0ms

Filtered

87 candidates to 140 candidates (-60.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	139	5	144

Merged error: 0.0b

Counts

144 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
0.3b	(/.f64 -1 (*.f64 x x))
0.5b	(/.f64 1 (pow.f64 x 3))
6.0b	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64` `times-frac_binary64`
39×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`
16×	`associate-r_binary64`
13×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
10×	`unpow3_binary64`
8×	`div-exp_binary64`
7×	`distribute-lft-out_binary64` `div-inv_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-r/_binary64` `associate-/l_binary64`
5×	`distribute-rgt-out_binary64`
4×	`sqr-pow_binary64` `cube-mult_binary64`
3×	`pow-to-exp_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `rec-exp_binary64` `frac-sub_binary64` `pow-exp_binary64`
2×	`flip3-+_binary64` `associate--r+_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-rgt1-in_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `flip--_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 146

Calls

4 calls:

34.0ms	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
4.0ms	(/.f64 -1 (*.f64 x x))
6.0ms	(/.f64 1 (pow.f64 x 3))
8.0ms	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
20.0ms	(/.f64 -1 (*.f64 x x))
25.0ms	(/.f64 1 (pow.f64 x 3))
16.0ms	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))

simplify95.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4926	2087
1	4926	2087

prune103.0ms

Filtered

86 candidates to 158 candidates (-83.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	158	5	163

Merged error: 0.0b

Counts

163 → 5

regimes24.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.5b

bsearch31.0ms

Steps

Iters	Range		Point
8	72.82139690898056	330257.8091303651	13072.014947429461
10	-44486250001524.586	-12.596229662909831	-10856.285190155952

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	75	59
1	75	59

end0.0ms

sample712.0ms

Algorithm

intervals

Results

263.0ms	1761×	body	1280	valid
153.0ms	1257×	body	640	valid
130.0ms	4079×	body	80	valid
54.0ms	589×	body	320	valid
19.0ms	314×	body	160	valid

Details

analyze4.0ms

sample25.0ms

simplify86.0ms

prune5.0ms

localize7.0ms

rewrite53.0ms

series62.0ms

simplify94.0ms

prune132.0ms

localize10.0ms

rewrite77.0ms

series75.0ms

simplify122.0ms

prune124.0ms

localize10.0ms

rewrite79.0ms

series113.0ms

simplify60.0ms

prune103.0ms

localize11.0ms

rewrite57.0ms

series110.0ms

simplify95.0ms

prune103.0ms

regimes24.0ms

bsearch31.0ms

simplify4.0ms

end0.0ms

sample712.0ms

Profiling