Details

analyze6.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample26.0ms

Algorithm

intervals

Results

9.0ms	64×	body	640	valid
5.0ms	129×	body	80	valid
4.0ms	21×	body	1280	valid
3.0ms	29×	body	320	valid
1.0ms	13×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	191	15
1	191	15

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 11.3b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
0.0b	(/.f64 1 (-.f64 x 1))
1.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
18×	`distribute-lft-out--_binary64`
17×	`distribute-lft-out_binary64`
14×	`difference-of-squares_binary64`
12×	`add-exp-log_binary64`
11×	`associate-/r*_binary64` `add-log-exp_binary64`
8×	`add-cbrt-cube_binary64` `div-inv_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`difference-of-sqr-1_binary64` `associate-/r/_binary64` `div-exp_binary64`
3×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

6.0ms	(/.f64 1 (+.f64 x 1))
20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
37.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series15.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/.f64 1 (+.f64 x 1))
3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))
8.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

simplify63.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4987	1726
1	4987	1726

prune101.0ms

Filtered

88 candidates to 147 candidates (-67.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	3	148

Merged error: 0.5b

Counts

148 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
1.9b	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
12.9b	(/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`associate-/r*_binary64` `add-log-exp_binary64` `difference-of-squares_binary64`
6×	`associate-/l*_binary64`
5×	`pow1_binary64`
4×	`difference-of-sqr-1_binary64` `associate-/r/_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `frac-add_binary64` `associate-+l-_binary64` `inv-pow_binary64` `prod-exp_binary64` `rec-exp_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 101

Calls

4 calls:

6.0ms	(/.f64 1 (-.f64 x 1))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
23.0ms	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
9.0ms	(/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x)))

series19.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
10.0ms	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
4.0ms	(/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5730	1305

prune70.0ms

Filtered

74 candidates to 113 candidates (-52.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	113	3	116

Merged error: 0.5b

Counts

116 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))
0.1b	(*.f64 (sqrt.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))) (sqrt.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))))
1.9b	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
1.9b	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

598×	`*-un-lft-identity_binary64`
192×	`distribute-lft-out_binary64`
179×	`sqrt-prod_binary64`
156×	`times-frac_binary64`
154×	`distribute-lft-out--_binary64`
95×	`div-inv_binary64`
72×	`swap-sqr_binary64`
65×	`sqrt-div_binary64`
45×	`frac-add_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`frac-times_binary64`
20×	`pow1_binary64`
16×	`associate-r_binary64` `associate-l_binary64`
15×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64`
14×	`add-log-exp_binary64`
13×	`add-cube-cbrt_binary64`
9×	`pow1/2_binary64` `sqrt-pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64` `associate-r/_binary64` `associate-l/_binary64`
4×	`unswap-sqr_binary64` `sum-log_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`sub-neg_binary64` `associate-+r-_binary64` `diff-log_binary64` `+-commutative_binary64` `associate-+r+_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 250

Calls

4 calls:

40.0ms	(sqrt.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))
90.0ms	(*.f64 (sqrt.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))) (sqrt.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))))
41.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
41.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))
8.0ms	(*.f64 (sqrt.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))) (sqrt.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))))
8.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
8.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))

simplify93.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4942	6620
1	4942	6620

prune188.0ms

Filtered

97 candidates to 262 candidates (-170.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	262	3	265

Merged error: 0.5b

Counts

265 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3)))
0.0b	(/.f64 2 (pow.f64 x 7))
0.1b	(/.f64 2 (pow.f64 x 5))
0.5b	(/.f64 2 (pow.f64 x 3))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac_binary64`
71×	`*-un-lft-identity_binary64`
63×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
36×	`unpow-prod-down_binary64`
26×	`associate-/r*_binary64`
19×	`add-exp-log_binary64`
12×	`sqr-pow_binary64` `cube-prod_binary64`
10×	`add-cbrt-cube_binary64`
9×	`associate-/l*_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`distribute-lft-out_binary64` `div-inv_binary64`
4×	`pow1_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64`
1×	`flip3-+_binary64` `frac-add_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 172

Calls

4 calls:

42.0ms	(+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3)))
7.0ms	(/.f64 2 (pow.f64 x 7))
5.0ms	(/.f64 2 (pow.f64 x 5))
6.0ms	(/.f64 2 (pow.f64 x 3))

series29.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3)))
8.0ms	(/.f64 2 (pow.f64 x 7))
5.0ms	(/.f64 2 (pow.f64 x 5))
4.0ms	(/.f64 2 (pow.f64 x 3))

simplify59.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5005	1727

prune134.0ms

Filtered

120 candidates to 184 candidates (-53.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	181	3	184
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	181	6	187

Merged error: 0b

Counts

187 → 6

regimes35.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 26.0b

bsearch28.0ms

Steps

Iters	Range		Point
11	0.007642193794192394	1.6763867049577024e+18	105.62426959319559
9	-176448000.86175188	-0.23391527846043206	-148.30320228357058

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	98	65
1	98	65

end0.0ms

sample730.0ms

Algorithm

intervals

Results

259.0ms	1894×	body	640	valid
154.0ms	4166×	body	80	valid
94.0ms	555×	body	1280	valid
92.0ms	923×	body	320	valid
31.0ms	462×	body	160	valid

Details

analyze6.0ms

sample26.0ms

simplify10.0ms

prune7.0ms

localize8.0ms

rewrite75.0ms

series15.0ms

simplify63.0ms

prune101.0ms

localize9.0ms

rewrite44.0ms

series19.0ms

simplify51.0ms

prune70.0ms

localize11.0ms

rewrite234.0ms

series34.0ms

simplify93.0ms

prune188.0ms

localize11.0ms

rewrite66.0ms

series29.0ms

simplify59.0ms

prune134.0ms

regimes35.0ms

bsearch28.0ms

simplify3.0ms

end0.0ms

sample730.0ms

Profiling