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

sample30.0ms

Algorithm

intervals

Results

8.0ms	56×	body	640	valid
7.0ms	29×	body	320	valid
5.0ms	128×	body	80	valid
3.0ms	19×	body	1280	valid
2.0ms	24×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	191	15
1	191	15

prune4.0ms

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: 9.8b

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))
2.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite72.0ms

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))
19.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
36.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series19.0ms

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))
10.0ms	(+.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

prune145.0ms

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: 0.2b

Counts

148 → 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)))))
2.1b	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
2.1b	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))

rewrite227.0ms

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))))
87.0ms	(*.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)))))
40.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
39.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))
11.0ms	(*.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)))))
10.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
10.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))

simplify91.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4942	6620
1	4942	6620

prune239.0ms

Filtered

97 candidates to 262 candidates (-170.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	262	3	265

Merged error: 0.2b

Counts

265 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (-.f64 x 1))
0.3b	(cbrt.f64 (-.f64 x 1))
0.3b	(cbrt.f64 (-.f64 x 1))
14.8b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (cbrt.f64 (-.f64 x 1))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
21×	`cbrt-prod_binary64`
19×	`add-sqr-sqrt_binary64`
12×	`times-frac_binary64`
9×	`add-log-exp_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `difference-of-squares_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/3_binary64` `frac-add_binary64` `difference-of-sqr-1_binary64` `div-inv_binary64`
2×	`sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64` `flip-+_binary64` `frac-sub_binary64`

Counts

4 → 75

Calls

4 calls:

3.0ms	(cbrt.f64 (-.f64 x 1))
3.0ms	(cbrt.f64 (-.f64 x 1))
3.0ms	(cbrt.f64 (-.f64 x 1))
101.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (cbrt.f64 (-.f64 x 1))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(cbrt.f64 (-.f64 x 1))
8.0ms	(cbrt.f64 (-.f64 x 1))
9.0ms	(cbrt.f64 (-.f64 x 1))
20.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (cbrt.f64 (-.f64 x 1))))

simplify59.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5152	1164

prune109.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	87	3	90

Merged error: 0.2b

Counts

90 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.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))
0.2b	(/.f64 2 (pow.f64 x 3))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64`
64×	`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`
11×	`distribute-lft-out_binary64`
10×	`add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `associate-/l*_binary64` `div-exp_binary64`
6×	`div-inv_binary64`
4×	`pow1_binary64` `frac-add_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`+-commutative_binary64` `associate-+r+_binary64`

Counts

4 → 177

Calls

4 calls:

57.0ms	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3))))
5.0ms	(/.f64 2 (pow.f64 x 7))
5.0ms	(/.f64 2 (pow.f64 x 5))
5.0ms	(/.f64 2 (pow.f64 x 3))

series29.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3))))
8.0ms	(/.f64 2 (pow.f64 x 7))
7.0ms	(/.f64 2 (pow.f64 x 5))
6.0ms	(/.f64 2 (pow.f64 x 3))

simplify39.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5408	2067

prune207.0ms

Filtered

124 candidates to 189 candidates (-52.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	185	7	192

Merged error: 0b

Counts

192 → 7

regimes53.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 25.6b

bsearch28.0ms

Steps

Iters	Range		Point
10	2.594079110446758e-09	94764.6880627797	94.7577384407541
9	-1891593633.0839963	-0.6309204020956032	-87.53679547805154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	70
1	72	70

end0.0ms

sample747.0ms

Algorithm

intervals

Results

258.0ms	1826×	body	640	valid
159.0ms	4210×	body	80	valid
100.0ms	940×	body	320	valid
98.0ms	558×	body	1280	valid
33.0ms	466×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze6.0ms

sample30.0ms

simplify10.0ms

prune4.0ms

localize8.0ms

rewrite72.0ms

series19.0ms

simplify63.0ms

prune145.0ms

localize11.0ms

rewrite227.0ms

series48.0ms

simplify91.0ms

prune239.0ms

localize12.0ms

rewrite113.0ms

series45.0ms

simplify59.0ms

prune109.0ms

localize11.0ms

rewrite80.0ms

series29.0ms

simplify39.0ms

prune207.0ms

regimes53.0ms

bsearch28.0ms

simplify3.0ms

end0.0ms

sample747.0ms

Profiling