Details

analyze12.0ms

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

sample27.0ms

Algorithm

intervals

Results

8.0ms	61×	body	640	valid
5.0ms	128×	body	80	valid
3.0ms	18×	body	1280	valid
3.0ms	27×	body	320	valid
2.0ms	22×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	193	22
1	193	22

prune3.0ms

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: 10.1b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.2b	(+.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:

7.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))
17.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
40.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 1 (-.f64 x 1))
7.0ms	(/.f64 1 (+.f64 x 1))
15.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
54.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

simplify105.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5069	2576

prune137.0ms

Filtered

88 candidates to 147 candidates (-67.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	2	148

Merged error: 0.1b

Counts

148 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (-.f64 x 1))
0.3b	(cbrt.f64 (-.f64 x 1))
0.3b	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
17.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 1 (cbrt.f64 (-.f64 x 1)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
16×	`cbrt-div_binary64`
14×	`swap-sqr_binary64` `add-cube-cbrt_binary64` `difference-of-squares_binary64`
12×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
11×	`pow1_binary64`
10×	`associate-r_binary64` `associate-l_binary64`
9×	`add-log-exp_binary64`
8×	`pow1/3_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
7×	`frac-times_binary64`
6×	`add-exp-log_binary64`
5×	`associate-r/_binary64` `associate-l/_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-sub_binary64`
3×	`un-div-inv_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `pow-plus_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 124

Calls

4 calls:

3.0ms	(cbrt.f64 (-.f64 x 1))
3.0ms	(cbrt.f64 (-.f64 x 1))
12.0ms	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
24.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 1 (cbrt.f64 (-.f64 x 1)))))

series171.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt.f64 (-.f64 x 1))
28.0ms	(cbrt.f64 (-.f64 x 1))
38.0ms	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
76.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 1 (cbrt.f64 (-.f64 x 1)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5043	3230

prune192.0ms

Filtered

94 candidates to 136 candidates (-44.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	136	2	138

Merged error: 0.1b

Counts

138 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 2 (pow.f64 x 5))
0.1b	(/.f64 2 (pow.f64 x 3))
0.2b	(/.f64 2 (pow.f64 x 7))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac_binary64`
60×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
36×	`unpow-prod-down_binary64`
26×	`associate-/r*_binary64`
18×	`add-exp-log_binary64`
12×	`sqr-pow_binary64` `cube-prod_binary64`
9×	`add-cbrt-cube_binary64` `associate-/l*_binary64` `div-exp_binary64`
4×	`unpow3_binary64` `cube-mult_binary64`
3×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

3 → 155

Calls

3 calls:

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

series91.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/.f64 2 (pow.f64 x 5))
23.0ms	(/.f64 2 (pow.f64 x 3))
36.0ms	(/.f64 2 (pow.f64 x 7))

simplify78.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4906	2191
1	4906	2191

prune160.0ms

Filtered

104 candidates to 164 candidates (-57.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	161	5	166

Merged error: 0.0b

Counts

166 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 2 (pow.f64 x 5))
0.1b	(/.f64 (/.f64 2 (*.f64 x x)) x)
0.2b	(/.f64 2 (pow.f64 x 7))
0.5b	(/.f64 2 (*.f64 x x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
28×	`add-exp-log_binary64`
24×	`unpow-prod-down_binary64`
22×	`add-cbrt-cube_binary64`
18×	`associate-/r*_binary64`
16×	`associate-/l*_binary64`
13×	`div-exp_binary64`
9×	`cbrt-undiv_binary64`
8×	`sqr-pow_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `pow-exp_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/.f64 2 (pow.f64 x 5))
7.0ms	(/.f64 (/.f64 2 (*.f64 x x)) x)
4.0ms	(/.f64 2 (pow.f64 x 7))
5.0ms	(/.f64 2 (*.f64 x x))

series123.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 2 (pow.f64 x 5))
29.0ms	(/.f64 (/.f64 2 (*.f64 x x)) x)
43.0ms	(/.f64 2 (pow.f64 x 7))
20.0ms	(/.f64 2 (*.f64 x x))

simplify124.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4977	2283
1	4977	2283

prune179.0ms

Filtered

122 candidates to 171 candidates (-40.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	171	5	176

Merged error: 0b

Counts

176 → 5

regimes26.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 25.7b

bsearch44.0ms

Steps

Iters	Range		Point
10	2.3043253668356612e-10	796.8629485042827	126.59925884127742
10	-235423.6517036655	-4.826735066471469e-14	-106.76785359664669

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	72	85
1	72	85

end0.0ms

sample764.0ms

Algorithm

intervals

Results

261.0ms	1845×	body	640	valid
160.0ms	4108×	body	80	valid
109.0ms	613×	body	1280	valid
107.0ms	976×	body	320	valid
33.0ms	458×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze12.0ms

sample27.0ms

simplify19.0ms

prune3.0ms

localize9.0ms

rewrite75.0ms

series84.0ms

simplify105.0ms

prune137.0ms

localize14.0ms

rewrite48.0ms

series171.0ms

simplify69.0ms

prune192.0ms

localize12.0ms

rewrite20.0ms

series91.0ms

simplify78.0ms

prune160.0ms

localize15.0ms

rewrite27.0ms

series123.0ms

simplify124.0ms

prune179.0ms

regimes26.0ms

bsearch44.0ms

simplify5.0ms

end0.0ms

sample764.0ms

Profiling