Details

analyze905.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
18.4%	81.3%	0.2%	13
29.5%	70.3%	0.2%	14

sample26.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
0.0ms	14×	body	80	invalid

simplify154.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (151.0ms)

Iter	Nodes	Cost
0	4786	11
1	4786	11

prune4.0ms

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: 11.9b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
0.0b	(*.f64 (-.f64 y z) t)
12.1b	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`associate-*l/_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 63

Calls

3 calls:

8.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
7.0ms	(*.f64 (-.f64 y z) t)
10.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

series58.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
8.0ms	(*.f64 (-.f64 y z) t)
18.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5590	683

prune62.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	7	73

Merged error: 0.0b

Counts

73 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
4.2b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
32×	`cbrt-prod_binary64`
30×	`associate-r_binary64`
25×	`add-exp-log_binary64`
24×	`add-cube-cbrt_binary64`
20×	`cbrt-div_binary64`
18×	`add-cbrt-cube_binary64`
17×	`associate-l_binary64`
10×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64`
5×	`frac-times_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r/_binary64` `pow1/3_binary64` `associate-l/_binary64`
2×	`div-inv_binary64`
1×	`pow-prod-down_binary64` `*-commutative_binary64`

Counts

4 → 122

Calls

4 calls:

6.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))
30.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))

series107.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt.f64 (-.f64 a z))
26.0ms	(cbrt.f64 (-.f64 a z))
26.0ms	(cbrt.f64 (-.f64 a z))
26.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))

simplify51.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5572	1901

prune72.0ms

Filtered

107 candidates to 134 candidates (-25.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	136	5	141

Merged error: 0.0b

Counts

141 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (pow.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) 1))
0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
2.0b	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
27×	`add-cube-cbrt_binary64`
22×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/l_binary64`
4×	`associate-/r/_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 114

Calls

3 calls:

5.0ms	(+.f64 x (pow.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) 1))
9.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
16.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)

series68.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+.f64 x (pow.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) 1))
11.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
25.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)

simplify42.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5032	1389

prune60.0ms

Filtered

85 candidates to 123 candidates (-44.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	122	6	128

Merged error: 0b

Counts

128 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) x))
2.0b	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
2.0b	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
2.0b	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt_binary64`
101×	`*-un-lft-identity_binary64`
93×	`associate-l_binary64`
78×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
30×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64`
6×	`cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `cbrt-prod_binary64` `associate-l/_binary64` `-commutative_binary64`
2×	`cbrt-div_binary64`
1×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`

Counts

4 → 163

Calls

4 calls:

11.0ms	(cbrt.f64 (+.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) x))
16.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
14.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
13.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)

series257.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt.f64 (+.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t) x))
28.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
25.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
26.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)

simplify41.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5219	1880

prune62.0ms

Filtered

120 candidates to 175 candidates (-45.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	175	6	181

Merged error: 0b

Counts

181 → 6

regimes412.0ms

Accuracy

53.1% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 1.4b

bsearch30.0ms

Steps

Iters	Range		Point
7	2.0284281137522668e-165	3.8699928885402184e-164	1.4513367647259287e-164
8	-1.8696597506577748e-26	-3.6040340576828607e-31	-5.369730380231295e-30

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	31
1	40	31

end0.0ms

sample623.0ms

Algorithm

intervals

Results

303.0ms	7998×	body	80	valid
30.0ms	730×	body	80	invalid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	320	valid

Details

analyze905.0ms

sample26.0ms

simplify154.0ms

prune4.0ms

localize8.0ms

rewrite27.0ms

series58.0ms

simplify44.0ms

prune62.0ms

localize12.0ms

rewrite48.0ms

series107.0ms

simplify51.0ms

prune72.0ms

localize9.0ms

rewrite34.0ms

series68.0ms

simplify42.0ms

prune60.0ms

localize12.0ms

rewrite62.0ms

series257.0ms

simplify41.0ms

prune62.0ms

regimes412.0ms

bsearch30.0ms

simplify2.0ms

end0.0ms

sample623.0ms

Profiling