Details

analyze2.2s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

sample47.0ms

Algorithm

intervals

Results

19.0ms	256×	body	128	valid
8.0ms	102×	body	128	nan
3.0ms	36×	body	128	invalid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5037	27

prune2.0ms

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: 14.1b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

2.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.3b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
6.6b	(/.f64 (.f64 M D) (.f64 2 d))
11.1b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
38×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
19×	`associate-r_binary64` `div-exp_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`times-frac_binary64`
13×	`associate-l_binary64`
10×	`unswap-sqr_binary64` `pow-exp_binary64`
7×	`pow1_binary64` `cbrt-unprod_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`unpow2_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `flip3--_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 116

Calls

4 calls:

9.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series1000.0ms

Counts

4 → 12

Calls

4 calls:

506.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
298.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
40.0ms	(/.f64 (.f64 M D) (.f64 2 d))
156.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

simplify55.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5849	2845

prune130.0ms

Filtered

84 candidates to 128 candidates (-52.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	6	129

Merged error: 7.7b

Counts

129 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.3b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
5.3b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.6b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
26×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64` `div-exp_binary64`
13×	`*-un-lft-identity_binary64`
10×	`associate-r_binary64` `add-cube-cbrt_binary64` `pow-exp_binary64`
6×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64` `times-frac_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `unswap-sqr_binary64`
3×	`associate-l_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 99

Calls

4 calls:

7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
8.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series953.0ms

Counts

4 → 12

Calls

4 calls:

568.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
190.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
153.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify49.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5062	2183

prune102.0ms

Filtered

69 candidates to 111 candidates (-60.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	111	6	117

Merged error: 6.1b

Counts

117 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

3.9b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
4.3b	(/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (.f64 2 d))) l)
6.6b	(/.f64 (.f64 M D) (.f64 2 d))
6.6b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

251×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
116×	`cbrt-unprod_binary64` `prod-exp_binary64`
87×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `times-frac_binary64`
5×	`associate-/r_binary64` `associate-l*_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `associate-*l/_binary64`
3×	`associate-/l/_binary64` `associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `frac-times_binary64` `-commutative_binary64`

Counts

4 → 153

Calls

4 calls:

9.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
19.0ms	(/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (.f64 2 d))) l)
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series353.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
170.0ms	(/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (.f64 2 d))) l)
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))
47.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify104.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5114	3130

prune87.0ms

Filtered

64 candidates to 165 candidates (-157.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	164	7	171

Merged error: 6.0b

Counts

171 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

3.9b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
4.3b	(/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (.f64 (.f64 M D) (/.f64 1/2 d))) l)
6.6b	(/.f64 (.f64 M D) (.f64 2 d))
6.7b	(.f64 (.f64 M D) (/.f64 1/2 d))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

251×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
130×	`cbrt-unprod_binary64` `prod-exp_binary64`
73×	`cbrt-undiv_binary64` `div-exp_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
14×	`times-frac_binary64`
11×	`pow1_binary64`
6×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `associate-/r_binary64` `add-log-exp_binary64` `associate-r/_binary64` `div-inv_binary64` `associate-*l/_binary64`
3×	`associate-/l/_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `-commutative_binary64`
1×	`unswap-sqr_binary64` `frac-times_binary64`

Counts

4 → 165

Calls

4 calls:

9.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
25.0ms	(/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (.f64 (.f64 M D) (/.f64 1/2 d))) l)
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
8.0ms	(.f64 (.f64 M D) (/.f64 1/2 d))

series343.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
163.0ms	(/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (.f64 (.f64 M D) (/.f64 1/2 d))) l)
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))
44.0ms	(.f64 (.f64 M D) (/.f64 1/2 d))

simplify125.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	5071	3444

prune92.0ms

Filtered

74 candidates to 177 candidates (-139.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	177	7	184

Merged error: 6.0b

Counts

184 → 7

regimes251.0ms

Accuracy

0% (1.6b remaining)

Error of 9.1b against oracle of 7.5b and baseline of 9.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	36
1	89	36

end0.0ms

sample1.6s

Algorithm

intervals

Results

610.0ms	8000×	body	128	valid
435.0ms	2933×	body	128	nan
110.0ms	1325×	body	128	invalid

Details

analyze2.2s

sample47.0ms

simplify47.0ms

prune2.0ms

localize18.0ms

rewrite44.0ms

series1000.0ms

simplify55.0ms

prune130.0ms

localize14.0ms

rewrite39.0ms

series953.0ms

simplify49.0ms

prune102.0ms

localize14.0ms

rewrite66.0ms

series353.0ms

simplify104.0ms

prune87.0ms

localize17.0ms

rewrite76.0ms

series343.0ms

simplify125.0ms

prune92.0ms

regimes251.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.6s

Profiling