Details

analyze2.3s

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

sample51.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
8.0ms	98×	body	80	nan
4.0ms	51×	body	80	invalid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5464	18

prune8.0ms

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: 15.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

3.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
9.3b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite36.0ms

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))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series214.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
66.0ms	(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))
32.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

simplify62.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4983	1890
1	4983	1890

prune196.0ms

Filtered

84 candidates to 128 candidates (-52.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 8.8b

Counts

129 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

3.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
6.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-exp-log_binary64`
88×	`prod-exp_binary64`
52×	`div-exp_binary64`
28×	`add-cbrt-cube_binary64`
25×	`pow-exp_binary64`
24×	`add-sqr-sqrt_binary64`
14×	`cbrt-unprod_binary64`
13×	`associate-l_binary64`
11×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
10×	`unswap-sqr_binary64`
8×	`cbrt-undiv_binary64`
7×	`pow1_binary64` `unpow-prod-down_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow-to-exp_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`unpow2_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `div-inv_binary64`
2×	`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 → 132

Calls

4 calls:

11.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
7.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
17.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

series251.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
63.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
71.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

simplify55.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5040	2476

prune156.0ms

Filtered

77 candidates to 144 candidates (-87.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	144	10	154

Merged error: 8.5b

Counts

154 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

3.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`*-un-lft-identity_binary64` `cbrt-undiv_binary64` `add-cube-cbrt_binary64` `div-exp_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`associate-r_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64`
2×	`associate-/r_binary64` `flip3--_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-inv_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

21.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
14.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series186.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
64.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify40.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5052	1355

prune128.0ms

Filtered

62 candidates to 93 candidates (-50.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 8.5b

Counts

103 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 h l) (/.f64 (.f64 M D) (.f64 2 d))))))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
8.9b	(.f64 (/.f64 h l) (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
26×	`cbrt-unprod_binary64` `prod-exp_binary64`
21×	`cbrt-undiv_binary64` `div-exp_binary64`
19×	`add-sqr-sqrt_binary64`
13×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `times-frac_binary64`
7×	`pow1_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64`
3×	`sqrt-prod_binary64`
2×	`associate-/r_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 109

Calls

4 calls:

6.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 h l) (/.f64 (.f64 M D) (.f64 2 d))))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
13.0ms	(.f64 (/.f64 h l) (/.f64 (.f64 M D) (*.f64 2 d)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 h l) (/.f64 (.f64 M D) (.f64 2 d))))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
18.0ms	(.f64 (/.f64 h l) (/.f64 (.f64 M D) (*.f64 2 d)))

simplify34.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5056	1435

prune101.0ms

Filtered

73 candidates to 121 candidates (-65.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	122	9	131

Merged error: 8.2b

Counts

131 → 9

regimes1.3s

Accuracy

0% (1.1b remaining)

Error of 8.6b against oracle of 7.5b and baseline of 8.6b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	99	38
1	99	38

end0.0ms

sample1.4s

Algorithm

intervals

Results

621.0ms	8000×	body	80	valid
244.0ms	3121×	body	80	nan
107.0ms	1298×	body	80	invalid

Details

analyze2.3s

sample51.0ms

simplify28.0ms

prune8.0ms

localize13.0ms

rewrite36.0ms

series214.0ms

simplify62.0ms

prune196.0ms

localize25.0ms

rewrite49.0ms

series251.0ms

simplify55.0ms

prune156.0ms

localize19.0ms

rewrite51.0ms

series186.0ms

simplify40.0ms

prune128.0ms

localize13.0ms

rewrite39.0ms

series96.0ms

simplify34.0ms

prune101.0ms

regimes1.3s

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.4s

Profiling