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

sample52.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
7.0ms	95×	body	80	nan
3.0ms	38×	body	80	invalid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5464	18

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: 15.6b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.2b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
6.3b	(/.f64 (.f64 M D) (.f64 2 d))
11.9b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite38.0ms

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:

11.0ms	(.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))
11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series207.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
64.0ms	(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))
31.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

simplify58.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4983	1890
1	4983	1890

prune136.0ms

Filtered

84 candidates to 128 candidates (-52.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Merged error: 7.5b

Counts

129 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

4.1b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
4.2b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
6.1b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
6.3b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite32.0ms

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:

8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
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)
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series188.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
109.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
40.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify32.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5284	1462

prune98.0ms

Filtered

69 candidates to 111 candidates (-60.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	110	9	119

Merged error: 7.2b

Counts

119 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

4.1b	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
4.2b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
4.8b	(*.f64 (/.f64 M 2) (/.f64 D d))
6.1b	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
43×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64` `prod-exp_binary64`
25×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
20×	`div-exp_binary64`
19×	`associate-r_binary64`
16×	`associate-l_binary64`
10×	`pow-exp_binary64`
7×	`pow1_binary64` `unswap-sqr_binary64`
6×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r*_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `unpow-prod-down_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 123

Calls

4 calls:

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

series189.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
110.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
6.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
37.0ms	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)

simplify35.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5393	1699

prune113.0ms

Filtered

92 candidates to 135 candidates (-46.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	136	8	144

Merged error: 7.2b

Counts

144 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

4.0b	(/.f64 h (/.f64 l (pow.f64 (*.f64 (/.f64 D d) (/.f64 M 2)) 2)))
4.2b	(sqrt.f64 (-.f64 1 (/.f64 h (/.f64 l (pow.f64 (*.f64 (/.f64 D d) (/.f64 M 2)) 2)))))
4.8b	(*.f64 (/.f64 D d) (/.f64 M 2))
5.5b	(/.f64 l (pow.f64 (*.f64 (/.f64 D d) (/.f64 M 2)) 2))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

192×	`times-frac_binary64`
131×	`add-sqr-sqrt_binary64`
100×	`*-un-lft-identity_binary64`
93×	`add-cube-cbrt_binary64`
67×	`add-exp-log_binary64`
34×	`div-exp_binary64`
28×	`associate-/r*_binary64`
23×	`add-cbrt-cube_binary64`
18×	`unpow2_binary64` `sqr-pow_binary64`
16×	`unpow-prod-down_binary64`
14×	`sqrt-prod_binary64`
13×	`associate-r_binary64` `associate-l_binary64`
12×	`prod-exp_binary64`
10×	`difference-of-squares_binary64` `pow-exp_binary64`
8×	`cbrt-undiv_binary64` `div-inv_binary64`
7×	`pow1_binary64`
6×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
2×	`pow-to-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 233

Calls

4 calls:

9.0ms	(/.f64 h (/.f64 l (pow.f64 (*.f64 (/.f64 D d) (/.f64 M 2)) 2)))
27.0ms	(sqrt.f64 (-.f64 1 (/.f64 h (/.f64 l (pow.f64 (*.f64 (/.f64 D d) (/.f64 M 2)) 2)))))
11.0ms	(*.f64 (/.f64 D d) (/.f64 M 2))
6.0ms	(/.f64 l (pow.f64 (*.f64 (/.f64 D d) (/.f64 M 2)) 2))

series182.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/.f64 h (/.f64 l (pow.f64 (*.f64 (/.f64 D d) (/.f64 M 2)) 2)))
71.0ms	(sqrt.f64 (-.f64 1 (/.f64 h (/.f64 l (pow.f64 (*.f64 (/.f64 D d) (/.f64 M 2)) 2)))))
12.0ms	(*.f64 (/.f64 D d) (/.f64 M 2))
34.0ms	(/.f64 l (pow.f64 (*.f64 (/.f64 D d) (/.f64 M 2)) 2))

simplify79.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4973	4336
1	4973	4336

prune192.0ms

Filtered

181 candidates to 245 candidates (-35.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	246	7	253

Merged error: 7.0b

Counts

253 → 7

regimes1.1s

Accuracy

0.2% (1.8b remaining)

Error of 8.3b against oracle of 6.5b and baseline of 8.3b

bsearch26.0ms

Steps

Iters	Range		Point
7	-7.997782824435526e+226	-3.8817865196339306e+225	-2.1608776803958767e+226

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	146	52
1	146	52

end0.0ms

sample1.4s

Algorithm

intervals

Results

602.0ms	8000×	body	80	valid
234.0ms	3022×	body	80	nan
101.0ms	1275×	body	80	invalid

Details

analyze2.3s

sample52.0ms

simplify29.0ms

prune4.0ms

localize14.0ms

rewrite38.0ms

series207.0ms

simplify58.0ms

prune136.0ms

localize14.0ms

rewrite32.0ms

series188.0ms

simplify32.0ms

prune98.0ms

localize13.0ms

rewrite38.0ms

series189.0ms

simplify35.0ms

prune113.0ms

localize13.0ms

rewrite64.0ms

series182.0ms

simplify79.0ms

prune192.0ms

regimes1.1s

bsearch26.0ms

simplify3.0ms

end0.0ms

sample1.4s

Profiling