Details

analyze2.4s

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

sample57.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
11.0ms	140×	body	80	nan
4.0ms	54×	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: 13.3b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

2.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.1b	(/.f64 (.f64 M D) (.f64 2 d))
4.7b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
9.6b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite35.0ms

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:

8.0ms	(.f64 w0 (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))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
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)))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
64.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
35.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

simplify60.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4983	1890
1	4983	1890

prune123.0ms

Filtered

84 candidates to 128 candidates (-52.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	121	8	129

Merged error: 8.0b

Counts

129 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

2.8b	(.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)))
4.1b	(/.f64 (.f64 M D) (.f64 2 d))
4.2b	(.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))))
4.7b	(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)))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

609×	`add-exp-log_binary64`
325×	`prod-exp_binary64`
184×	`div-exp_binary64`
75×	`pow-exp_binary64`
54×	`add-cbrt-cube_binary64`
45×	`associate-r_binary64`
43×	`cbrt-unprod_binary64` `times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
36×	`cbrt-prod_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`cbrt-undiv_binary64`
15×	`pow-to-exp_binary64`
11×	`associate-l_binary64`
8×	`unswap-sqr_binary64`
7×	`pow1_binary64` `unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `div-inv_binary64`
3×	`unpow2_binary64` `sqr-pow_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `flip--_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 245

Calls

4 calls:

26.0ms	(.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))))
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)))))

series176.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(.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))))
65.0ms	(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)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5036	5159

prune144.0ms

Filtered

119 candidates to 257 candidates (-116.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	255	2	257
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	255	10	265

Merged error: 8.0b

Counts

265 → 10

localize34.0ms

Local error

Found 4 expressions with local error:

4.7b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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)))))
32.4b	(cbrt.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)))))
32.4b	(cbrt.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)))))
32.4b	(cbrt.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)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cbrt-div_binary64` `associate-*r/_binary64` `pow1/3_binary64` `sqrt-prod_binary64` `cbrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`

Counts

4 → 45

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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)))))
12.0ms	(cbrt.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)))))
12.0ms	(cbrt.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)))))
12.0ms	(cbrt.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)))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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)))))
102.0ms	(cbrt.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)))))
104.0ms	(cbrt.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)))))
106.0ms	(cbrt.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)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5789	1475

prune93.0ms

Filtered

48 candidates to 57 candidates (-18.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	57	10	67

Merged error: 8.0b

Counts

67 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

4.1b	(/.f64 (.f64 M D) (.f64 2 d))
4.1b	(/.f64 (.f64 M D) (.f64 2 d))
4.7b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 h l) (/.f64 (.f64 M D) (.f64 2 d))))))
9.2b	(.f64 (/.f64 h l) (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite37.0ms

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	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
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))))))
14.0ms	(.f64 (/.f64 h l) (/.f64 (.f64 M D) (*.f64 2 d)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
66.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 h l) (/.f64 (.f64 M D) (.f64 2 d))))))
18.0ms	(.f64 (/.f64 h l) (/.f64 (.f64 M D) (*.f64 2 d)))

simplify31.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5056	1435

prune77.0ms

Filtered

73 candidates to 121 candidates (-65.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	3	3	6
Picked	1	0	1
Done	1	2	3
Total	124	7	131

Merged error: 8.0b

Counts

131 → 7

regimes849.0ms

Accuracy

0% (2.0b remaining)

Error of 9.1b against oracle of 7.2b and baseline of 9.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	156	33
1	156	33

end0.0ms

sample1.5s

Algorithm

intervals

Results

632.0ms	8000×	body	80	valid
264.0ms	3213×	body	80	nan
111.0ms	1313×	body	80	invalid

Details

analyze2.4s

sample57.0ms

simplify29.0ms

prune4.0ms

localize13.0ms

rewrite35.0ms

series214.0ms

simplify60.0ms

prune123.0ms

localize24.0ms

rewrite79.0ms

series176.0ms

simplify70.0ms

prune144.0ms

localize34.0ms

rewrite41.0ms

series390.0ms

simplify42.0ms

prune93.0ms

localize13.0ms

rewrite37.0ms

series97.0ms

simplify31.0ms

prune77.0ms

regimes849.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.5s

Profiling