Details

sample110.0ms

Algorithm

intervals

Results

30.0ms	120×	body	320	valid
27.0ms	135×	body	160	valid
17.0ms	201×	body	80	nan
0.0ms	1×	body	80	valid

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	43	21
1	122	21
2	299	21
3	591	21
4	931	21
5	1162	21
6	1388	21
7	2798	21
8	5001	21

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 40.1b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

7.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
11.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
32.9b	(sqrt (- (* g g) (* h h)))
32.9b	(sqrt (- (* g g) (* h h)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
11.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
3.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
63.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify43.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	386	766
1	1391	724
2	5002	718

prune257.0ms

Filtered

72 candidates to 64 candidates (11.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	54	18	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	18	73

Merged error: 35.0b

Counts

73 → 18

localize23.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
7.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
32.9b	(sqrt (- (* g g) (* h h)))
32.9b	(sqrt (- (* g g) (* h h)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
11.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
65.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	298	569
1	1198	537
2	5002	533

prune235.0ms

Filtered

71 candidates to 59 candidates (16.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	71	18	89

Merged error: 34.3b

Counts

89 → 18

localize19.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
7.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
32.9b	(sqrt (- (* g g) (* h h)))
32.9b	(sqrt (- (* g g) (* h h)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (* g g) (* h h))
62.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	298	569
1	1198	537
2	5002	533

prune220.0ms

Filtered

71 candidates to 59 candidates (16.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	17	17
Picked	1	0	1
Done	0	0	0
Total	71	18	89

Merged error: 34.3b

Counts

89 → 18

localize20.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
11.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
32.9b	(sqrt (- (* g g) (* h h)))
32.9b	(sqrt (- (* g g) (* h h)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
13.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
60.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	321	569
1	1271	537
2	5002	533

prune329.0ms

Filtered

71 candidates to 59 candidates (16.9%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	71	18	89

Merged error: 34.3b

Counts

89 → 18

regimes930.0ms

Accuracy

84.8% (0.6b remaining)

Error of 32.9b against oracle of 32.4b and baseline of 36.0b

bsearch150.0ms

Steps

Iters	Range		Point
12	2.897146004413971e-210	3.6410551725971376e-135	5.53107825321531e-161

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	41
1	48	41
2	52	41
3	55	41
4	55	41

end0.0ms

sample2.7s

Algorithm

intervals

Results

967.0ms	3721×	body	320	valid
713.0ms	4143×	body	160	valid
525.0ms	6211×	body	80	nan
12.0ms	136×	body	80	valid

Details

sample110.0ms

simplify118.0ms

prune4.0ms

localize20.0ms

rewrite31.0ms

series140.0ms

simplify43.0ms

prune257.0ms

localize23.0ms

rewrite23.0ms

series84.0ms

simplify37.0ms

prune235.0ms

localize19.0ms

rewrite24.0ms

series83.0ms

simplify37.0ms

prune220.0ms

localize20.0ms

rewrite25.0ms

series81.0ms

simplify39.0ms

prune329.0ms

regimes930.0ms

bsearch150.0ms

simplify3.0ms

end0.0ms

sample2.7s

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