Details

sample1.0s

Algorithm

intervals

sampling

Space saved by range analysis: 45.490083%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

27.0ms	110×	body	320	valid
26.0ms	142×	body	160	valid
1.0ms	18×	body	80	nan
0.0ms	4×	body	80	valid

simplify114.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 35.0b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))

rewrite35.0ms

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))))))
12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
6.0ms	(sqrt (- (* g g) (* h h)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
69.0ms	(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 (33.0ms)

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

prune271.0ms

Filtered

64 candidates to 72 candidates (-12.5%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	52	20	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	20	73

Merged error: 31.8b

Counts

73 → 20

localize19.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(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`
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:

4.0ms	(- (* 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)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
66.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune238.0ms

Filtered

59 candidates to 71 candidates (-20.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	1	18	19
Picked	1	0	1
Done	0	0	0
Total	69	22	91

Merged error: 31.7b

Counts

91 → 22

localize18.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))

rewrite26.0ms

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:

4.0ms	(- (* g g) (* h h))
14.0ms	(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)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
68.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))

simplify35.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

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

prune226.0ms

Filtered

59 candidates to 71 candidates (-20.3%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	21	21
Picked	0	1	1
Done	0	0	0
Total	71	22	93

Merged error: 31.7b

Counts

93 → 22

localize22.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(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:

4.0ms	(- (* 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)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
70.0ms	(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)))

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

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

prune146.0ms

Filtered

59 candidates to 71 candidates (-20.3%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	3	17	20
Picked	1	0	1
Done	0	1	1
Total	72	21	93

Merged error: 31.7b

Counts

93 → 21

regimes889.0ms

Accuracy

78.9% (0.7b remaining)

Error of 31.8b against oracle of 31.1b and baseline of 34.3b

bsearch107.0ms

Steps

Iters	Range		Point
8	2.0624178133855318e-162	1.5956763801875407e-159	1.2205975679263499e-161

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	37
1	48	37
2	52	37
3	55	37
4	55	37

end0.0ms

sample3.1s

Algorithm

intervals

sampling

Space saved by range analysis: 45.490083%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

928.0ms	3725×	body	320	valid
884.0ms	4123×	body	160	valid
59.0ms	718×	body	80	nan
15.0ms	152×	body	80	valid

Details

sample1.0s

simplify114.0ms

prune4.0ms

localize17.0ms

rewrite35.0ms

series148.0ms

simplify43.0ms

prune271.0ms

localize19.0ms

rewrite24.0ms

series86.0ms

simplify37.0ms

prune238.0ms

localize18.0ms

rewrite26.0ms

series89.0ms

simplify35.0ms

prune226.0ms

localize22.0ms

rewrite24.0ms

series90.0ms

simplify36.0ms

prune146.0ms

regimes889.0ms

bsearch107.0ms

simplify3.0ms

end0.0ms

sample3.1s

Profiling