Details

sample94.0ms

Algorithm

intervals

Results

28.0ms	118×	body	320	valid
22.0ms	280×	body	80	nan
21.0ms	136×	body	160	valid
0.0ms	2×	body	80	valid

simplify116.0ms

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

prune6.0ms

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: 34.5b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
10.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
28.0b	(sqrt (- (* g g) (* h h)))
28.0b	(sqrt (- (* g g) (* h h)))

rewrite32.0ms

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

series140.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(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)))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (33.0ms)

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

prune260.0ms

Filtered

72 candidates to 64 candidates (11.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	51	21	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	21	73

Merged error: 29.4b

Counts

73 → 21

localize19.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
5.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
28.0b	(sqrt (- (* g g) (* h h)))
28.0b	(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)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
63.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
8.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune236.0ms

Filtered

71 candidates to 59 candidates (16.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	70	22	92

Merged error: 29.1b

Counts

92 → 22

localize18.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
5.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
28.0b	(sqrt (- (* g g) (* h h)))
28.0b	(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:

3.0ms	(- (* g g) (* h h))
12.0ms	(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)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (* 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)))

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune237.0ms

Filtered

71 candidates to 59 candidates (16.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	21	21
Picked	1	0	1
Done	0	0	0
Total	68	25	93

Merged error: 29.0b

Counts

93 → 25

localize20.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
10.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
28.0b	(sqrt (- (* g g) (* h h)))
28.0b	(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:

3.0ms	(- (* 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)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (* g g) (* h h))
64.0ms	(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	321	569
1	1271	537
2	5002	533

prune139.0ms

Filtered

71 candidates to 59 candidates (16.9%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	4	20	24
Picked	1	0	1
Done	0	0	0
Total	72	24	96

Merged error: 29.0b

Counts

96 → 24

regimes1.1s

Accuracy

80.5% (0.6b remaining)

Error of 31.5b against oracle of 30.9b and baseline of 33.9b

bsearch59.0ms

Steps

Iters	Range		Point
5	2.4585323721607486e-159	7.473810393674044e-159	2.9583808105567004e-159

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	56
1	61	56
2	71	56
3	90	56
4	100	56
5	112	56
6	117	56
7	124	56
8	134	56
9	143	56
10	153	56
11	163	56
12	177	56
13	177	56

end0.0ms

sample2.8s

Algorithm

intervals

Results

890.0ms	3717×	body	320	valid
664.0ms	4140×	body	160	valid
627.0ms	8019×	body	80	nan
12.0ms	143×	body	80	valid

Iter	Nodes	Cost
0	49	56
1	61	56
2	71	56
3	90	56
4	100	56
5	112	56
6	117	56
7	124	56
8	134	56
9	143	56
10	153	56
11	163	56
12	177	56
13	177	56

Iter	Nodes	Cost
0	49	56
1	61	56
2	71	56
3	90	56
4	100	56
5	112	56
6	117	56
7	124	56
8	134	56
9	143	56
10	153	56
11	163	56
12	177	56
13	177	56

Details

sample94.0ms

simplify116.0ms

prune6.0ms

localize17.0ms

rewrite32.0ms

series140.0ms

simplify42.0ms

prune260.0ms

localize19.0ms

rewrite24.0ms

series84.0ms

simplify36.0ms

prune236.0ms

localize18.0ms

rewrite24.0ms

series84.0ms

simplify36.0ms

prune237.0ms

localize20.0ms

rewrite24.0ms

series83.0ms

simplify37.0ms

prune139.0ms

regimes1.1s

bsearch59.0ms

simplify8.0ms

end0.0ms

sample2.8s

Profiling

Iter	Nodes	Cost
0	49	56
1	61	56
2	71	56
3	90	56
4	100	56
5	112	56
6	117	56
7	124	56
8	134	56
9	143	56
10	153	56
11	163	56
12	177	56
13	177	56