Details

sample69.0ms

Algorithm

intervals

Results

22.0ms	130×	body	320	valid
15.0ms	266×	body	80	nan
14.0ms	122×	body	160	valid
0.0ms	4×	body	80	valid

simplify128.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	21
1	125	21
2	317	21
3	648	21
4	1073	21
5	1417	21
6	1725	21
7	3333	21
8	5002	21

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 39.3b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
10.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
32.8b	(sqrt (- (* g g) (* h h)))
32.8b	(sqrt (- (* g g) (* h h)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

34×	`cbrt-div`
20×	`frac-times`
16×	`*-commutative`
12×	`associate-/r*`
10×	`associate-*l/`
8×	`flip3--` `sqrt-prod` `flip--` `difference-of-squares`
6×	`cbrt-prod` `frac-2neg` `flip3-+` `clear-num` `flip-+`
4×	`sqrt-div` `associate-*r/`
2×	`pow1/2` `pow1/3` `associate-l` `div-inv`

Counts

4 → 56

Calls

4 calls:

9.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series723.0ms

Counts

4 → 12

Calls

4 calls:

307.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
321.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify70.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	617	1026
1	2787	1026
2	5001	1026

prune427.0ms

Filtered

68 candidates to 62 candidates (91.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	50	18	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	18	69

Merged error: 34.5b

Counts

69 → 18

localize20.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.8b	(sqrt (- (* g g) (* h h)))
32.8b	(sqrt (- (* g g) (* h h)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-commutative`
17×	`cbrt-div`
12×	`difference-of-squares`
10×	`frac-times`
9×	`flip3--` `flip--`
8×	`sqrt-prod`
6×	`associate-/r*`
5×	`associate-*l/`
4×	`sqrt-div` `prod-diff`
3×	`cbrt-prod` `frac-2neg` `clear-num`
2×	`pow1/2` `fma-neg` `associate-*r/`
1×	`sub-neg` `pow1/3` `associate-l` `div-inv`

Counts

4 → 49

Calls

4 calls:

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

series438.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
309.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify48.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	405	630
1	1808	627
2	5001	624

prune344.0ms

Filtered

61 candidates to 44 candidates (72.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	52	9	61
Fresh	10	7	17
Picked	1	0	1
Done	0	0	0
Total	63	16	79

Merged error: 33.9b

Counts

79 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
3.2b	(- (* g g) (* h h))
32.8b	(sqrt (- (* g g) (* h h)))
32.8b	(sqrt (- (* g g) (* h h)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-commutative`
16×	`difference-of-squares`
8×	`prod-diff` `sqrt-prod`
4×	`flip3--` `fma-neg` `sqrt-div` `flip--`
2×	`sub-neg` `pow1/2`

Counts

4 → 42

Calls

4 calls:

5.0ms	(- (* g g) (* h h))
5.0ms	(- (* g g) (* h h))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
36.0ms	(- (* g g) (* h h))
45.0ms	(sqrt (- (* g g) (* h h)))
52.0ms	(sqrt (- (* g g) (* h h)))

simplify88.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	92	234
1	321	228
2	816	222
3	2639	196
4	5002	196

prune258.0ms

Filtered

54 candidates to 28 candidates (51.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	54	16	70

Merged error: 33.9b

Counts

70 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
3.2b	(- (* g g) (* h h))
32.8b	(sqrt (- (* g g) (* h h)))
32.8b	(sqrt (- (* g g) (* h h)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-commutative`
16×	`difference-of-squares`
8×	`prod-diff` `sqrt-prod`
4×	`flip3--` `fma-neg` `sqrt-div` `flip--`
2×	`sub-neg` `pow1/2`

Counts

4 → 42

Calls

4 calls:

5.0ms	(- (* g g) (* h h))
5.0ms	(- (* g g) (* h h))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
51.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify93.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	92	234
1	321	228
2	816	222
3	2639	196
4	5002	196

prune363.0ms

Filtered

54 candidates to 28 candidates (51.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	54	16	70

Merged error: 33.9b

Counts

70 → 16

regimes597.0ms

Accuracy

53.4% (0.6b remaining)

Error of 31.9b against oracle of 31.3b and baseline of 32.6b

bsearch182.0ms

Steps

Iters	Range		Point
12	9.882066756411172e-177	1.6329938810163285e-136	5.803774567702152e-156

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	43
1	57	43
2	61	43
3	64	43
4	64	43

end0.0ms

sample1.9s

Algorithm

intervals

Results

627.0ms	3791×	body	320	valid
456.0ms	4069×	body	160	valid
441.0ms	8105×	body	80	nan
8.0ms	140×	body	80	valid