Details

sample133.0ms

Algorithm

intervals

Results

28.0ms	44×	body	2560	valid
18.0ms	169×	body	80	valid
18.0ms	33×	body	1280	valid
9.0ms	89×	body	80	nan
6.0ms	15×	body	640	valid
4.0ms	5×	body	5120	valid
3.0ms	8×	body	320	valid
2.0ms	9×	body	160	valid

simplify407.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (404.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 38.2b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
26.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 72

Calls

4 calls:

23.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
7.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
17.0ms	(- (* b b) (* 4.0 (* a c)))
29.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
27.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5340	1324

prune364.0ms

Filtered

62 candidates to 84 candidates (-35.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	73	11	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	11	85

Merged error: 6.3b

Counts

85 → 11

localize7.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify5.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune70.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	10	10
Picked	1	1
Done	0	0
Total	11	11

Merged error: 6.3b

Counts

11 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
26.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
34×	`times-frac`
32×	`*-un-lft-identity`
26×	`add-exp-log`
22×	`add-cube-cbrt` `associate-r`
16×	`add-cbrt-cube`
13×	`associate-l`
8×	`div-exp` `prod-exp` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`unswap-sqr`
4×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 107

Calls

4 calls:

38.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
8.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series129.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
14.0ms	(- (* b b) (* 4.0 (* a c)))
26.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
26.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4968	1958
1	4968	1958

prune399.0ms

Filtered

83 candidates to 119 candidates (-43.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	117	13	130

Merged error: 6.2b

Counts

130 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
26.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `div-exp`
8×	`pow1` `add-log-exp`
7×	`add-cube-cbrt`
6×	`prod-exp`
4×	`cbrt-undiv` `sqrt-prod`
3×	`rec-exp` `flip3--` `times-frac` `1-exp` `flip--` `associate-/l*`
2×	`sub-neg` `pow-flip` `sqrt-div` `diff-log` `cbrt-unprod` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 75

Calls

4 calls:

33.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series147.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
17.0ms	(- (* b b) (* 4.0 (* a c)))
30.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
29.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4995	1252
1	4995	1252

prune185.0ms

Filtered

57 candidates to 87 candidates (-52.6%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	86	14	100

Merged error: 6.2b

Counts

100 → 14

regimes828.0ms

Accuracy

86% (4.8b remaining)

Error of 10.4b against oracle of 5.7b and baseline of 39.5b

bsearch121.0ms

Steps

Iters	Range		Point
8	1.1014370434386659e-116	2.8344605185111195e-113	2.3420279175473307e-113
9	-7.957515769842868e+111	-7.937815030826972e+105	-3.3421727427471946e+111

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	92	40
1	92	40

end0.0ms

sample3.2s

Algorithm

intervals

Results

664.0ms	1082×	body	2560	valid
613.0ms	5801×	body	80	valid
445.0ms	888×	body	1280	valid
290.0ms	2933×	body	80	nan
189.0ms	455×	body	640	valid
77.0ms	256×	body	320	valid
73.0ms	99×	body	5120	valid
24.0ms	119×	body	160	valid

Details

sample133.0ms

simplify407.0ms

prune16.0ms

localize21.0ms

rewrite58.0ms

series126.0ms

simplify73.0ms

prune364.0ms

localize7.0ms

rewrite0.0ms

series0.0ms

simplify5.0ms

prune70.0ms

localize25.0ms

rewrite79.0ms

series129.0ms

simplify102.0ms

prune399.0ms

localize24.0ms

rewrite69.0ms

series147.0ms

simplify75.0ms

prune185.0ms

regimes828.0ms

bsearch121.0ms

simplify3.0ms

end0.0ms

sample3.2s

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