Details

sample61.0ms

Algorithm

intervals

Results

11.0ms	197×	body	80	valid
11.0ms	32×	body	2560	valid
9.0ms	100×	body	80	nan
8.0ms	31×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	91	16
1	91	16

prune8.0ms

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: 32.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
0.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.8b	(- (* b b) (* 4.0 (* a c)))
23.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

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:

10.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
6.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4959	1319
1	4959	1319

prune158.0ms

Filtered

62 candidates to 84 candidates (-35.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Merged error: 5.0b

Counts

85 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* 2.0 (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
0.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.8b	(- (* b b) (* 4.0 (* a c)))
23.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 75

Calls

4 calls:

14.0ms	(/ 1 (* 2.0 (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (* 2.0 (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify61.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4959	1235
1	4959	1235

prune126.0ms

Filtered

58 candidates to 87 candidates (-50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	85	9	94

Merged error: 4.9b

Counts

94 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.2b	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
0.8b	(- (* b b) (* 4.0 (* a c)))
23.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

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:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
17.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
34.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
11.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4962	1952
1	4962	1952

prune173.0ms

Filtered

82 candidates to 119 candidates (-45.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	119	9	128

Merged error: 4.9b

Counts

128 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (* b b) (* 4.0 (* a c)))
23.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4956	836
1	4956	836

prune126.0ms

Filtered

50 candidates to 66 candidates (-32.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	66	9	75

Merged error: 4.9b

Counts

75 → 9

regimes317.0ms

Accuracy

83.2% (4.8b remaining)

Error of 10.5b against oracle of 5.7b and baseline of 34.0b

bsearch60.0ms

Steps

Iters	Range		Point
7	5.816120864114621e-92	2.0250992463148254e-90	1.0789308332029793e-91
8	-3.07876034479492e+94	-2.6562780769531156e+90	-1.887155650852303e+94

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	40
1	34	40

end0.0ms

sample1.7s

Algorithm

intervals

Results

353.0ms	1071×	body	2560	valid
334.0ms	5903×	body	80	valid
242.0ms	885×	body	1280	valid
158.0ms	2907×	body	80	nan
96.0ms	458×	body	640	valid
39.0ms	221×	body	320	valid
39.0ms	98×	body	5120	valid
13.0ms	125×	body	160	valid

Details

sample61.0ms

simplify4.0ms

prune8.0ms

localize11.0ms

rewrite25.0ms

series65.0ms

simplify49.0ms

prune158.0ms

localize13.0ms

rewrite31.0ms

series73.0ms

simplify61.0ms

prune126.0ms

localize12.0ms

rewrite34.0ms

series74.0ms

simplify67.0ms

prune173.0ms

localize17.0ms

rewrite16.0ms

series46.0ms

simplify69.0ms

prune126.0ms

regimes317.0ms

bsearch60.0ms

simplify1.0ms

end0.0ms

sample1.7s

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