Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	187×	body	80	valid
6.0ms	27×	body	2560	valid
6.0ms	33×	body	1280	valid
3.0ms	76×	body	80	nan
2.0ms	13×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	10×	body	320	valid
0.0ms	3×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune2.0ms

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: 33.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

14.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune208.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	9	90

Merged error: 5.9b

Counts

90 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

15.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
43.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	469	991
1	2048	866
2	5002	857

prune200.0ms

Filtered

97 candidates to 65 candidates (67.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	96	10	106

Merged error: 5.9b

Counts

106 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.3b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
10×	`add-log-exp`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`times-frac` `distribute-lft-out` `associate-/l*`
3×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`flip3--` `sqrt-div` `associate-*l/` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 71

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
158.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify103.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	502	969
1	3079	812
2	5002	794

prune202.0ms

Filtered

83 candidates to 63 candidates (75.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	6	2	8
Picked	0	1	1
Done	0	1	1
Total	85	8	93

Merged error: 5.8b

Counts

93 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.4b	(/ (/ (* 4.0 (* a c)) 2.0) a)
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
25×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
10×	`add-log-exp`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`pow1` `div-inv`
3×	`prod-exp` `associate-/r*` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `neg-log` `clear-num` `flip-+` `associate-/l/`

Counts

4 → 92

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	543	780
1	2606	706
2	5001	702

prune233.0ms

Filtered

104 candidates to 79 candidates (76.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	105	7	112

Merged error: 5.8b

Counts

112 → 7

regimes209.0ms

Accuracy

93% (1.7b remaining)

Error of 7.1b against oracle of 5.4b and baseline of 29.7b

bsearch153.0ms

Steps

Iters	Range		Point
9	1.314833454423355e+61	1.6016599845544569e+66	1.532226663922431e+66
6	4.965075808081927e-298	7.082005123311157e-297	5.584936701048256e-297
7	-2.501148282372368e+59	-1.593441833549377e+57	-2.21751057489785e+59

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	24
1	45	24

end0.0ms

sample1.1s

Algorithm

intervals

Results

253.0ms	1065×	body	2560	valid
235.0ms	5841×	body	80	valid
166.0ms	860×	body	1280	valid
108.0ms	2902×	body	80	nan
74.0ms	481×	body	640	valid
27.0ms	242×	body	320	valid
26.0ms	85×	body	5120	valid
8.0ms	114×	body	160	valid