Details

sample43.0ms

Algorithm

intervals

Results

11.0ms	37×	body	2560	valid
7.0ms	196×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	91×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
2.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune222.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
7.5b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
141.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
179.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	651	2692
1	3139	2439
2	5002	2426

prune433.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
0.5b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0b	(/ (* 2.0 a) (* 4.0 (* a c)))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

2.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	429	637
1	2471	542
2	5003	534

prune215.0ms

Filtered

82 candidates to 55 candidates (67.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b	(- (* b b) (* (* 4.0 a) c))
0.5b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

49.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
2.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	445	997
1	1857	906
2	5001	896

prune248.0ms

Filtered

101 candidates to 73 candidates (72.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

regimes165.0ms

Accuracy

81.5% (4.5b remaining)

Error of 9.8b against oracle of 5.3b and baseline of 29.5b

bsearch90.0ms

Steps

Iters	Range		Point
8	2.531505514381809e+64	5.72577144612764e+68	1.6161993363323858e+68
3	-2.3762030729656124e-61	-1.6676843733113775e-61	-1.889096466953326e-61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	19
1	55	19
2	59	19
3	59	19

end0.0ms

sample1.2s

Algorithm

intervals

Results

264.0ms	1122×	body	2560	valid
242.0ms	5762×	body	80	valid
162.0ms	856×	body	1280	valid
103.0ms	2821×	body	80	nan
66.0ms	449×	body	640	valid
36.0ms	128×	body	5120	valid
28.0ms	255×	body	320	valid
9.0ms	123×	body	160	valid