Details

sample38.0ms

Algorithm

intervals

Results

15.0ms	281×	body	80	valid
4.0ms	94×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	79	18
2	136	18
3	161	18
4	173	18
5	177	18
6	177	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize91.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 63

Calls

4 calls:

24.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	246	646
1	890	606
2	3702	588
3	5001	584

prune280.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.6b

localize96.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.3b	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
8.8b	(/ (* a c) b)
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
10.0ms	(/ (* a c) b)
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
20.0ms	(/ (* a c) b)
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	487	658
1	2217	575
2	5001	569

prune325.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.3b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite92.0ms

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-/r*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 69

Calls

4 calls:

45.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
52.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	368	755
1	1530	656
2	5001	644

prune293.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize93.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 c) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
26×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube`
15×	`add-sqr-sqrt` `times-frac`
14×	`add-cube-cbrt`
12×	`prod-exp`
10×	`pow1` `add-log-exp`
8×	`distribute-lft-out`
6×	`cbrt-unprod`
4×	`distribute-rgt-neg-in` `div-exp`
3×	`pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `rec-exp` `flip3--` `flip3-+` `sqrt-div` `1-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

78.0ms	(* (* 2.0 c) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (* 2.0 c) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
90.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	502	952
1	2367	793
2	5002	764

prune291.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

regimes193.0ms

Accuracy

92.2% (1.1b remaining)

Error of 7.6b against oracle of 6.4b and baseline of 21.1b

bsearch281.0ms

Steps

Iters	Range	Point
8	3.1248942757642245e+89	1.1714167766929137e+92	1.378005060912798e+90
10	1.2311923035801406e-286	5.850504429783805e-277	1.24767440801605e-286
10	-5.024868303916657e+156	-7.485719939656648e+141	-1.8635862169116412e+149

Iters

Range

Point

3.1248942757642245e+89

1.1714167766929137e+92

1.378005060912798e+90

1.2311923035801406e-286

5.850504429783805e-277

1.24767440801605e-286

-5.024868303916657e+156

-7.485719939656648e+141

-1.8635862169116412e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	58
1	58	58

end0.0ms

sample942.0ms

Algorithm

intervals

Results

444.0ms	8738×	body	80	valid
136.0ms	2943×	body	80	nan