Details

sample41.0ms

Algorithm

intervals

Results

6.0ms	184×	body	80	valid
5.0ms	34×	body	1280	valid
5.0ms	25×	body	2560	valid
4.0ms	115×	body	80	nan
2.0ms	9×	body	5120	valid
2.0ms	15×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	5×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 3.0 a) c))
0.4b	(* (* 3.0 a) c)
1.7b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `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` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(* (* 3.0 a) c)
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(* (* 3.0 a) c)
69.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
63.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5002	417

prune186.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.5b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.0b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite185.0ms

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:

23.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
86.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
59.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
158.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
164.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
62.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify146.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (124.0ms)

Iter	Nodes	Cost
0	647	2692
1	3114	2439
2	5001	2426

prune422.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 3.0 a) c)
1.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.7b	(/ (* 3.0 a) (* 3.0 (* a c)))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

18.0ms	(* (* 3.0 a) c)
25.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (* 3.0 a) c)
67.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
10.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
62.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	440	600
1	2971	486
2	5001	456

prune203.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 3.0 a) c))
0.4b	(* (* 3.0 a) c)
1.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `associate-l` `neg-log` `*-commutative`

Counts

4 → 63

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(* (* 3.0 a) c)
23.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(* (* 3.0 a) c)
71.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
63.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	298	517
1	1262	478
2	5001	471

prune168.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.6b

regimes287.0ms

Accuracy

93.8% (1.4b remaining)

Error of 9.0b against oracle of 7.6b and baseline of 29.5b

bsearch153.0ms

Steps

Iters	Range	Point
9	2.5943009456277367e+151	2.863179527023367e+158	1.5374040547673884e+153
6	-3.405927582379186e-150	-4.860750269204613e-151	-4.9276367402926466e-151
9	-2.3517657564579724e+121	-1.0016636615098116e+114	-1.78846664658268e+121

Iters

Range

Point

2.5943009456277367e+151

2.863179527023367e+158

1.5374040547673884e+153

-3.405927582379186e-150

-4.860750269204613e-151

-4.9276367402926466e-151

-2.3517657564579724e+121

-1.0016636615098116e+114

-1.78846664658268e+121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	45
1	57	45
2	57	45

end0.0ms

sample1.2s

Algorithm

intervals

Results

222.0ms	1059×	body	2560	valid
217.0ms	5786×	body	80	valid
145.0ms	897×	body	1280	valid
100.0ms	2934×	body	80	nan
63.0ms	489×	body	640	valid
29.0ms	114×	body	5120	valid
23.0ms	230×	body	320	valid
7.0ms	119×	body	160	valid