Details

Time bar (total: 4.7s)

sample43.0ms

Algorithm
intervals
Results
18.0ms284×body80valid
5.0ms115×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize91.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

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:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (106.0ms)

IterNodesCost
0246646
1890606
23702588
35001584

prune283.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize93.0ms

Local error

Found 4 expressions with local error:

1.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.9b
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
6.0b
(/ (* a c) b)
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite90.0ms

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))))
49.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
9.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
17.0ms
(/ (* a c) b)
62.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify54.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0487658
12217575
25001569

prune349.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.4b
(- (* b b) (* (* 4.0 a) c))
1.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

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:
16.0ms
(* (* 4.0 a) c)
7.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series199.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (* 4.0 a) c)
40.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0307469
11303428
25001417

prune279.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

localize93.0ms

Local error

Found 4 expressions with local error:

15.0b
(cbrt (* (* 4.0 a) c))
15.0b
(cbrt (* (* 4.0 a) c))
15.0b
(cbrt (* (* 4.0 a) c))
23.8b
(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 42
Calls
4 calls:
12.0ms
(cbrt (* (* 4.0 a) c))
16.0ms
(cbrt (* (* 4.0 a) c))
12.0ms
(cbrt (* (* 4.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(cbrt (* (* 4.0 a) c))
91.0ms
(cbrt (* (* 4.0 a) c))
91.0ms
(cbrt (* (* 4.0 a) c))
118.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
0205528
1568487
21926468
35001466

prune260.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

regimes254.0ms

Accuracy

93.3% (1.0b remaining)

Error of 7.4b against oracle of 6.5b and baseline of 21.0b

bsearch300.0ms

Steps
ItersRangePoint
9
1.7695728335377845e+74
3.738006738925262e+80
2.1545230570852197e+80
10
6.536821534934946e-309
9.399667015780106e-299
6.89180526786005e-309
8
-8.193557888742793e+156
-8.757358666576022e+152
-1.3750424287373025e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06484
16684
26684

end0.0ms

sample924.0ms

Algorithm
intervals
Results
438.0ms8757×body80valid
142.0ms2949×body80nan