Details

Time bar (total: 5.9s)

sample80.0ms

Algorithm
intervals
Results
19.0ms195×body80valid
17.0ms36×body2560valid
13.0ms25×body1280valid
9.0ms100×body80nan
4.0ms13×body640valid
2.0ms4×body5120valid
2.0ms7×body320valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

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:
35.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
53.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0404890
11481801
25001796

prune258.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 125
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
110.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify68.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05331804
125441605
250021531

prune265.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.2b
(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

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×sub-neg div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv distribute-rgt-in frac-times rec-exp distribute-rgt-neg-in distribute-lft-in sqrt-div 1-exp associate-*r/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ *-commutative div-inv unswap-sqr
Counts
4 → 88
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
56.0ms
(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series509.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
312.0ms
(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify62.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04751025
12257896
25001893

prune229.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.7b

localize22.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0b
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
18.5b
(- (pow b 2) (pow b 2))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
23×*-un-lft-identity
22×unpow-prod-down
19×add-exp-log
16×difference-of-squares
15×add-cube-cbrt
13×add-cbrt-cube
12×unpow2 sqr-pow
10×distribute-rgt-out-- add-log-exp
8×distribute-lft-out--
7×div-exp
5×pow1 associate-/l/
4×cbrt-undiv prod-exp
3×flip3-+ times-frac associate-/r* sqrt-prod flip-+
2×frac-times flip3-- sqrt-div associate-*r/ sum-log flip-- cbrt-unprod distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square rec-exp distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 +-inverses diff-log 1-exp neg-log associate-*l/ clear-num div-inv associate-/l*
Counts
4 → 107
Calls
4 calls:
11.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
79.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
11.0ms
(- (pow b 2) (pow b 2))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series166.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
1.0ms
(- (pow b 2) (pow b 2))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify205.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (195.0ms)

IterNodesCost
0595778
13991571
25002555

prune297.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.7b

regimes208.0ms

Accuracy

89% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 34.3b

bsearch252.0ms

Steps
ItersRangePoint
7
6.714891876596302e+121
1.686395921989292e+123
1.1800329617120703e+123
9
-2.9544973625012568e-276
-7.002078871801916e-282
-1.1885507100476909e-281
9
-3.648537902993238e+76
-1.3447839841174185e+67
-1.8746290509448952e+74

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04931
14931

end0.0ms

sample2.3s

Algorithm
intervals
Results
598.0ms5865×body80valid
539.0ms1094×body2560valid
351.0ms871×body1280valid
278.0ms2931×body80nan
149.0ms453×body640valid
61.0ms240×body320valid
58.0ms101×body5120valid
20.0ms117×body160valid