Details

Time bar (total: 6.3s)

sample82.0ms

Algorithm
intervals
Results
20.0ms195×body80valid
17.0ms36×body2560valid
13.0ms100×body80nan
10.0ms25×body1280valid
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))))

rewrite59.0ms

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:
38.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms
(- (- 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))))

series289.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0404890
11481801
25001796

prune269.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize12.0ms

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))))

rewrite52.0ms

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:
13.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.0ms
(/ 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))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
112.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
50.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05331804
125441605
250021531

prune281.0ms

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

rewrite80.0ms

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×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
59.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
97.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
44.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0469991
12048866
25002857

prune246.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.7b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.1b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
11.4b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
63×*-un-lft-identity
52×times-frac
51×add-exp-log
30×add-cube-cbrt associate-*l*
27×add-cbrt-cube
20×prod-exp difference-of-squares
16×div-exp
13×sqrt-prod distribute-lft-out
10×distribute-lft-out--
8×cbrt-undiv cbrt-unprod
7×pow1 associate-*r*
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip-- associate-/l*
3×div-inv
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 152
Calls
4 calls:
20.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
66.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
31.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series725.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
365.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
205.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify121.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
07642421
137162067
250012044

prune390.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.7b

regimes185.0ms

Accuracy

88.1% (3.1b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 31.9b

bsearch254.0ms

Steps
ItersRangePoint
7
6.714891876596302e+121
1.686395921989292e+123
1.1800329617120703e+123
9
-3.9915988204775135e-284
-1.6488370871160183e-290
-1.1084181013772221e-289
9
-3.648537902993238e+76
-1.3447839841174185e+67
-1.8746290509448952e+74

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04326
14526
24526

end0.0ms

sample2.3s

Algorithm
intervals
Results
592.0ms5865×body80valid
548.0ms1094×body2560valid
350.0ms871×body1280valid
275.0ms2931×body80nan
146.0ms453×body640valid
59.0ms240×body320valid
59.0ms101×body5120valid
21.0ms117×body160valid