Details

Time bar (total: 4.5s)

sample39.0ms

Algorithm
intervals
Results
8.0ms201×body80valid
6.0ms35×body1280valid
6.0ms27×body2560valid
3.0ms87×body80nan
2.0ms12×body640valid
1.0ms7×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

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: 32.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

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))
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))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0404890
11481801
25001796

prune250.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite82.0ms

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:
57.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
15.0ms
(- (- 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:
94.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0469991
12048866
25002857

prune235.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.8b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
10.3b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite126.0ms

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:
18.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
69.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
26.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series513.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
165.0ms
(* (/ (+ 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))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify122.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
07642421
137162067
250012044

prune396.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
1.9b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0b
(/ (* 4.0 (* a c)) (* 2.0 a))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×add-log-exp
7×*-un-lft-identity
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l* distribute-lft-out--
Counts
4 → 67
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
19.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series205.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0403576
12221498
25001498

prune193.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes154.0ms

Accuracy

95.9% (0.9b remaining)

Error of 6.7b against oracle of 5.8b and baseline of 28.8b

bsearch163.0ms

Steps
ItersRangePoint
8
2.1878188410446244e+107
3.8616146939177386e+111
2.8568501197790958e+109
9
2.1745589989703455e-245
7.342308417195682e-240
2.5402182456312607e-243
6
-2.0136180636941443e+142
-1.4127342237564056e+141
-2.61268387266151e+141

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04523
14723
24723

end0.0ms

sample1.1s

Algorithm
intervals
Results
254.0ms1110×body2560valid
225.0ms5789×body80valid
158.0ms885×body1280valid
114.0ms2998×body80nan
63.0ms448×body640valid
27.0ms101×body5120valid
27.0ms253×body320valid
11.0ms126×body160valid