Details

Time bar (total: 15.6s)

sample68.0ms

Algorithm
intervals
Results
11.0ms191×body80valid
10.0ms25×body2560valid
9.0ms26×body1280valid
6.0ms92×body80nan
6.0ms18×body640valid
3.0ms6×body5120valid
2.0ms10×body320valid
0.0ms2×body160valid

simplify75.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (* b b) (* (* 4.0 a) c))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
23.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
119.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify833.0ms

Counts
82 → 82

prune340.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize39.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite290.0ms

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:
33.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
130.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
101.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series786.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
268.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
285.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
119.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
166 → 166

prune736.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.6b
(/ (* 2.0 a) (* 4.0 (* a c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4.0 a) c))
56.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
35.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
125.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
82 → 82

prune356.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
113×add-exp-log
51×prod-exp
44×div-exp
29×add-cbrt-cube
16×rec-exp 1-exp
14×associate-/r/
12×add-sqr-sqrt
11×pow1 frac-times *-un-lft-identity
10×cbrt-undiv add-log-exp
9×cbrt-unprod
8×flip3-- flip--
7×add-cube-cbrt associate-*l/
5×associate-*r/
4×sqrt-prod
3×pow-flip times-frac diff-log pow-prod-down un-div-inv associate-/l*
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r* div-inv inv-pow
Counts
4 → 116
Calls
4 calls:
226.0ms
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms
(- (* b b) (* (* 4.0 a) c))
58.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series559.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
62.0ms
(- (* b b) (* (* 4.0 a) c))
129.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
128 → 128

prune406.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

regimes305.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 29.8b

bsearch293.0ms

Steps
ItersRangePoint
10
1.1938117014962488e+94
7.783906932586822e+104
1.2749218400875242e+104
8
-1.373264203576674e-281
-7.437867491150874e-285
-1.0518595521494322e-283
8
-9.386613231324957e+115
-9.035077376741492e+112
-3.01058925795013e+115

simplify1.1s

end0.0ms

sample3.5s

Algorithm
intervals
Results
933.0ms1063×body2560valid
729.0ms5781×body80valid
538.0ms893×body1280valid
313.0ms2847×body80nan
202.0ms502×body640valid
76.0ms118×body5120valid
54.0ms235×body320valid
16.0ms109×body160valid