Details

Time bar (total: 13.9s)

sample84.0ms

Algorithm
intervals
Results
29.0ms178×body80valid
14.0ms38×body2560valid
8.0ms29×body1280valid
5.0ms79×body80nan
2.0ms10×body640valid
2.0ms3×body5120valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify61.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b
(- (* b b) (* (* 3.0 a) c))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite71.0ms

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:
27.0ms
(* (* 3.0 a) c)
23.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms
(- (* b b) (* (* 3.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* 3.0 a) c)
107.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
54.0ms
(- (* b b) (* (* 3.0 a) c))
96.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify759.0ms

Counts
72 → 72

prune262.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 3.0 a) c))
0.6b
(- (* b b) (* (* 3.0 a) c))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
14.0ms
(- (* b b) (* (* 3.0 a) c))
8.0ms
(- (* b b) (* (* 3.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* (* 3.0 a) c))
84.0ms
(- (* b b) (* (* 3.0 a) c))
104.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
94.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts
66 → 66

prune329.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.3b

localize48.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
19.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
94.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
94.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.2s

Counts
72 → 72

prune480.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.3b

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.9b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.9b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite289.0ms

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:
47.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
131.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
94.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series693.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
228.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
276.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
102.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.6s

Counts
166 → 166

prune570.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 8.7b

regimes649.0ms

Accuracy

95.5% (1.0b remaining)

Error of 12.4b against oracle of 11.4b and baseline of 34.3b

bsearch327.0ms

Steps
ItersRangePoint
8
2.9949035539067785e+135
2.209941139196072e+139
2.1801101637387535e+139
10
7.400183392008244e-228
2.487538800449476e-217
1.345485627050489e-224
9
-4.4874797001979404e+160
-1.588602326591779e+153
-1.3506760573432116e+154

simplify951.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.1s1087×body2560valid
407.0ms931×body1280valid
387.0ms5807×body80valid
264.0ms2994×body80nan
115.0ms447×body640valid
101.0ms117×body5120valid
77.0ms209×body320valid
13.0ms114×body160valid