Details

Time bar (total: 6.2s)

sample52.0ms

Algorithm
intervals
Results
10.0ms35×body2560valid
10.0ms185×body80valid
6.0ms24×body1280valid
4.0ms76×body80nan
3.0ms17×body640valid
1.0ms4×body5120valid
1.0ms6×body320valid
0.0ms4×body160valid

simplify7.0ms

Counts
1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite115.0ms

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:
67.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series328.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
54.0ms
(- (* b b) (* 4.0 (* a c)))
85.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Counts
89 → 89

prune259.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- 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)))))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite95.0ms

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:
50.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series336.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
86.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
79.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify66.0ms

Counts
137 → 137

prune284.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize34.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity
10×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg distribute-rgt-neg-in neg-log
Counts
4 → 63
Calls
4 calls:
26.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
81.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify101.0ms

Counts
75 → 75

prune307.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
5.5b
(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
21.7b
(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×*-un-lft-identity
10×add-log-exp
8×add-cube-cbrt log-prod exp-sum
7×pow1 sqrt-prod
6×exp-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log log-pow difference-of-squares
2×sub-neg log-div sqrt-pow1 pow1/2 exp-diff distribute-lft-out--
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in neg-log rem-exp-log
Counts
4 → 68
Calls
4 calls:
9.0ms
(- (* b b) (* 4.0 (* a c)))
19.0ms
(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
28.0ms
(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
88.0ms
(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
80.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify111.0ms

Counts
80 → 80

prune213.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

regimes321.0ms

Accuracy

89.5% (3.0b remaining)

Error of 8.4b against oracle of 5.4b and baseline of 34.1b

bsearch249.0ms

Steps
ItersRangePoint
8
9.012561940608131e+125
4.309422734686771e+129
1.156413586509535e+129
8
-8.286393182168363e-290
-4.532619757041417e-294
-3.38929022928694e-293
10
-1.6145330241135586e+155
-4.1230913930237915e+136
-5.978111652548667e+136

simplify2.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
530.0ms5896×body80valid
505.0ms1059×body2560valid
489.0ms2942×body80nan
269.0ms916×body1280valid
125.0ms458×body640valid
97.0ms85×body5120valid
39.0ms244×body320valid
11.0ms107×body160valid