Details

Time bar (total: 18.7s)

sample136.0ms

Algorithm
intervals
Results
46.0ms199×body80valid
26.0ms32×body2560valid
15.0ms26×body1280valid
11.0ms97×body80nan
8.0ms16×body640valid
8.0ms7×body5120valid
2.0ms6×body320valid
1.0ms4×body160valid

simplify260.0ms

Counts
1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize36.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b b) (* 4 (* a c))))
1.1b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.8b
(- (* b b) (* 4 (* a c)))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×times-frac add-cube-cbrt associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- insert-posit16 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 clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 81
Calls
4 calls:
Slowest
81.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
21.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
14.0ms
(sqrt (- (* b b) (* 4 (* a c))))
10.0ms
(- (* b b) (* 4 (* a c)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
100.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
83.0ms
(sqrt (- (* b b) (* 4 (* a c))))
66.0ms
(- (* b b) (* 4 (* a c)))

simplify1.7s

Counts
93 → 93

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize44.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b b) (* 4 (* a c))))
1.1b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.8b
(- (* b b) (* 4 (* a c)))
0.2b
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))

rewrite98.0ms

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
4×insert-posit16
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log cbrt-unprod pow-flip inv-pow
Counts
4 → 129
Calls
4 calls:
Slowest
49.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
26.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
10.0ms
(sqrt (- (* b b) (* 4 (* a c))))
8.0ms
(- (* b b) (* 4 (* a c)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
115.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
105.0ms
(sqrt (- (* b b) (* 4 (* a c))))
80.0ms
(- (* b b) (* 4 (* a c)))

simplify589.0ms

Counts
141 → 141

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.9b

localize34.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b b) (* 4 (* a c))))
1.1b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.8b
(- (* b b) (* 4 (* a c)))
0.2b
(* (/ 1 (* 2 a)) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))

rewrite112.0ms

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×sub-neg div-exp cbrt-unprod insert-posit16 distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×distribute-rgt-in frac-times cbrt-undiv rec-exp distribute-rgt-neg-in distribute-lft-in sqrt-div 1-exp associate-*r/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ *-commutative div-inv unswap-sqr
Counts
4 → 92
Calls
4 calls:
Slowest
75.0ms
(* (/ 1 (* 2 a)) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))
15.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
11.0ms
(sqrt (- (* b b) (* 4 (* a c))))
8.0ms
(- (* b b) (* 4 (* a c)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(* (/ 1 (* 2 a)) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))
119.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
100.0ms
(sqrt (- (* b b) (* 4 (* a c))))
63.0ms
(- (* b b) (* 4 (* a c)))

simplify495.0ms

Counts
104 → 104

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.9b

localize56.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b b) (* 4 (* a c))))
1.1b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.8b
(- (* b b) (* 4 (* a c)))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×times-frac add-cube-cbrt associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- insert-posit16 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 clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 81
Calls
4 calls:
Slowest
52.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
29.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
23.0ms
(- (* b b) (* 4 (* a c)))
15.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
126.0ms
(sqrt (- (* b b) (* 4 (* a c))))
120.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
104.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
54.0ms
(- (* b b) (* 4 (* a c)))

simplify2.0s

Counts
93 → 93

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.9b

regimes525.0ms

Accuracy

82.5% (5.0b remaining)

Error of 10.4b against oracle of 5.5b and baseline of 33.9b

bsearch244.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.2s1139×body2560valid
1.1s953×body1280valid
833.0ms2788×body80nan
767.0ms5730×body80valid
232.0ms402×body640valid
119.0ms96×body5120valid
107.0ms215×body320valid
38.0ms149×body160valid