Details

Time bar (total: 22.0s)

sample117.0ms

Algorithm
intervals
Results
23.0ms186×body80valid
22.0ms29×body2560valid
18.0ms32×body1280valid
17.0ms22×body640valid
11.0ms96×body80nan
3.0ms3×body5120valid
2.0ms7×body320valid
1.0ms4×body160valid

simplify234.0ms

Counts
1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize22.0ms

Local error

Found 4 expressions with local error:

21.5b
(sqrt (- (* b b) (* 4 (* a c))))
1.0b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.0b
(- (* b b) (* 4 (* a c)))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

rewrite83.0ms

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
42.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
22.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
11.0ms
(- (* b b) (* 4 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
94.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
82.0ms
(sqrt (- (* b b) (* 4 (* a c))))
53.0ms
(- (* b b) (* 4 (* a c)))

simplify2.2s

Counts
93 → 93

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.7b

localize39.0ms

Local error

Found 4 expressions with local error:

21.5b
(sqrt (- (* b b) (* 4 (* a c))))
1.0b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.0b
(- (* b b) (* 4 (* a c)))
0.2b
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
13×associate-*r* add-cube-cbrt
10×times-frac add-log-exp
9×add-cbrt-cube add-exp-log
7×pow1 associate-*l*
5×flip3-- sqrt-prod flip--
4×insert-posit16 distribute-lft-out-- difference-of-squares
3×diff-log
2×frac-times sub-neg distribute-rgt-neg-in sqrt-div associate-*l/ prod-exp cbrt-unprod unswap-sqr
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down neg-log associate-*r/ *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
Slowest
70.0ms
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
17.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
9.0ms
(- (* b b) (* 4 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
132.0ms
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
92.0ms
(sqrt (- (* b b) (* 4 (* a c))))
60.0ms
(- (* b b) (* 4 (* a c)))

simplify630.0ms

Counts
101 → 101

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.7b

localize29.0ms

Local error

Found 4 expressions with local error:

21.5b
(sqrt (- (* b b) (* 4 (* a c))))
1.0b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.0b
(- (* b b) (* 4 (* a c)))
0.2b
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))

rewrite93.0ms

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
36.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
29.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
14.0ms
(sqrt (- (* b b) (* 4 (* a c))))
10.0ms
(- (* b b) (* 4 (* a c)))

series473.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
113.0ms
(sqrt (- (* b b) (* 4 (* a c))))
112.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
69.0ms
(- (* b b) (* 4 (* a c)))

simplify824.0ms

Counts
141 → 141

prune1.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.6b

localize26.0ms

Local error

Found 4 expressions with local error:

21.5b
(sqrt (- (* b b) (* 4 (* a c))))
1.0b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.0b
(- (* b b) (* 4 (* a c)))
0.2b
(/ (/ 1/2 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
897×times-frac
528×add-sqr-sqrt
527×*-un-lft-identity
355×add-cube-cbrt
86×distribute-lft-out-- difference-of-squares
46×sqrt-prod
43×distribute-rgt-neg-in div-inv
29×associate-/r/
27×associate-/r*
26×add-exp-log
17×flip3-- flip--
16×add-cbrt-cube div-exp
13×associate-/l*
10×add-log-exp
8×cbrt-undiv
5×pow1
4×insert-posit16
3×diff-log
2×rec-exp sub-neg sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 464
Calls
4 calls:
Slowest
59.0ms
(/ (/ 1/2 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
21.0ms
(- (* b b) (* 4 (* a c)))
14.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series812.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
481.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
138.0ms
(/ (/ 1/2 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
132.0ms
(sqrt (- (* b b) (* 4 (* a c))))
60.0ms
(- (* b b) (* 4 (* a c)))

simplify1.1s

Counts
476 → 476

prune6.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.6b

regimes266.0ms

Accuracy

84.1% (4.5b remaining)

Error of 10.0b against oracle of 5.6b and baseline of 33.6b

bsearch187.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s1060×body2560valid
829.0ms5855×body80valid
632.0ms899×body1280valid
382.0ms2935×body80nan
212.0ms455×body640valid
106.0ms239×body320valid
105.0ms127×body5120valid
48.0ms115×body160valid