Details

Time bar (total: 22.4s)

sample103.0ms

Algorithm
intervals
Results
22.0ms80×body80nan
20.0ms191×body80valid
19.0ms29×body2560valid
14.0ms26×body1280valid
8.0ms18×body640valid
3.0ms8×body320valid
2.0ms3×body5120valid
0.0ms2×body160valid

simplify225.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize23.0ms

Local error

Found 4 expressions with local error:

20.9b
(sqrt (- (* b b) (* 4 (* a c))))
1.0b
(- (* b b) (* 4 (* a c)))
0.3b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

rewrite115.0ms

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
54.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
29.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
16.0ms
(- (* b b) (* 4 (* a c)))
15.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series507.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
142.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
118.0ms
(sqrt (- (* b b) (* 4 (* a c))))
84.0ms
(- (* b b) (* 4 (* a c)))

simplify2.2s

Counts
93 → 93

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize25.0ms

Local error

Found 4 expressions with local error:

20.9b
(sqrt (- (* b b) (* 4 (* a c))))
1.0b
(- (* b b) (* 4 (* a c)))
0.3b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.2b
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))

rewrite113.0ms

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
73.0ms
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
15.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
14.0ms
(- (* b b) (* 4 (* a c)))
9.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series387.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
107.0ms
(sqrt (- (* b b) (* 4 (* a c))))
106.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
61.0ms
(- (* b b) (* 4 (* a c)))

simplify670.0ms

Counts
101 → 101

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

localize34.0ms

Local error

Found 4 expressions with local error:

20.9b
(sqrt (- (* b b) (* 4 (* a c))))
1.0b
(- (* b b) (* 4 (* a c)))
0.3b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.2b
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))

rewrite115.0ms

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
56.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
15.0ms
(- (* b b) (* 4 (* a c)))
12.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series415.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
149.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
97.0ms
(sqrt (- (* b b) (* 4 (* a c))))
97.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
72.0ms
(- (* b b) (* 4 (* a c)))

simplify647.0ms

Counts
141 → 141

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize40.0ms

Local error

Found 4 expressions with local error:

20.9b
(sqrt (- (* b b) (* 4 (* a c))))
1.0b
(- (* b b) (* 4 (* a c)))
0.3b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.3b
(/ (/ 1/2 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))

rewrite84.0ms

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
33.0ms
(/ (/ 1/2 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
20.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms
(- (* b b) (* 4 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series396.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(/ (/ 1/2 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
95.0ms
(sqrt (- (* b b) (* 4 (* a c))))
91.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
53.0ms
(- (* b b) (* 4 (* a c)))

simplify1.3s

Counts
476 → 476

prune5.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

regimes333.0ms

Accuracy

83.9% (4.4b remaining)

Error of 9.7b against oracle of 5.3b and baseline of 32.7b

bsearch240.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s1075×body2560valid
1.1s846×body1280valid
949.0ms5877×body80valid
319.0ms2806×body80nan
277.0ms462×body640valid
110.0ms113×body5120valid
110.0ms221×body320valid
28.0ms102×body160valid