Details

Time bar (total: 24.5s)

sample151.0ms

Algorithm
intervals
Results
38.0ms38×body2560valid
30.0ms189×body80valid
24.0ms30×body1280valid
17.0ms15×body640valid
13.0ms87×body80nan
3.0ms6×body320valid
3.0ms2×body5120valid

simplify130.0ms

Counts
1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize38.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (- (* b b) (* (* c a) 4)))
0.3b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b
(- (* b b) (* (* c a) 4))
0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- insert-posit16 flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 76
Calls
4 calls:
Slowest
101.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
38.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
17.0ms
(- (* b b) (* (* c a) 4))
8.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
102.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
95.0ms
(sqrt (- (* b b) (* (* c a) 4)))
62.0ms
(- (* b b) (* (* c a) 4))

simplify2.3s

Counts
88 → 88

prune899.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize24.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (- (* b b) (* (* c a) 4)))
5.2b
(- (/ (sqrt (- (* b b) (* (* c a) 4))) (* 2 a)) (/ b (* 2 a)))
0.2b
(- (* b b) (* (* c a) 4))
0.1b
(/ (sqrt (- (* b b) (* (* c a) 4))) (* 2 a))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×add-sqr-sqrt
9×add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod
8×times-frac add-log-exp
6×associate-/l*
5×pow1
4×flip3-- sqrt-div insert-posit16 flip--
3×div-inv
2×cbrt-undiv sub-neg diff-log div-exp distribute-lft-out-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 prod-exp frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 78
Calls
4 calls:
Slowest
55.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) (* 2 a)) (/ b (* 2 a)))
27.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) (* 2 a))
11.0ms
(- (* b b) (* (* c a) 4))
11.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) (* 2 a))
130.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) (* 2 a)) (/ b (* 2 a)))
89.0ms
(sqrt (- (* b b) (* (* c a) 4)))
57.0ms
(- (* b b) (* (* c a) 4))

simplify2.2s

Counts
90 → 90

prune899.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize41.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (- (* b b) (* (* c a) 4)))
10.2b
(- (/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* c a) 4))))) (/ b (* 2 a)))
0.2b
(/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* c a) 4)))))
0.2b
(- (* b b) (* (* c a) 4))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
62×times-frac
38×add-sqr-sqrt
34×*-un-lft-identity
30×add-cube-cbrt
25×add-exp-log
15×sqrt-prod
13×add-cbrt-cube
12×associate-/r* div-exp
10×sqrt-div
9×associate-/r/
8×add-log-exp
7×flip3-- flip--
6×pow1 div-inv
5×cbrt-undiv
4×insert-posit16
3×rec-exp 1-exp prod-exp associate-/l* difference-of-squares
2×sub-neg diff-log distribute-lft-out--
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 frac-sub cbrt-unprod pow-flip inv-pow
Counts
4 → 125
Calls
4 calls:
Slowest
90.0ms
(- (/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* c a) 4))))) (/ b (* 2 a)))
37.0ms
(/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* c a) 4)))))
10.0ms
(- (* b b) (* (* c a) 4))
8.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(- (/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* c a) 4))))) (/ b (* 2 a)))
109.0ms
(/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* c a) 4)))))
94.0ms
(sqrt (- (* b b) (* (* c a) 4)))
63.0ms
(- (* b b) (* (* c a) 4))

simplify673.0ms

Counts
137 → 137

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.8b

localize47.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (- (* b b) (* (* c a) 4)))
22.6b
(sqrt (- (* b b) (* (* c a) 4)))
14.4b
(- (* (/ 1 (/ 2 (sqrt (sqrt (- (* b b) (* (* c a) 4)))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* c a) 4))))))) (/ b (* 2 a)))
0.3b
(* (/ 1 (/ 2 (sqrt (sqrt (- (* b b) (* (* c a) 4)))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* c a) 4)))))))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
612×times-frac
532×add-sqr-sqrt
276×sqrt-prod
260×*-un-lft-identity
188×add-cube-cbrt
172×add-exp-log
104×associate-*r* associate-*l*
98×div-exp
81×unswap-sqr
49×prod-exp
40×add-cbrt-cube
28×rec-exp sqrt-div 1-exp
18×cbrt-undiv
14×associate-/r/
10×pow1
9×flip3-- cbrt-unprod flip--
8×div-inv
6×add-log-exp
4×frac-sub insert-posit16
3×pow-prod-down
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ associate-*r/ un-div-inv pow-flip inv-pow
1×sub-neg diff-log *-commutative
Counts
4 → 412
Calls
4 calls:
Slowest
112.0ms
(* (/ 1 (/ 2 (sqrt (sqrt (- (* b b) (* (* c a) 4)))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* c a) 4)))))))
36.0ms
(- (* (/ 1 (/ 2 (sqrt (sqrt (- (* b b) (* (* c a) 4)))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* c a) 4))))))) (/ b (* 2 a)))
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(* (/ 1 (/ 2 (sqrt (sqrt (- (* b b) (* (* c a) 4)))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* c a) 4)))))))
125.0ms
(- (* (/ 1 (/ 2 (sqrt (sqrt (- (* b b) (* (* c a) 4)))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* c a) 4))))))) (/ b (* 2 a)))
103.0ms
(sqrt (- (* b b) (* (* c a) 4)))
91.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify1.6s

Counts
424 → 424

prune6.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.8b

regimes391.0ms

Accuracy

83.4% (4.6b remaining)

Error of 10.6b against oracle of 6.0b and baseline of 33.5b

bsearch201.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.4s1070×body2560valid
1.3s5902×body80valid
609.0ms864×body1280valid
375.0ms2867×body80nan
320.0ms458×body640valid
129.0ms102×body5120valid
103.0ms207×body320valid
27.0ms112×body160valid