Details

Time bar (total: 19.4s)

sample92.0ms

Algorithm
intervals
Results
28.0ms189×body80valid
21.0ms38×body2560valid
13.0ms30×body1280valid
8.0ms87×body80nan
5.0ms15×body640valid
2.0ms6×body320valid
1.0ms2×body5120valid

simplify166.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize43.0ms

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))

rewrite146.0ms

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
72.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
51.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(- (* b b) (* (* c a) 4))

series391.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
107.0ms
(sqrt (- (* b b) (* (* c a) 4)))
101.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
56.0ms
(- (* b b) (* (* c a) 4))

simplify2.1s

Counts
88 → 88

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize47.0ms

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))

rewrite116.0ms

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
80.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) (* 2 a)) (/ b (* 2 a)))
15.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) (* 2 a))
12.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(- (* b b) (* (* c a) 4))

series462.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) (* 2 a))
132.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) (* 2 a)) (/ b (* 2 a)))
100.0ms
(sqrt (- (* b b) (* (* c a) 4)))
79.0ms
(- (* b b) (* (* c a) 4))

simplify1.8s

Counts
90 → 90

prune718.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize26.0ms

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))

rewrite107.0ms

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
71.0ms
(- (/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* c a) 4))))) (/ b (* 2 a)))
20.0ms
(/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* c a) 4)))))
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(- (* b b) (* (* c a) 4))

series339.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(- (/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* c a) 4))))) (/ b (* 2 a)))
99.0ms
(/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* c a) 4)))))
74.0ms
(sqrt (- (* b b) (* (* c a) 4)))
46.0ms
(- (* b b) (* (* c a) 4))

simplify510.0ms

Counts
137 → 137

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.8b

localize40.0ms

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)))))))

rewrite141.0ms

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
73.0ms
(* (/ 1 (/ 2 (sqrt (sqrt (- (* b b) (* (* c a) 4)))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* c a) 4)))))))
38.0ms
(- (* (/ 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)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(* (/ 1 (/ 2 (sqrt (sqrt (- (* b b) (* (* c a) 4)))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* c a) 4)))))))
107.0ms
(- (* (/ 1 (/ 2 (sqrt (sqrt (- (* b b) (* (* c a) 4)))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* c a) 4))))))) (/ b (* 2 a)))
77.0ms
(sqrt (- (* b b) (* (* c a) 4)))
75.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify985.0ms

Counts
424 → 424

prune5.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.8b

regimes265.0ms

Accuracy

83.4% (4.6b remaining)

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

bsearch153.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
970.0ms5902×body80valid
741.0ms1070×body2560valid
481.0ms864×body1280valid
332.0ms2867×body80nan
202.0ms458×body640valid
67.0ms102×body5120valid
54.0ms207×body320valid
21.0ms112×body160valid