Details

Time bar (total: 46.4s)

sample118.0ms

Algorithm
intervals
Results
37.0ms38×body2560valid
21.0ms36×body1280valid
21.0ms183×body80valid
11.0ms97×body80nan
5.0ms9×body640valid
5.0ms11×body320valid
3.0ms3×body5120valid
1.0ms4×body160valid

simplify61.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
61.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize36.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (- (* b_2 b_2) (* a c)))
1.6b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1 distribute-rgt-neg-in
4×flip3-- insert-posit16 flip--
3×associate-/r* diff-log
2×sub-neg sqrt-div associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log div-inv
Counts
4 → 95
Calls
4 calls:
Slowest
72.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))
7.0ms
(- (* b_2 b_2) (* a c))

series367.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
104.0ms
(sqrt (- (* b_2 b_2) (* a c)))
102.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
51.0ms
(- (* b_2 b_2) (* a c))

simplify4.9s

Counts
81 → 107
Calls
81 calls:
Slowest
436.0ms
(/ (* (* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (* (* a a) a))
376.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
351.0ms
(- (pow (- b_2) 3) (pow (sqrt (- (* b_2 b_2) (* a c))) 3))
217.0ms
(- (* (- b_2) (- b_2)) (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))))
203.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize32.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (- (* b_2 b_2) (* a c)))
7.0b
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
1.2b
(- (* b_2 b_2) (* a c))
0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
37×times-frac
24×add-cube-cbrt
17×sqrt-prod
8×add-log-exp
7×distribute-lft-out--
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×flip3-- sqrt-div insert-posit16 flip--
3×associate-/r* distribute-rgt-neg-in div-inv
2×sub-neg diff-log associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-sub div-exp frac-sub sub-div
Counts
4 → 101
Calls
4 calls:
Slowest
31.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))
12.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
7.0ms
(- (* b_2 b_2) (* a c))

series418.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
126.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))
62.0ms
(- (* b_2 b_2) (* a c))

simplify4.8s

Counts
99 → 113
Calls
99 calls:
Slowest
307.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
257.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
237.0ms
(/ (* (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (- (* b_2 b_2) (* a c)))) (* (* a a) a))
224.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
190.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize47.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (- (* b_2 b_2) (* a c)))
10.5b
(- (/ (- b_2) a) (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))))
1.2b
(- (* b_2 b_2) (* a c))
0.2b
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
175×times-frac
132×add-sqr-sqrt
99×*-un-lft-identity
82×add-cube-cbrt
43×sqrt-prod
24×associate-/r*
15×add-exp-log
14×difference-of-squares
10×sqrt-div
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1 div-inv
4×insert-posit16 distribute-lft-out--
3×cbrt-undiv associate-/l*
2×rec-exp sub-neg diff-log 1-exp
1×associate--l- neg-sub0 rem-sqrt-square clear-num distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 div-sub frac-sub pow-flip inv-pow
Counts
4 → 183
Calls
4 calls:
Slowest
58.0ms
(- (/ (- b_2) a) (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))))
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))
18.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms
(- (* b_2 b_2) (* a c))

series378.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(- (/ (- b_2) a) (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))))
117.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))
52.0ms
(- (* b_2 b_2) (* a c))

simplify20.2s

Counts
236 → 195
Calls
236 calls:
Slowest
521.0ms
(/ (* (* 1 1) 1) (* (* (/ a (sqrt (- (* b_2 b_2) (* a c)))) (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ a (sqrt (- (* b_2 b_2) (* a c))))))
406.0ms
(/ 1 (/ a (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))))
368.0ms
(/ (sqrt 1) (/ a (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))))
365.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ a (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))))
355.0ms
(/ (* (* 1 1) 1) (/ (* (* a a) a) (* (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (- (* b_2 b_2) (* a c))))))

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

localize56.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (- (* b_2 b_2) (* c a)))
18.4b
(- (/ (- b_2) a) (* (/ 1 (* (cbrt a) (cbrt a))) (/ (sqrt (- (* b_2 b_2) (* c a))) (cbrt a))))
1.2b
(- (* b_2 b_2) (* c a))
0.6b
(cbrt a)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity add-cube-cbrt add-log-exp
7×add-sqr-sqrt
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16
3×cbrt-prod flip3-- frac-sub sqrt-prod flip--
2×sub-neg times-frac sqrt-div diff-log distribute-lft-out--
1×associate--l- neg-sub0 frac-times rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 pow1/3 div-sub associate-*l/ associate-*r/
Counts
4 → 60
Calls
4 calls:
Slowest
23.0ms
(- (/ (- b_2) a) (* (/ 1 (* (cbrt a) (cbrt a))) (/ (sqrt (- (* b_2 b_2) (* c a))) (cbrt a))))
14.0ms
(- (* b_2 b_2) (* c a))
7.0ms
(sqrt (- (* b_2 b_2) (* c a)))
1.0ms
(cbrt a)

series593.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
280.0ms
(cbrt a)
156.0ms
(- (/ (- b_2) a) (* (/ 1 (* (cbrt a) (cbrt a))) (/ (sqrt (- (* b_2 b_2) (* c a))) (cbrt a))))
87.0ms
(sqrt (- (* b_2 b_2) (* c a)))
70.0ms
(- (* b_2 b_2) (* c a))

simplify3.7s

Counts
35 → 72
Calls
35 calls:
Slowest
830.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* c a) 3)))
509.0ms
(/ (exp (/ (- b_2) a)) (exp (* (/ 1 (* (cbrt a) (cbrt a))) (/ (sqrt (- (* b_2 b_2) (* c a))) (cbrt a)))))
429.0ms
(- (* (- b_2) (cbrt a)) (* a (* (/ 1 (* (cbrt a) (cbrt a))) (sqrt (- (* b_2 b_2) (* c a))))))
305.0ms
(- (* (- b_2) (* (cbrt a) (cbrt a))) (* a (* 1 (/ (sqrt (- (* b_2 b_2) (* c a))) (cbrt a)))))
240.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune991.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.5b

regimes606.0ms

Accuracy

85.6% (4.1b remaining)

Error of 9.4b against oracle of 5.3b and baseline of 34.0b

bsearch349.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
859.0ms1118×body2560valid
807.0ms5816×body80valid
642.0ms440×body640valid
562.0ms871×body1280valid
362.0ms2861×body80nan
152.0ms119×body5120valid
106.0ms246×body320valid
23.0ms108×body160valid