Details

Time bar (total: 19.2s)

sample126.0ms

Algorithm
intervals
Results
34.0ms511×pre80true
22.0ms150×body160valid
18.0ms255×body80nan
11.0ms50×body320valid
4.0ms56×body80valid

simplify66.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series413.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(- (* b b) (* (* 4.0 a) c))
140.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
114.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify817.0ms

Counts
82 → 82

prune327.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite327.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
45.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
176.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
80.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series687.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(- (* b b) (* (* 4.0 a) c))
200.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
290.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.1s

Counts
163 → 163

prune824.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
0.4b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite720.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt times-frac
118×pow1
92×*-un-lft-identity
66×pow-prod-down
56×add-exp-log add-cbrt-cube
52×add-cube-cbrt
42×difference-of-squares
39×associate-/l*
29×prod-exp cbrt-unprod
20×sqrt-prod distribute-lft-out--
12×associate-/r*
10×distribute-rgt-neg-in
9×pow-sqr pow-prod-up
8×cbrt-undiv div-exp associate-/r/
5×div-inv associate-/l/
4×unpow-prod-down flip3-- flip-- add-log-exp sqr-pow
3×frac-2neg pow-plus clear-num
2×flip3-+ flip-+
1×pow2 div-sub swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 235
Calls
4 calls:
313.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
219.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
51.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
122.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series883.0ms

Counts
4 → 12
Calls
4 calls:
281.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
409.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
149.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
44.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify730.0ms

Counts
247 → 247

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
0.5b
(* (* b b) (* b b))
0.7b
(pow (* b b) 3)
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
243×pow1
93×pow-prod-down
61×add-exp-log add-cbrt-cube
46×pow-prod-up
39×prod-exp cbrt-unprod
32×pow-sqr
22×pow-plus
15×pow2
9×pow-pow
6×add-sqr-sqrt add-cube-cbrt pow-unpow *-un-lft-identity
5×pow-exp rem-cube-cbrt
4×add-log-exp
2×cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod swap-sqr associate-*r* associate-*l* *-commutative sqr-pow
1×unswap-sqr
Counts
4 → 174
Calls
4 calls:
107.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
55.0ms
(* (* b b) (* b b))
12.0ms
(pow (* b b) 3)
17.0ms
(pow (* (* 4.0 a) c) 3)

series238.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
37.0ms
(* (* b b) (* b b))
89.0ms
(pow (* b b) 3)
72.0ms
(pow (* (* 4.0 a) c) 3)

simplify1.4s

Counts
186 → 186

prune633.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes184.0ms

Accuracy

1.3% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.4s

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.3s4851×body160valid
1.3s8116×body80nan
623.0ms16116×pre80true
383.0ms1366×body320valid
134.0ms1783×body80valid