Details

Time bar (total: 13.4s)

sample322.0ms

Algorithm
intervals
Results
95.0ms119×body320valid
23.0ms500×pre80true
23.0ms244×body80nan
20.0ms98×body160valid
4.0ms10×body640valid
3.0ms29×body80valid

simplify12.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b
(- (* b b) (* (* 4.0 a) c))
26.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite205.0ms

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:
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series515.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
190.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
93.0ms
(- (* b b) (* (* 4.0 a) c))
128.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify52.0ms

Counts
82 → 82

prune355.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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))
0.2b
(/ (/ (+ 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:
50.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(- (* b b) (* (* 4.0 a) c))
157.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
88.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series721.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(- (* b b) (* (* 4.0 a) c))
231.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
317.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify102.0ms

Counts
163 → 163

prune749.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 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)))

rewrite747.0ms

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:
307.0ms
(/ (/ (+ 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))
198.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
71.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
146.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series839.0ms

Counts
4 → 12
Calls
4 calls:
299.0ms
(/ (/ (+ 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))
347.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
127.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
66.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify82.0ms

Counts
247 → 247

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c)))))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite459.0ms

Algorithm
rewrite-expression-head
Rules
232×pow1
132×pow-prod-down
90×add-exp-log times-frac add-cbrt-cube
78×*-un-lft-identity
68×add-sqr-sqrt
56×prod-exp cbrt-unprod
38×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×pow-sqr pow-prod-up
10×distribute-rgt-neg-in sqrt-prod
8×associate-/r*
7×cbrt-undiv div-exp
6×pow-plus associate-/r/
4×div-inv add-log-exp
3×flip3-- flip-- associate-/l/
2×pow2 frac-2neg swap-sqr associate-*r* associate-*l* clear-num *-commutative
1×flip3-+ flip-+
Counts
4 → 241
Calls
4 calls:
91.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c)))))))) (* 2.0 a))
75.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))))
121.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
135.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series786.0ms

Counts
4 → 12
Calls
4 calls:
311.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c)))))))) (* 2.0 a))
353.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (/ (sqrt (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c))))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))))
53.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))
68.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify215.0ms

Counts
253 → 253

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes220.0ms

Accuracy

39% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify24.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.2s2955×body160valid
853.0ms3578×body320valid
695.0ms16228×pre80true
559.0ms8228×body80nan
170.0ms527×body640valid
55.0ms940×body80valid