Details

Time bar (total: 18.5s)

sample91.0ms

Algorithm
intervals
Results
19.0ms97×body80valid
15.0ms159×body160valid
14.0ms302×body80nan
14.0ms558×pre80true

simplify78.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
31.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite190.0ms

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:
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(- (* b b) (* (* 4.0 a) c))
125.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series458.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms
(- (* b b) (* (* 4.0 a) c))
173.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
109.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify807.0ms

Counts
82 → 82

prune240.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* 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)))))

rewrite304.0ms

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:
46.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
150.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
90.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series717.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms
(- (* b b) (* (* 4.0 a) c))
206.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
274.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.1s

Counts
163 → 163

prune760.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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)))

rewrite741.0ms

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:
329.0ms
(/ (/ (+ 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))
189.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
78.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
113.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series830.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(/ (/ (+ 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))
361.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
157.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
53.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify749.0ms

Counts
247 → 247

prune1.3s

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
(- (- b) (sqrt (- (* 1.0 (pow b 2)) (* 4.0 (* a c)))))
0.2b
(- (* 1.0 (pow b 2)) (* 4.0 (* a c)))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* 1.0 (pow b 2)) (* 4.0 (* a c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* 1.0 (pow b 2)) (* 4.0 (* a c))))))

rewrite308.0ms

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:
29.0ms
(- (- b) (sqrt (- (* 1.0 (pow b 2)) (* 4.0 (* a c)))))
22.0ms
(- (* 1.0 (pow b 2)) (* 4.0 (* a c)))
149.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* 1.0 (pow b 2)) (* 4.0 (* a c)))))) (* 2.0 a))
101.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* 1.0 (pow b 2)) (* 4.0 (* a c))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
265.0ms
(- (- b) (sqrt (- (* 1.0 (pow b 2)) (* 4.0 (* a c)))))
96.0ms
(- (* 1.0 (pow b 2)) (* 4.0 (* a c)))
400.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* 1.0 (pow b 2)) (* 4.0 (* a c)))))) (* 2.0 a))
410.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* 1.0 (pow b 2)) (* 4.0 (* a c))))))

simplify1.9s

Counts
163 → 163

prune749.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes232.0ms

Accuracy

41.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify833.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.3s16755×pre80true
778.0ms4499×body160valid
755.0ms8755×body80nan
298.0ms3500×body80valid
0.0ms1×body320valid