Details

Time bar (total: 22.4s)

sample70.0ms

Algorithm
intervals
Results
14.0ms159×body160valid
12.0ms274×body80nan
11.0ms530×pre80true
6.0ms43×body320valid
2.0ms54×body80valid

simplify63.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize14.0ms

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))
38.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite138.0ms

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))
72.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
46.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series415.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
52.0ms
(- (* b b) (* (* 4.0 a) c))
168.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
97.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify721.0ms

Counts
82 → 82

prune292.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

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))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite281.0ms

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:
24.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(- (* b b) (* (* 4.0 a) c))
121.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
112.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series699.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
89.0ms
(- (* b b) (* (* 4.0 a) c))
203.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
273.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.8s

Counts
163 → 163

prune687.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))))
0.5b
(* (* b b) (* b b))
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
130×pow1
47×add-sqr-sqrt
36×pow-prod-up
35×*-un-lft-identity
33×add-exp-log add-cbrt-cube
32×pow-prod-down
28×times-frac
22×pow-sqr
19×add-cube-cbrt
18×pow-plus
17×prod-exp cbrt-unprod
13×pow2
12×difference-of-squares
8×associate-/r* sqrt-prod distribute-lft-out--
4×distribute-rgt-neg-in associate-*r* add-log-exp
3×pow-unpow pow-pow pow-exp associate-/l* rem-cube-cbrt
2×flip3-+ associate-*r/ associate-*l* associate-/r/ *-commutative flip-+ associate-/l/
1×cbrt-undiv distribute-rgt-in cube-mult pow-to-exp unpow-prod-down flip3-- frac-2neg distribute-lft-in unpow3 cube-prod swap-sqr div-exp clear-num flip-- div-inv unswap-sqr sqr-pow
Counts
4 → 164
Calls
4 calls:
190.0ms
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
750.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))))
61.0ms
(* (* b b) (* b b))
19.0ms
(pow (* (* 4.0 a) c) 3)

series679.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
420.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))))
39.0ms
(* (* b b) (* b b))
93.0ms
(pow (* (* 4.0 a) c) 3)

simplify3.5s

Counts
176 → 176

prune838.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))) (* 4.0 a)) c)
0.3b
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
0.5b
(* (* b b) (* b b))
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
130×pow1
72×times-frac
55×add-sqr-sqrt
43×*-un-lft-identity
40×add-exp-log add-cbrt-cube
36×pow-prod-up
32×pow-prod-down
27×add-cube-cbrt
22×pow-sqr
18×pow-plus prod-exp cbrt-unprod
13×pow2
12×associate-/l* difference-of-squares
8×sqrt-prod distribute-lft-out--
5×cbrt-undiv div-exp div-inv
4×distribute-rgt-neg-in associate-*r* add-log-exp
3×pow-unpow pow-pow pow-exp associate-/r* rem-cube-cbrt
2×div-sub associate-*r/ associate-*l* *-commutative
1×distribute-rgt-in cube-mult pow-to-exp unpow-prod-down frac-2neg distribute-lft-in flip3-+ unpow3 cube-prod swap-sqr clear-num flip-+ associate-/l/ unswap-sqr sqr-pow
Counts
4 → 182
Calls
4 calls:
1.2s
(/ (/ (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))) (* 4.0 a)) c)
168.0ms
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
57.0ms
(* (* b b) (* b b))
24.0ms
(pow (* (* 4.0 a) c) 3)

series604.0ms

Counts
4 → 12
Calls
4 calls:
337.0ms
(/ (/ (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))) (* 4.0 a)) c)
134.0ms
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
50.0ms
(* (* b b) (* b b))
82.0ms
(pow (* (* 4.0 a) c) 3)

simplify2.4s

Counts
194 → 194

prune903.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes211.0ms

Accuracy

-1.2% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.5s

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.0s16343×pre80true
784.0ms4758×body160valid
669.0ms8343×body80nan
366.0ms1401×body320valid
198.0ms1841×body80valid