Details

Time bar (total: 42.3s)

sample148.0ms

Algorithm
intervals
Results
47.0ms188×body80valid
28.0ms37×body1280valid
24.0ms27×body2560valid
12.0ms87×body80nan
11.0ms20×body640valid
3.0ms6×body320valid
2.0ms2×body5120valid
1.0ms3×body160valid

simplify548.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
548.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize48.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (fma b b (* (* a c) -4)))
2.0b
(fma b b (* (* a c) -4))
0.8b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.1b
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
Slowest
33.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
15.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
3.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series421.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
115.0ms
(sqrt (fma b b (* (* a c) -4)))
103.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
65.0ms
(fma b b (* (* a c) -4))

simplify15.5s

Counts
225 → 191
Calls
225 calls:
Slowest
397.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
243.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
237.0ms
(- b (* 2 (/ (* a c) b)))
188.0ms
(/ (* (* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (* (* a a) a))
187.0ms
(/ (/ (* (* (- (sqrt (fma b b (* (* a c) -4))) b) (- (sqrt (fma b b (* (* a c) -4))) b)) (- (sqrt (fma b b (* (* a c) -4))) b)) (* (* 2 2) 2)) (* (* a a) a))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize21.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (fma (* -4 c) a (* b b)))
0.8b
(- (sqrt (fma (* -4 c) a (* b b))) b)
0.2b
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))
0.0b
(fma (* -4 c) a (* b b))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r*
10×times-frac
9×add-cbrt-cube add-exp-log
7×pow1
6×fma-neg associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×flip3-- flip--
2×frac-times associate-*l/ prod-exp cbrt-unprod distribute-lft-out-- unswap-sqr
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv
Counts
4 → 111
Calls
4 calls:
Slowest
24.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))
7.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
1.0ms
(sqrt (fma (* -4 c) a (* b b)))
0.0ms
(fma (* -4 c) a (* b b))

series422.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))
114.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
108.0ms
(sqrt (fma (* -4 c) a (* b b)))
77.0ms
(fma (* -4 c) a (* b b))

simplify5.4s

Counts
96 → 123
Calls
96 calls:
Slowest
612.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) 1/2)
286.0ms
(* (+ (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (+ (* b b) (* (sqrt (fma (* -4 c) a (* b b))) b))) a)
277.0ms
(* (- (pow (sqrt (fma (* -4 c) a (* b b))) 3) (pow b 3)) (/ 1/2 a))
229.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) (/ 1/2 a))
222.0ms
(* (* (* (- (sqrt (fma (* -4 c) a (* b b))) b) (- (sqrt (fma (* -4 c) a (* b b))) b)) (- (sqrt (fma (* -4 c) a (* b b))) b)) (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize51.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (fma (* a c) -4 (* b b)))
1.6b
(fma (* a c) -4 (* b b))
0.8b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.2b
(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1/2 a))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r*
10×times-frac
9×add-cbrt-cube add-exp-log
7×pow1
6×fma-neg associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×flip3-- flip--
2×frac-times associate-*l/ prod-exp cbrt-unprod distribute-lft-out-- unswap-sqr
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv
Counts
4 → 111
Calls
4 calls:
Slowest
24.0ms
(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1/2 a))
11.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series490.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1/2 a))
115.0ms
(sqrt (fma (* a c) -4 (* b b)))
100.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
96.0ms
(fma (* a c) -4 (* b b))

simplify5.5s

Counts
96 → 123
Calls
96 calls:
Slowest
729.0ms
(* (- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (* b b)) 1/2)
287.0ms
(* (+ (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (+ (* b b) (* (sqrt (fma (* a c) -4 (* b b))) b))) a)
282.0ms
(* (- (pow (sqrt (fma (* a c) -4 (* b b))) 3) (pow b 3)) (/ 1/2 a))
208.0ms
(* (* (* (- (sqrt (fma (* a c) -4 (* b b))) b) (- (sqrt (fma (* a c) -4 (* b b))) b)) (- (sqrt (fma (* a c) -4 (* b b))) b)) (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)))
185.0ms
(* (- (pow (sqrt (fma (* a c) -4 (* b b))) 3) (pow b 3)) 1/2)

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize63.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (fma b b (* (* a c) -4)))
21.1b
(sqrt (fma b b (* (* a c) -4)))
2.0b
(fma b b (* (* a c) -4))
2.0b
(fma b b (* (* a c) -4))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 54
Calls
4 calls:
Slowest
2.0ms
(sqrt (fma b b (* (* a c) -4)))
2.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))
0.0ms
(fma b b (* (* a c) -4))

series409.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(sqrt (fma b b (* (* a c) -4)))
119.0ms
(sqrt (fma b b (* (* a c) -4)))
88.0ms
(fma b b (* (* a c) -4))
67.0ms
(fma b b (* (* a c) -4))

simplify1.4s

Counts
22 → 66
Calls
22 calls:
Slowest
259.0ms
(- b (* 2 (/ (* a c) b)))
233.0ms
(- b (* 2 (/ (* a c) b)))
103.0ms
(- (pow b 2) (* 4 (* a c)))
99.0ms
(- (* 2 (/ (* a c) b)) b)
85.0ms
(- (* 2 (/ (* a c) b)) b)

prune955.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

regimes465.0ms

Accuracy

85.5% (4.1b remaining)

Error of 9.8b against oracle of 5.7b and baseline of 34.1b

bsearch448.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.4s5844×body80valid
1.1s1089×body2560valid
1.0s904×body1280valid
510.0ms2799×body80nan
287.0ms465×body640valid
197.0ms121×body5120valid
115.0ms206×body320valid
28.0ms107×body160valid