Details

Time bar (total: 18.7s)

sample80.0ms

Algorithm
intervals
Results
46.0ms271×body80valid
13.0ms106×body80nan

simplify206.0ms

Calls
1 calls:
Slowest
205.0ms
(if (>= b 0) (/ (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)) (/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize162.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma (* -4 a) c (* b b)))
26.1b
(sqrt (fma (* -4 a) c (* b b)))
1.1b
(- (sqrt (fma (* -4 a) c (* b b))) b)
0.5b
(- (- b) (sqrt (fma (* -4 a) c (* b b))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×*-un-lft-identity
24×prod-diff
23×add-cube-cbrt
22×sqrt-prod
10×fma-neg
7×neg-mul-1
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×rem-sqrt-square sub-neg flip3-- pow1/2 flip-- difference-of-squares
1×associate--l- neg-sub0 diff-log distribute-lft-out--
Calls
4 calls:
Slowest
13.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
12.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms
(sqrt (fma (* -4 a) c (* b b)))
2.0ms
(sqrt (fma (* -4 a) c (* b b)))

series232.0ms

Calls
4 calls:
Slowest
69.0ms
(sqrt (fma (* -4 a) c (* b b)))
59.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
53.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
50.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify4.5s

Calls
81 calls:
Slowest
137.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
127.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
127.0ms
(fma -1 b (- (* (sqrt (fma (* -4 a) c (* b b))) (sqrt 1))))
116.0ms
(* -2 (/ (* a c) b))
114.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.4b

localize122.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma (* -4 a) c (* b b)))
4.5b
(* (/ c b) a)
3.8b
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
1.1b
(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube fma-neg add-exp-log sqrt-prod
4×expm1-log1p-u pow1 associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/
2×flip3-- div-inv flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg times-frac pow1/2 div-exp *-commutative associate-/l*
Calls
4 calls:
Slowest
12.0ms
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
6.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
5.0ms
(* (/ c b) a)
3.0ms
(sqrt (fma (* -4 a) c (* b b)))

series168.0ms

Calls
4 calls:
Slowest
65.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
51.0ms
(sqrt (fma (* -4 a) c (* b b)))
37.0ms
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
16.0ms
(* (/ c b) a)

simplify2.4s

Calls
31 calls:
Slowest
699.0ms
(- (log (* (- (* (/ c b) a) b) 2)) (log (* 2 a)))
664.0ms
(/ (* (* (* (- (* (/ c b) a) b) 2) (* (- (* (/ c b) a) b) 2)) (* (- (* (/ c b) a) b) 2)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
356.0ms
(* (- (pow (* (/ c b) a) 3) (pow b 3)) 2)
177.0ms
(* (- (* (* (/ c b) a) (* (/ c b) a)) (* b b)) 2)
67.0ms
(/ (- (* (/ c b) a) b) 2)

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.4b

localize85.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma (* -4 a) c (* b b)))
1.1b
(- (sqrt (fma (* -4 a) c (* b b))) b)
0.5b
(fma (* -4 a) c (* b b))
0.1b
(/ c (- (sqrt (fma (* -4 a) c (* b b))) b))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×fma-neg sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r*
2×flip3-- associate-/r/ flip--
1×rem-sqrt-square clear-num sub-neg frac-2neg pow1/2 fma-udef div-inv
Calls
4 calls:
Slowest
6.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
4.0ms
(/ c (- (sqrt (fma (* -4 a) c (* b b))) b))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
0.0ms
(fma (* -4 a) c (* b b))

series317.0ms

Calls
4 calls:
Slowest
151.0ms
(/ c (- (sqrt (fma (* -4 a) c (* b b))) b))
68.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
59.0ms
(sqrt (fma (* -4 a) c (* b b)))
40.0ms
(fma (* -4 a) c (* b b))

simplify805.0ms

Calls
26 calls:
Slowest
125.0ms
(+ (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (+ (* b b) (* (sqrt (fma (* -4 a) c (* b b))) b)))
86.0ms
(- (pow b 2) (* 4 (* a c)))
62.0ms
(- (pow b 2) (* 4 (* a c)))
55.0ms
(- (pow b 2) (* 4 (* a c)))
55.0ms
(+ (sqrt (fma (* -4 a) c (* b b))) b)

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.1b

localize111.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma (* a c) -4 (* b b)))
1.1b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.6b
(fma (* a c) -4 (* b b))
0.1b
(/ c (- (sqrt (fma (* a c) -4 (* b b))) b))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×fma-neg sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r*
2×flip3-- associate-/r/ flip--
1×rem-sqrt-square clear-num sub-neg frac-2neg pow1/2 fma-udef div-inv
Calls
4 calls:
Slowest
7.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
3.0ms
(/ c (- (sqrt (fma (* a c) -4 (* b b))) b))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series305.0ms

Calls
4 calls:
Slowest
141.0ms
(/ c (- (sqrt (fma (* a c) -4 (* b b))) b))
64.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
54.0ms
(sqrt (fma (* a c) -4 (* b b)))
46.0ms
(fma (* a c) -4 (* b b))

simplify840.0ms

Calls
26 calls:
Slowest
128.0ms
(+ (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (+ (* b b) (* (sqrt (fma (* a c) -4 (* b b))) b)))
77.0ms
(- (pow b 2) (* 4 (* a c)))
65.0ms
(- (pow b 2) (* 4 (* a c)))
60.0ms
(sqrt (- (sqrt (fma (* a c) -4 (* b b))) b))
58.0ms
(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.1b

regimes290.0ms

Accuracy

90.5% (0.8b remaining)

Error of 13.3b against oracle of 12.6b and baseline of 20.7b

bsearch67.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.0s8698×body80valid
443.0ms2870×body80nan