Details

Time bar (total: 25.1s)

sample122.0ms

Algorithm
intervals
Results
76.0ms272×body80valid
21.0ms89×body80nan

simplify288.0ms

Calls
1 calls:
Slowest
287.0ms
(if (>= b 0) (/ (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)) (/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize161.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma (* -4 a) c (* b b)))
25.3b
(sqrt (fma (* -4 a) c (* b b)))
1.0b
(- (sqrt (fma (* -4 a) c (* b b))) b)
0.7b
(- (- b) (sqrt (fma (* -4 a) c (* b b))))

rewrite15.0ms

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
6.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
6.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))

series425.0ms

Calls
4 calls:
Slowest
119.0ms
(sqrt (fma (* -4 a) c (* b b)))
111.0ms
(sqrt (fma (* -4 a) c (* b b)))
98.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
98.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))

simplify4.9s

Calls
81 calls:
Slowest
141.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (cbrt (fma (* -4 a) c (* b b)))) (sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b))))))))
141.0ms
(- (* 2 (/ (* a c) b)) (* 2 b))
140.0ms
(fma 1 (- 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))))))))
125.0ms
(fma 1 (- b) (- (* (sqrt (cbrt (fma (* -4 a) c (* b b)))) (sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b))))))))
111.0ms
(* -2 (/ (* a c) b))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

localize161.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma (* -4 a) c (* b b)))
6.4b
(* (/ c b) a)
4.3b
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
1.0b
(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite39.0ms

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
23.0ms
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
9.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
5.0ms
(* (/ c b) a)
2.0ms
(sqrt (fma (* -4 a) c (* b b)))

series322.0ms

Calls
4 calls:
Slowest
114.0ms
(sqrt (fma (* -4 a) c (* b b)))
109.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
63.0ms
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
35.0ms
(* (/ c b) a)

simplify2.4s

Calls
31 calls:
Slowest
738.0ms
(- (log (* (- (* (/ c b) a) b) 2)) (log (* 2 a)))
637.0ms
(/ (* (* (* (- (* (/ c b) a) b) 2) (* (- (* (/ c b) a) b) 2)) (* (- (* (/ c b) a) b) 2)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
324.0ms
(* (- (pow (* (/ c b) a) 3) (pow b 3)) 2)
169.0ms
(* (- (* (* (/ c b) a) (* (/ c b) a)) (* b b)) 2)
129.0ms
(/ (- (* (/ c b) a) b) 2)

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

localize109.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma (* -4 a) c (* b b)))
25.3b
(sqrt (fma (* -4 a) c (* b b)))
6.4b
(* (/ c b) a)
4.3b
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log sqrt-prod
4×expm1-log1p-u pow1 associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/
2×rem-sqrt-square pow1/2 div-inv associate-/l/
1×cbrt-undiv clear-num associate-/r* frac-2neg times-frac flip3-- div-exp *-commutative flip-- associate-/l*
Calls
4 calls:
Slowest
26.0ms
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
3.0ms
(* (/ c b) a)
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))

series277.0ms

Calls
4 calls:
Slowest
112.0ms
(sqrt (fma (* -4 a) c (* b b)))
86.0ms
(sqrt (fma (* -4 a) c (* b b)))
52.0ms
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
27.0ms
(* (/ c b) a)

simplify2.5s

Calls
30 calls:
Slowest
831.0ms
(- (log (* (- (* (/ c b) a) b) 2)) (log (* 2 a)))
650.0ms
(/ (* (* (* (- (* (/ c b) a) b) 2) (* (- (* (/ c b) a) b) 2)) (* (- (* (/ c b) a) b) 2)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
357.0ms
(* (- (pow (* (/ c b) a) 3) (pow b 3)) 2)
180.0ms
(* (- (* (* (/ c b) a) (* (/ c b) a)) (* b b)) 2)
89.0ms
(/ (- (* (/ c b) a) b) 2)

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

localize124.0ms

Local error

Found 4 expressions with local error:

26.1b
(cbrt (fma (* -4 a) c (* b b)))
26.1b
(cbrt (fma (* -4 a) c (* b b)))
26.1b
(cbrt (fma (* -4 a) c (* b b)))
25.3b
(sqrt (fma (* -4 a) c (* b b)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square pow1/2
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
1.0ms
(cbrt (fma (* -4 a) c (* b b)))
1.0ms
(cbrt (fma (* -4 a) c (* b b)))
1.0ms
(cbrt (fma (* -4 a) c (* b b)))

series878.0ms

Calls
4 calls:
Slowest
288.0ms
(cbrt (fma (* -4 a) c (* b b)))
246.0ms
(cbrt (fma (* -4 a) c (* b b)))
242.0ms
(cbrt (fma (* -4 a) c (* b b)))
100.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify2.5s

Calls
25 calls:
Slowest
317.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
297.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
288.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
284.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
231.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

regimes364.0ms

Accuracy

91.8% (0.7b remaining)

Error of 12.8b against oracle of 12.1b and baseline of 20.8b

bsearch141.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.2s8706×body80valid
473.0ms2916×body80nan