Details

Time bar (total: 16.3s)

sample124.0ms

Algorithm
intervals
Results
32.0ms38×body2560valid
25.0ms180×body80valid
22.0ms106×body80nan
16.0ms23×body1280valid
10.0ms19×body640valid
3.0ms4×body5120valid
1.0ms5×body160valid
0.0ms2×body320valid

simplify173.0ms

Calls
1 calls:
Slowest
173.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.2b

localize19.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma c (* -4 a) (* b b)))
1.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.5b
(fma c (* -4 a) (* b b))
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite20.0ms

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 associate-/l* add-log-exp
2×div-sub div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg flip3-- pow1/2 fma-udef flip-- associate-/l/
Calls
4 calls:
Slowest
12.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
6.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series205.0ms

Calls
4 calls:
Slowest
72.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
53.0ms
(sqrt (fma c (* -4 a) (* b b)))
42.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
37.0ms
(fma c (* -4 a) (* b b))

simplify665.0ms

Calls
26 calls:
Slowest
90.0ms
(- (pow b 2) (* 4 (* a c)))
77.0ms
(- (pow b 2) (* 4 (* a c)))
64.0ms
(- (pow b 2) (* 4 (* a c)))
44.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
44.0ms
(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))

prune918.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 29.8b

localize19.0ms

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

rewrite35.0ms

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 associate-/l* add-log-exp
2×div-sub div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg flip3-- pow1/2 fma-udef flip-- associate-/l/
Calls
4 calls:
Slowest
23.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
9.0ms
(- (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))

series219.0ms

Calls
4 calls:
Slowest
83.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
57.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
47.0ms
(sqrt (fma (* a c) -4 (* b b)))
31.0ms
(fma (* a c) -4 (* b b))

simplify754.0ms

Calls
26 calls:
Slowest
68.0ms
(* (cbrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
68.0ms
(sqrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))
64.0ms
(- (pow b 2) (* 4 (* a c)))
64.0ms
(- (pow b 2) (* 4 (* a c)))
59.0ms
(- (pow b 2) (* 4 (* a c)))

prune983.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 29.8b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt fma-neg sqrt-prod
10×*-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
2×rem-sqrt-square sub-neg flip3-- pow1/2 flip--
Calls
4 calls:
Slowest
12.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
11.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))

series209.0ms

Calls
4 calls:
Slowest
68.0ms
(sqrt (fma (* a c) -4 (* b b)))
54.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
47.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
40.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify640.0ms

Calls
30 calls:
Slowest
59.0ms
(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))
56.0ms
(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))
52.0ms
(sqrt (sqrt (fma (* a c) -4 (* b b))))
52.0ms
(sqrt (sqrt (fma (* a c) -4 (* b b))))
51.0ms
(sqrt (sqrt (fma (* a c) -4 (* b b))))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 29.8b

localize50.0ms

Local error

Found 4 expressions with local error:

26.9b
(cbrt (fma (* a c) -4 (* b b)))
26.9b
(cbrt (fma (* a c) -4 (* b b)))
26.9b
(cbrt (fma (* a c) -4 (* b b)))
26.1b
(sqrt (fma (* a c) -4 (* b b)))

rewrite3.0ms

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 (* a c) -4 (* b b)))
1.0ms
(cbrt (fma (* a c) -4 (* b b)))
1.0ms
(cbrt (fma (* a c) -4 (* b b)))
1.0ms
(cbrt (fma (* a c) -4 (* b b)))

series671.0ms

Calls
4 calls:
Slowest
220.0ms
(cbrt (fma (* a c) -4 (* b b)))
194.0ms
(cbrt (fma (* a c) -4 (* b b)))
193.0ms
(cbrt (fma (* a c) -4 (* b b)))
64.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify2.7s

Calls
25 calls:
Slowest
339.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
328.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
309.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
294.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
284.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 29.8b

regimes430.0ms

Accuracy

82.9% (0.9b remaining)

Error of 29.7b against oracle of 28.8b and baseline of 34.3b

bsearch95.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.4s1032×body2560valid
862.0ms5797×body80valid
838.0ms2865×body80nan
724.0ms915×body1280valid
371.0ms488×body640valid
124.0ms122×body5120valid
110.0ms217×body320valid
26.0ms109×body160valid