Details

Time bar (total: 16.0s)

sample76.0ms

Algorithm
intervals
Results
37.0ms277×body80valid
11.0ms97×body80nan

simplify202.0ms

Calls
1 calls:
Slowest
202.0ms
(if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.7b

localize132.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma -4 (* c a) (* b b)))
25.3b
(sqrt (fma -4 (* c a) (* b b)))
1.5b
(- (sqrt (fma -4 (* c a) (* b b))) b)
0.8b
(fma -4 (* c a) (* b b))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
6×fma-neg
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square pow1/2
1×sub-neg flip3-- fma-udef flip--
Calls
4 calls:
Slowest
11.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
5.0ms
(sqrt (fma -4 (* c a) (* b b)))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
0.0ms
(fma -4 (* c a) (* b b))

series403.0ms

Calls
4 calls:
Slowest
117.0ms
(sqrt (fma -4 (* c a) (* b b)))
101.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
98.0ms
(sqrt (fma -4 (* c a) (* b b)))
87.0ms
(fma -4 (* c a) (* b b))

simplify554.0ms

Calls
25 calls:
Slowest
59.0ms
(- (pow b 2) (* 4 (* a c)))
58.0ms
(- (pow b 2) (* 4 (* a c)))
56.0ms
(- (pow b 2) (* 4 (* a c)))
45.0ms
(* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b)))))
44.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.6b

localize98.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma -4 (* c a) (* b b)))
1.5b
(- (sqrt (fma -4 (* c a) (* b b))) b)
0.8b
(fma -4 (* c a) (* b b))
0.3b
(/ (- (sqrt (fma -4 (* c a) (* b b))) b) (* 2 a))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube fma-neg add-exp-log sqrt-prod
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×times-frac associate-/l*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg pow1/2 div-sub div-exp fma-udef div-inv
Calls
4 calls:
Slowest
25.0ms
(/ (- (sqrt (fma -4 (* c a) (* b b))) b) (* 2 a))
12.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
0.0ms
(fma -4 (* c a) (* b b))

series423.0ms

Calls
4 calls:
Slowest
124.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
112.0ms
(sqrt (fma -4 (* c a) (* b b)))
108.0ms
(/ (- (sqrt (fma -4 (* c a) (* b b))) b) (* 2 a))
79.0ms
(fma -4 (* c a) (* b b))

simplify2.0s

Calls
34 calls:
Slowest
544.0ms
(- (* (sqrt (fma -4 (* c a) (* b b))) (sqrt (fma -4 (* c a) (* b b)))) (* b b))
199.0ms
(- (pow (sqrt (fma -4 (* c a) (* b b))) 3) (pow b 3))
180.0ms
(/ (* (* (- (sqrt (fma -4 (* c a) (* b b))) b) (- (sqrt (fma -4 (* c a) (* b b))) b)) (- (sqrt (fma -4 (* c a) (* b b))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
129.0ms
(- (log (- (sqrt (fma -4 (* c a) (* b b))) b)) (log (* 2 a)))
93.0ms
(- (pow b 2) (* 4 (* a c)))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.6b

localize120.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma -4 (* c a) (* b b)))
1.5b
(- (sqrt (fma -4 (* c a) (* b b))) b)
0.8b
(fma -4 (* c a) (* b b))
0.3b
(/ (* 2 a) (- (sqrt (fma -4 (* c a) (* b b))) b))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube fma-neg add-exp-log sqrt-prod
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac
2×flip3-- associate-/r/ flip--
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg pow1/2 div-exp fma-udef div-inv associate-/l*
Calls
4 calls:
Slowest
17.0ms
(/ (* 2 a) (- (sqrt (fma -4 (* c a) (* b b))) b))
12.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
0.0ms
(fma -4 (* c a) (* b b))

series612.0ms

Calls
4 calls:
Slowest
300.0ms
(/ (* 2 a) (- (sqrt (fma -4 (* c a) (* b b))) b))
122.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
117.0ms
(sqrt (fma -4 (* c a) (* b b)))
72.0ms
(fma -4 (* c a) (* b b))

simplify1.3s

Calls
34 calls:
Slowest
205.0ms
(/ (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* (- (sqrt (fma -4 (* c a) (* b b))) b) (- (sqrt (fma -4 (* c a) (* b b))) b)) (- (sqrt (fma -4 (* c a) (* b b))) b)))
147.0ms
(- (log (* 2 a)) (log (- (sqrt (fma -4 (* c a) (* b b))) b)))
120.0ms
(+ (* (sqrt (fma -4 (* c a) (* b b))) (sqrt (fma -4 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -4 (* c a) (* b b))) b)))
92.0ms
(- (pow b 2) (* 4 (* a c)))
62.0ms
(- (pow b 2) (* 4 (* a c)))

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.6b

localize100.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma -4 (* c a) (* b b)))
25.3b
(sqrt (fma -4 (* c a) (* b b)))
25.3b
(sqrt (fma -4 (* c a) (* b b)))
1.5b
(- (sqrt (fma -4 (* c a) (* b b))) b)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
6×fma-neg
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square pow1/2
1×sub-neg flip3-- flip--
Calls
4 calls:
Slowest
8.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))

series409.0ms

Calls
4 calls:
Slowest
121.0ms
(sqrt (fma -4 (* c a) (* b b)))
102.0ms
(sqrt (fma -4 (* c a) (* b b)))
96.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
90.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify487.0ms

Calls
29 calls:
Slowest
46.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
46.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
44.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
41.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))
40.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 14.6b

regimes244.0ms

Accuracy

83.5% (1.4b remaining)

Error of 13.7b against oracle of 12.3b and baseline of 20.6b

bsearch194.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.9s8729×body80valid
987.0ms2941×body80nan