Details

Time bar (total: 19.5s)

sample109.0ms

Algorithm
intervals
Results
67.0ms277×body80valid
18.0ms87×body80nan

simplify246.0ms

Calls
1 calls:
Slowest
246.0ms
(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: 17.4b

localize139.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma -4 (* c a) (* b b)))
19.5b
(sqrt (fma -4 (* c a) (* b b)))
1.1b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
0.8b
(fma -4 (* c a) (* b b))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×prod-diff
23×*-un-lft-identity
21×add-cube-cbrt
19×sqrt-prod
7×neg-mul-1
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
2×rem-sqrt-square pow1/2 difference-of-squares
1×associate--l- neg-sub0 sub-neg flip3-- diff-log fma-udef flip-- distribute-lft-out--
Calls
4 calls:
Slowest
11.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
4.0ms
(sqrt (fma -4 (* c a) (* b b)))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
0.0ms
(fma -4 (* c a) (* b b))

series212.0ms

Calls
4 calls:
Slowest
68.0ms
(sqrt (fma -4 (* c a) (* b b)))
49.0ms
(sqrt (fma -4 (* c a) (* b b)))
48.0ms
(fma -4 (* c a) (* b b))
46.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))

simplify4.6s

Calls
76 calls:
Slowest
117.0ms
(fma 1 (- b) (- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))
116.0ms
(/ (exp (- b)) (exp (sqrt (fma -4 (* c a) (* b b)))))
112.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (cbrt (fma -4 (* c a) (* b b)))) (sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b))))))))
110.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (cbrt (fma -4 (* c a) (* b b)))) (sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b))))))))
101.0ms
(fma 1 (- b) (- (* (sqrt (fma -4 (* c a) (* b b))) (sqrt 1))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.3b

localize137.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma -4 (* c a) (* b b)))
19.5b
(sqrt (fma -4 (* c a) (* b b)))
19.5b
(sqrt (fma -4 (* c a) (* b b)))
7.1b
(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×*-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×rem-sqrt-square pow1/2
1×sub-neg flip3-- fma-neg flip--
Calls
4 calls:
Slowest
19.0ms
(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (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)))

series237.0ms

Calls
4 calls:
Slowest
74.0ms
(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)
64.0ms
(sqrt (fma -4 (* c a) (* b b)))
52.0ms
(sqrt (fma -4 (* c a) (* b b)))
46.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify257.0ms

Calls
25 calls:
Slowest
27.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))
26.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))
26.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
26.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))
24.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.3b

localize122.0ms

Local error

Found 4 expressions with local error:

20.3b
(cbrt (fma -4 (* c a) (* b b)))
20.3b
(cbrt (fma -4 (* c a) (* b b)))
20.3b
(cbrt (fma -4 (* c a) (* b b)))
19.5b
(sqrt (* (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))) (cbrt (fma -4 (* c a) (* b b)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-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
1×pow1/2 sqrt-prod
Calls
4 calls:
Slowest
8.0ms
(sqrt (* (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))) (cbrt (fma -4 (* c a) (* b b)))))
2.0ms
(cbrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))

series641.0ms

Calls
4 calls:
Slowest
208.0ms
(cbrt (fma -4 (* c a) (* b b)))
192.0ms
(cbrt (fma -4 (* c a) (* b b)))
175.0ms
(cbrt (fma -4 (* c a) (* b b)))
66.0ms
(sqrt (* (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))) (cbrt (fma -4 (* c a) (* b b)))))

simplify2.6s

Calls
22 calls:
Slowest
321.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
319.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
312.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
304.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
299.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 11.3b

localize121.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma -4 (* c a) (* b b)))
19.5b
(sqrt (fma -4 (* c a) (* b b)))
19.5b
(sqrt (fma -4 (* c a) (* b b)))
19.5b
(sqrt (fma -4 (* c a) (* b b)))

rewrite8.0ms

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

series218.0ms

Calls
4 calls:
Slowest
67.0ms
(sqrt (fma -4 (* c a) (* b b)))
58.0ms
(sqrt (fma -4 (* c a) (* b b)))
50.0ms
(sqrt (fma -4 (* c a) (* b b)))
44.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify470.0ms

Calls
28 calls:
Slowest
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)))))
44.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
43.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
42.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))

prune1.3s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 11.3b

regimes851.0ms

Accuracy

91.1% (0.6b remaining)

Error of 13.0b against oracle of 12.4b and baseline of 19.3b

bsearch138.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.7s8739×body80valid
619.0ms3030×body80nan