Details

Time bar (total: 24.0s)

sample100.0ms

Algorithm
intervals
Results
53.0ms283×body80valid
14.0ms95×body80nan

simplify215.0ms

Calls
1 calls:
Slowest
214.0ms
(if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize128.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (fma -4 (* c a) (* b b)))
24.0b
(sqrt (fma -4 (* c a) (* b b)))
1.0b
(- (sqrt (fma -4 (* c a) (* b b))) b)
0.7b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))

rewrite18.0ms

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 (* c a) (* b b))) b)
6.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
3.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))

series452.0ms

Calls
4 calls:
Slowest
122.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
122.0ms
(sqrt (fma -4 (* c a) (* b b)))
110.0ms
(sqrt (fma -4 (* c a) (* b b)))
97.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))

simplify4.7s

Calls
81 calls:
Slowest
129.0ms
(fma 1 (- b) (- (* (sqrt (fma -4 (* c a) (* b b))) (sqrt 1))))
127.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (fma -4 (* c a) (* b b))) 1)))
125.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))
124.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (fma -4 (* c a) (* b b))) (sqrt 1))))
124.0ms
(fma 1 (- b) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.3b

localize97.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (fma -4 (* c a) (* b b)))
24.0b
(sqrt (fma -4 (* c a) (* b b)))
24.0b
(sqrt (fma -4 (* c a) (* b b)))
1.0b
(- (sqrt (fma -4 (* c a) (* b b))) b)

rewrite21.0ms

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
16.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))

series396.0ms

Calls
4 calls:
Slowest
113.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
102.0ms
(sqrt (fma -4 (* c a) (* b b)))
94.0ms
(sqrt (fma -4 (* c a) (* b b)))
86.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify498.0ms

Calls
29 calls:
Slowest
45.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
45.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))
44.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
42.0ms
(sqrt (fma -4 (* c a) (* b b)))
41.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.3b

localize139.0ms

Local error

Found 4 expressions with local error:

24.7b
(cbrt (fma -4 (* c a) (* b b)))
24.7b
(cbrt (fma -4 (* c a) (* b b)))
24.7b
(cbrt (fma -4 (* c a) (* b b)))
24.0b
(sqrt (fma -4 (* c a) (* b b)))

rewrite4.0ms

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 (* c a) (* b b)))
1.0ms
(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)))

series805.0ms

Calls
4 calls:
Slowest
254.0ms
(cbrt (fma -4 (* c a) (* b b)))
228.0ms
(cbrt (fma -4 (* c a) (* b b)))
216.0ms
(cbrt (fma -4 (* c a) (* b b)))
107.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify2.8s

Calls
25 calls:
Slowest
378.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
346.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
343.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
308.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
298.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.3b

localize140.0ms

Local error

Found 4 expressions with local error:

24.7b
(cbrt (fma -4 (* c a) (* b b)))
24.7b
(cbrt (fma -4 (* c a) (* b b)))
24.7b
(cbrt (fma -4 (* c a) (* b b)))
24.0b
(sqrt (fma -4 (* c a) (* 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 -4 (* c a) (* b b)))
1.0ms
(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)))

series818.0ms

Calls
4 calls:
Slowest
245.0ms
(cbrt (fma -4 (* c a) (* b b)))
236.0ms
(cbrt (fma -4 (* c a) (* b b)))
229.0ms
(cbrt (fma -4 (* c a) (* b b)))
108.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify2.6s

Calls
25 calls:
Slowest
334.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
327.0ms
(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))))
282.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
270.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.3b

regimes393.0ms

Accuracy

89.5% (0.8b remaining)

Error of 12.9b against oracle of 12.1b and baseline of 19.3b

bsearch199.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.9s8714×body80valid
968.0ms2917×body80nan