Details

Time bar (total: 55.1s)

sample113.0ms

Algorithm
intervals
Results
67.0ms288×body80valid
20.0ms106×body80nan

simplify646.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
646.0ms
(if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize159.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (fma -4 (* c a) (* b b)))
20.3b
(sqrt (fma -4 (* c a) (* b b)))
0.9b
(- (sqrt (fma -4 (* c a) (* b b))) b)
0.9b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 flip--
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
Slowest
22.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
9.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
3.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))

series490.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(sqrt (fma -4 (* c a) (* b b)))
115.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
112.0ms
(sqrt (fma -4 (* c a) (* b b)))
103.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)

simplify15.1s

Counts
204 → 177
Calls
204 calls:
Slowest
247.0ms
(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))))))))
246.0ms
(fma (* (cbrt b) (cbrt b)) (- (cbrt 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))))))))
228.0ms
(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))))))))
223.0ms
(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))))))))
222.0ms
(fma (- (cbrt (sqrt (fma -4 (* c a) (* b 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)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b)))))))

prune3.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.0b

localize204.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (fma (* -4 a) c (* b b)))
20.3b
(sqrt (fma -4 (* c a) (* b b)))
0.9b
(- (sqrt (fma (* -4 a) c (* b b))) b)
0.9b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 flip--
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
Slowest
22.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
13.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
113.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
104.0ms
(sqrt (fma -4 (* c a) (* b b)))
91.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify15.4s

Counts
204 → 177
Calls
204 calls:
Slowest
295.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- 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))))))))
250.0ms
(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))))))))
241.0ms
(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))))))))
240.0ms
(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))))))))
231.0ms
(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))))))))

prune3.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.0b

localize203.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (fma (* -4 a) c (* b b)))
20.3b
(sqrt (fma -4 (* c a) (* b b)))
20.3b
(sqrt (fma -4 (* c a) (* b b)))
9.0b
(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip-- difference-of-squares
Counts
4 → 86
Calls
4 calls:
Slowest
21.0ms
(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
2.0ms
(sqrt (fma (* -4 a) c (* b b)))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(sqrt (fma -4 (* c a) (* b b)))
119.0ms
(sqrt (fma -4 (* c a) (* b b)))
119.0ms
(sqrt (fma (* -4 a) c (* b b)))
113.0ms
(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))

simplify2.9s

Counts
58 → 98
Calls
58 calls:
Slowest
347.0ms
(/ (/ 1 (exp b)) (exp (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))
302.0ms
(/ (exp (- b)) (exp (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))
139.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))
138.0ms
(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))
113.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))

prune2.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.0b

localize193.0ms

Local error

Found 4 expressions with local error:

21.0b
(cbrt (fma -4 (* c a) (* b b)))
21.0b
(cbrt (fma -4 (* c a) (* b b)))
21.0b
(cbrt (fma -4 (* c a) (* b b)))
20.3b
(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
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma (* -4 a) c (* 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)))

series880.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
285.0ms
(cbrt (fma -4 (* c a) (* b b)))
240.0ms
(cbrt (fma -4 (* c a) (* b b)))
229.0ms
(cbrt (fma -4 (* c a) (* b b)))
125.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify2.9s

Counts
26 → 70
Calls
26 calls:
Slowest
349.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
346.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
322.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
306.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
280.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune2.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 10.0b

regimes506.0ms

Accuracy

87.1% (0.9b remaining)

Error of 13.7b against oracle of 12.8b and baseline of 19.8b

bsearch143.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.1s8708×body80valid
529.0ms2839×body80nan