Details

Time bar (total: 50.5s)

sample92.0ms

Algorithm
intervals
Results
58.0ms276×body80valid
16.0ms99×body80nan

simplify218.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
218.0ms
(if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize145.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (fma -4 (* c a) (* b b)))
20.7b
(sqrt (fma -4 (* c a) (* b b)))
1.3b
(- (sqrt (fma -4 (* c a) (* b b))) b)
1.0b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))

rewrite29.0ms

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
10.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
8.0ms
(- (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)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(sqrt (fma -4 (* c a) (* b b)))
110.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
101.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
85.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify14.3s

Counts
204 → 177
Calls
204 calls:
Slowest
238.0ms
(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))))))))
237.0ms
(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 (* (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))))))))
213.0ms
(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))))))))
210.0ms
(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))))))))

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.9b

localize178.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (fma (* -4 c) a (* b b)))
20.7b
(sqrt (fma -4 (* c a) (* b b)))
1.3b
(- (sqrt (fma (* -4 c) a (* b b))) b)
1.0b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))

rewrite46.0ms

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
21.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
15.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
3.0ms
(sqrt (fma -4 (* c a) (* b b)))
3.0ms
(sqrt (fma (* -4 c) a (* b b)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(sqrt (fma (* -4 c) a (* b b)))
114.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
112.0ms
(sqrt (fma -4 (* c a) (* b b)))
103.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))

simplify15.3s

Counts
204 → 177
Calls
204 calls:
Slowest
269.0ms
(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))))))))
254.0ms
(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))))))))
233.0ms
(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))))))))
228.0ms
(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)))))))
228.0ms
(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))))))))

prune3.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.9b

localize176.0ms

Local error

Found 4 expressions with local error:

21.4b
(cbrt (fma -4 (* c a) (* b b)))
21.4b
(cbrt (fma -4 (* c a) (* b b)))
21.4b
(cbrt (fma -4 (* c a) (* b b)))
20.7b
(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
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 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)))

series799.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
260.0ms
(cbrt (fma -4 (* c a) (* b b)))
246.0ms
(cbrt (fma -4 (* c a) (* b b)))
183.0ms
(cbrt (fma -4 (* c a) (* b b)))
110.0ms
(sqrt (fma (* -4 c) a (* b b)))

simplify2.6s

Counts
26 → 70
Calls
26 calls:
Slowest
341.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
302.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
284.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
254.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
247.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.9b

localize142.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (fma (* -4 c) a (* b b)))
20.7b
(sqrt (fma (* -4 c) a (* b b)))
20.7b
(sqrt (fma -4 (* c a) (* b b)))
1.3b
(- (sqrt (fma (* -4 c) a (* b b))) b)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
23×*-un-lft-identity
22×sqrt-prod
21×add-cube-cbrt
18×prod-diff
7×pow1
6×fma-neg add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 90
Calls
4 calls:
Slowest
7.0ms
(- (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)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(sqrt (fma (* -4 c) a (* b b)))
88.0ms
(sqrt (fma -4 (* c a) (* b b)))
87.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
83.0ms
(sqrt (fma (* -4 c) a (* b b)))

simplify2.3s

Counts
74 → 102
Calls
74 calls:
Slowest
95.0ms
(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 b) (* (cbrt b) (cbrt b)))))
92.0ms
(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)))) (- (* (sqrt b) (sqrt b))))
89.0ms
(/ (exp (sqrt (fma (* -4 c) a (* b b)))) (exp b))
80.0ms
(fma 1 (sqrt (fma (* -4 c) a (* b b))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
76.0ms
(fma (sqrt (* (cbrt (fma (* -4 c) a (* b b))) (cbrt (fma (* -4 c) a (* b b))))) (sqrt (cbrt (fma (* -4 c) a (* b b)))) (- (* (sqrt b) (sqrt b))))

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.9b

regimes353.0ms

Accuracy

92% (0.6b remaining)

Error of 12.6b against oracle of 12.0b and baseline of 19.4b

bsearch132.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.0s8727×body80valid
610.0ms2896×body80nan