Details

Time bar (total: 51.1s)

sample134.0ms

Algorithm
intervals
Results
90.0ms280×body80valid
16.0ms79×body80nan

simplify196.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
195.0ms
(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: 16.6b

localize160.0ms

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)))
2.7b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.1b
(- (sqrt (fma -4 (* c a) (* b b))) b)

rewrite49.0ms

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))))
13.0ms
(- (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)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
114.0ms
(sqrt (fma -4 (* c a) (* b b)))
112.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
99.0ms
(sqrt (fma -4 (* c a) (* b b)))
89.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))

simplify14.7s

Counts
204 → 177
Calls
204 calls:
Slowest
278.0ms
(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))))))))
249.0ms
(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))))))))
247.0ms
(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))))))))
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))))))))
239.0ms
(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))))))))

prune2.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.2b

localize209.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma (* -4 a) c (* b b)))
19.5b
(sqrt (fma -4 (* c a) (* b b)))
2.7b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.1b
(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite27.0ms

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))))
9.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))

series502.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(sqrt (fma -4 (* c a) (* b b)))
127.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
125.0ms
(sqrt (fma (* -4 a) c (* b b)))
116.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))

simplify15.7s

Counts
204 → 177
Calls
204 calls:
Slowest
609.0ms
(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))))))))
307.0ms
(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))))))))
274.0ms
(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))))))))
259.0ms
(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))))))))
243.0ms
(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))))))))

prune3.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.2b

localize164.0ms

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)))
19.5b
(sqrt (fma -4 (* c a) (* b b)))
18.3b
(fma (fabs (cbrt (fma -4 (* c a) (* b b)))) (sqrt (cbrt (fma -4 (* c a) (* b b)))) b)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×cbrt-prod
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 55
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)))
0.0ms
(fma (fabs (cbrt (fma -4 (* c a) (* b b)))) (sqrt (cbrt (fma -4 (* c a) (* b b)))) b)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
404.0ms
(fma (fabs (cbrt (fma -4 (* c a) (* b b)))) (sqrt (cbrt (fma -4 (* c a) (* b b)))) b)
260.0ms
(cbrt (fma -4 (* c a) (* b b)))
259.0ms
(cbrt (fma -4 (* c a) (* b b)))
121.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify2.9s

Counts
23 → 67
Calls
23 calls:
Slowest
399.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
361.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
354.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
340.0ms
(+ b (* (fabs (pow (fma -4 (* a c) (pow b 2)) 1/3)) (exp (* 1/6 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a))))))))
289.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.2b

localize172.0ms

Local error

Found 4 expressions with local error:

20.3b
(cbrt (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)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 62
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
(cbrt (fma -4 (* c a) (* b b)))

series554.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
228.0ms
(cbrt (fma -4 (* c a) (* b b)))
114.0ms
(sqrt (fma -4 (* c a) (* b b)))
107.0ms
(sqrt (fma -4 (* c a) (* b b)))
105.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.3s

Counts
30 → 74
Calls
30 calls:
Slowest
332.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
271.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
228.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a))))))
43.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
43.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.2b

regimes407.0ms

Accuracy

90.7% (0.7b remaining)

Error of 12.7b against oracle of 12.0b and baseline of 19.4b

bsearch144.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.3s8786×body80valid
565.0ms2868×body80nan