Details

Time bar (total: 36.4s)

sample112.0ms

Algorithm
intervals
Results
72.0ms268×body80valid
17.0ms78×body80nan

simplify232.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
232.0ms
(if (>= b 0) (/ (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)) (/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.6b

localize196.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (fma (* -4 a) c (* b b)))
20.7b
(sqrt (fma (* -4 a) c (* b b)))
2.7b
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.1b
(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite35.0ms

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
15.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
9.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
5.0ms
(sqrt (fma (* -4 a) c (* b b)))
2.0ms
(sqrt (fma (* -4 a) c (* b b)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
108.0ms
(sqrt (fma (* -4 a) c (* b b)))
108.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
99.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify15.6s

Counts
204 → 177
Calls
204 calls:
Slowest
277.0ms
(fma 1 (- b) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
275.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
260.0ms
(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
252.0ms
(fma 1 (- b) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
233.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.3b

localize160.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (fma (* -4 a) c (* b b)))
20.7b
(sqrt (fma (* -4 a) c (* b b)))
20.7b
(sqrt (fma (* -4 a) c (* b b)))
17.6b
(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×fma-udef
Counts
4 → 59
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
0.0ms
(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))

series759.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
387.0ms
(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))
133.0ms
(sqrt (fma (* -4 a) c (* b b)))
123.0ms
(sqrt (fma (* -4 a) c (* b b)))
116.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify1.0s

Counts
27 → 71
Calls
27 calls:
Slowest
367.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
138.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
60.0ms
(sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b)))))
60.0ms
(sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b)))))
57.0ms
(sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b)))))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.0b

localize126.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (fma (* -4 a) c (* b b)))
20.7b
(sqrt (fma (* -4 a) c (* b b)))
20.7b
(sqrt (fma (* -4 a) c (* b b)))
13.7b
(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))

rewrite15.0ms

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
10.0ms
(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))
2.0ms
(sqrt (fma (* -4 a) c (* b b)))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
126.0ms
(sqrt (fma (* -4 a) c (* b b)))
107.0ms
(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))
105.0ms
(sqrt (fma (* -4 a) c (* b b)))
93.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify2.9s

Counts
58 → 98
Calls
58 calls:
Slowest
334.0ms
(/ (/ 1 (exp b)) (exp (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
242.0ms
(/ (exp (- b)) (exp (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
120.0ms
(* -2 (/ (* a c) b))
112.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
106.0ms
(fma 1 (- b) (- (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.0b

localize153.0ms

Local error

Found 4 expressions with local error:

24.0b
(fma (fabs (cbrt (fma (* -4 a) c (* b b)))) (sqrt (cbrt (fma (* -4 a) c (* b b)))) b)
21.4b
(cbrt (fma (* -4 a) c (* b b)))
21.4b
(cbrt (fma (* -4 a) c (* b b)))
20.7b
(sqrt (fma (* -4 a) c (* b b)))

rewrite4.0ms

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 a) c (* b b)))
1.0ms
(cbrt (fma (* -4 a) c (* b b)))
1.0ms
(cbrt (fma (* -4 a) c (* b b)))
0.0ms
(fma (fabs (cbrt (fma (* -4 a) c (* b b)))) (sqrt (cbrt (fma (* -4 a) c (* b b)))) b)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
416.0ms
(fma (fabs (cbrt (fma (* -4 a) c (* b b)))) (sqrt (cbrt (fma (* -4 a) c (* b b)))) b)
255.0ms
(cbrt (fma (* -4 a) c (* b b)))
229.0ms
(cbrt (fma (* -4 a) c (* b b)))
107.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify2.8s

Counts
23 → 67
Calls
23 calls:
Slowest
386.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
312.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
297.0ms
(+ (* (fabs (pow (fma (* -4 a) c (pow b 2)) 1/3)) (exp (* 1/6 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a))))))) b)
286.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
272.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.7s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 13.0b

regimes353.0ms

Accuracy

86.4% (1.0b remaining)

Error of 13.0b against oracle of 12.0b and baseline of 19.4b

bsearch128.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.8s8727×body80valid
509.0ms2848×body80nan