Details

Time bar (total: 36.1s)

sample66.0ms

Algorithm
intervals
Results
36.0ms279×body80valid
14.0ms81×body80nan

simplify220.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
220.0ms
(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: 18.6b

localize165.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (fma -4 (* c a) (* b b)))
22.4b
(sqrt (fma -4 (* c a) (* b b)))
1.1b
(- (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
21.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
10.0ms
(- (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)))

series491.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(sqrt (fma -4 (* c a) (* b b)))
135.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
110.0ms
(sqrt (fma -4 (* c a) (* b b)))
110.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))

simplify14.5s

Counts
204 → 177
Calls
204 calls:
Slowest
257.0ms
(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))))))))
236.0ms
(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))))))))
232.0ms
(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))))))))
225.0ms
(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 (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))))))))

prune2.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.8b

localize151.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (fma -4 (* c a) (* b b)))
22.4b
(sqrt (fma -4 (* c a) (* b b)))
22.4b
(sqrt (fma -4 (* c a) (* b b)))
19.2b
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* 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
2.0ms
(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)))
0.0ms
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- b))

series738.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
425.0ms
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- b))
112.0ms
(sqrt (fma -4 (* c a) (* b b)))
110.0ms
(sqrt (fma -4 (* c a) (* b b)))
90.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify856.0ms

Counts
27 → 71
Calls
27 calls:
Slowest
293.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
168.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
45.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
45.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
42.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.4b

localize188.0ms

Local error

Found 4 expressions with local error:

23.1b
(cbrt (fma -4 (* c a) (* b b)))
23.1b
(cbrt (fma -4 (* c a) (* b b)))
23.1b
(cbrt (fma -4 (* c a) (* b b)))
22.4b
(sqrt (fma -4 (* c a) (* b b)))

rewrite7.0ms

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
2.0ms
(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)))

series891.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
287.0ms
(cbrt (fma -4 (* c a) (* b b)))
265.0ms
(cbrt (fma -4 (* c a) (* b b)))
226.0ms
(cbrt (fma -4 (* c a) (* b b)))
113.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify3.4s

Counts
26 → 70
Calls
26 calls:
Slowest
645.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a))))))
380.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
377.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
306.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
293.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.6s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 13.4b

localize277.0ms

Local error

Found 4 expressions with local error:

23.1b
(cbrt (fma -4 (* c a) (* b b)))
23.1b
(cbrt (fma -4 (* c a) (* b b)))
22.4b
(sqrt (fma -4 (* c a) (* b b)))
22.4b
(sqrt (fma -4 (* c a) (* b b)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 60
Calls
4 calls:
Slowest
3.0ms
(sqrt (fma -4 (* c a) (* b b)))
2.0ms
(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)))

series789.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
292.0ms
(cbrt (fma -4 (* c a) (* b b)))
255.0ms
(cbrt (fma -4 (* c a) (* b b)))
131.0ms
(sqrt (fma -4 (* c a) (* b b)))
111.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify2.0s

Counts
28 → 72
Calls
28 calls:
Slowest
304.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
297.0ms
(- (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))))))
269.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
212.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a))))))

prune1.8s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 13.4b

regimes472.0ms

Accuracy

85.2% (1.0b remaining)

Error of 13.0b against oracle of 12.0b and baseline of 18.9b

bsearch126.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.4s8682×body80valid
590.0ms2862×body80nan