Details

Time bar (total: 33.2s)

sample87.0ms

Algorithm
intervals
Results
48.0ms284×body80valid
14.0ms99×body80nan

simplify257.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
256.0ms
(if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize151.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (fma -4 (* c a) (* b b)))
20.2b
(sqrt (fma -4 (* c a) (* b b)))
1.7b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.2b
(fma -4 (* c a) (* b b))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg flip3-- neg-log fma-udef flip--
Counts
4 → 134
Calls
4 calls:
Slowest
20.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
5.0ms
(sqrt (fma -4 (* c a) (* b b)))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
0.0ms
(fma -4 (* c a) (* b b))

series384.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
101.0ms
(sqrt (fma -4 (* c a) (* b b)))
98.0ms
(sqrt (fma -4 (* c a) (* b b)))
78.0ms
(fma -4 (* c a) (* b b))

simplify14.6s

Counts
157 → 146
Calls
157 calls:
Slowest
503.0ms
(fma (- (sqrt (fma -4 (* c a) (* b b)))) (sqrt 1) (* (sqrt (fma -4 (* c a) (* b b))) (sqrt 1)))
264.0ms
(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))))))))
251.0ms
(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))))))))
248.0ms
(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))))))))
244.0ms
(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))))))))

prune2.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.6b

localize216.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (fma -4 (* c a) (* b b)))
20.2b
(sqrt (fma -4 (* c a) (* b b)))
20.2b
(sqrt (fma -4 (* c a) (* b b)))
9.2b
(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×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 prod-diff
1×sub-neg flip3-- fma-neg diff-log flip-- difference-of-squares
Counts
4 → 68
Calls
4 calls:
Slowest
27.0ms
(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)
3.0ms
(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)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)
110.0ms
(sqrt (fma -4 (* c a) (* b b)))
100.0ms
(sqrt (fma -4 (* c a) (* b b)))
95.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify975.0ms

Counts
37 → 80
Calls
37 calls:
Slowest
270.0ms
(/ (exp (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))) (exp b))
61.0ms
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
53.0ms
(- (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt b))
52.0ms
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- (* b 1)))
49.0ms
(+ (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt b))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.6b

localize150.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (fma -4 (* c a) (* b b)))
20.2b
(sqrt (fma -4 (* c a) (* b b)))
20.2b
(sqrt (fma -4 (* c a) (* b b)))
9.2b
(+ (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) (- b))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×sum-log
1×neg-sub0 +-commutative associate-+r- fma-def flip3-+ unsub-neg neg-log flip-+
Counts
4 → 67
Calls
4 calls:
Slowest
11.0ms
(+ (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) (- b))
1.0ms
(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)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(sqrt (fma -4 (* c a) (* b b)))
107.0ms
(sqrt (fma -4 (* c a) (* b b)))
106.0ms
(sqrt (fma -4 (* c a) (* b b)))
104.0ms
(+ (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) (- b))

simplify1.2s

Counts
30 → 79
Calls
30 calls:
Slowest
382.0ms
(* (exp (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))) (/ 1 (exp b)))
331.0ms
(* (exp (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))) (exp (- b)))
48.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
46.0ms
(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))))

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.6b

localize161.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (fma -4 (* c a) (* b b)))
20.2b
(sqrt (fma -4 (* c a) (* b b)))
20.2b
(sqrt (fma -4 (* c a) (* b b)))
10.0b
(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))

rewrite14.0ms

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

series450.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(sqrt (fma -4 (* c a) (* b b)))
115.0ms
(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
112.0ms
(sqrt (fma -4 (* c a) (* b b)))
108.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify3.0s

Counts
58 → 98
Calls
58 calls:
Slowest
492.0ms
(/ (/ 1 (exp b)) (exp (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))
299.0ms
(/ (exp (- b)) (exp (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))
140.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))
122.0ms
(- (* 2 (/ (* a c) b)) (* 2 b))
117.0ms
(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))

prune1.6s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 10.6b

regimes424.0ms

Accuracy

89.3% (0.7b remaining)

Error of 12.9b against oracle of 12.2b and baseline of 19.1b

bsearch105.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.8s8751×body80valid
492.0ms2889×body80nan