Details

Time bar (total: 15.0s)

sample88.0ms

Algorithm
intervals
Results
52.0ms271×body80valid
17.0ms106×body80nan

simplify242.0ms

Calls
1 calls:
Slowest
242.0ms
(if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.7b

localize175.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma -4 (* c a) (* b b)))
26.1b
(sqrt (fma -4 (* c a) (* b b)))
1.1b
(- (sqrt (fma -4 (* c a) (* b b))) b)
0.6b
(fma -4 (* c a) (* b b))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
6×fma-neg
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square pow1/2
1×sub-neg flip3-- fma-udef flip--
Calls
4 calls:
Slowest
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)))
0.0ms
(fma -4 (* c a) (* b b))

series195.0ms

Calls
4 calls:
Slowest
78.0ms
(sqrt (fma -4 (* c a) (* b b)))
45.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
41.0ms
(sqrt (fma -4 (* c a) (* b b)))
30.0ms
(fma -4 (* c a) (* b b))

simplify593.0ms

Calls
25 calls:
Slowest
92.0ms
(- (pow b 2) (* 4 (* a c)))
67.0ms
(- (pow b 2) (* 4 (* a c)))
62.0ms
(- (pow b 2) (* 4 (* a c)))
41.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))
39.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.6b

localize130.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma -4 (* c a) (* b b)))
1.1b
(- (sqrt (fma -4 (* c a) (* b b))) b)
0.6b
(fma -4 (* c a) (* b b))
0.5b
(/ (- (sqrt (fma -4 (* c a) (* b b))) b) (* 2 a))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube fma-neg add-exp-log sqrt-prod
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×times-frac associate-/l*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg pow1/2 div-sub div-exp fma-udef div-inv
Calls
4 calls:
Slowest
26.0ms
(/ (- (sqrt (fma -4 (* c a) (* b b))) b) (* 2 a))
13.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
0.0ms
(fma -4 (* c a) (* b b))

series199.0ms

Calls
4 calls:
Slowest
77.0ms
(/ (- (sqrt (fma -4 (* c a) (* b b))) b) (* 2 a))
46.0ms
(sqrt (fma -4 (* c a) (* b b)))
42.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
34.0ms
(fma -4 (* c a) (* b b))

simplify1.9s

Calls
34 calls:
Slowest
603.0ms
(- (* (sqrt (fma -4 (* c a) (* b b))) (sqrt (fma -4 (* c a) (* b b)))) (* b b))
203.0ms
(/ (* (* (- (sqrt (fma -4 (* c a) (* b b))) b) (- (sqrt (fma -4 (* c a) (* b b))) b)) (- (sqrt (fma -4 (* c a) (* b b))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
167.0ms
(- (pow (sqrt (fma -4 (* c a) (* b b))) 3) (pow b 3))
98.0ms
(- (log (- (sqrt (fma -4 (* c a) (* b b))) b)) (log (* 2 a)))
95.0ms
(- (pow b 2) (* 4 (* a c)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.1b

localize93.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma -4 (* c a) (* b b)))
26.1b
(sqrt (fma -4 (* c a) (* b b)))
1.1b
(- (sqrt (fma -4 (* c a) (* b b))) b)
1.1b
(- (sqrt (fma -4 (* c a) (* b b))) b)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt fma-neg sqrt-prod
10×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sub-neg flip3-- pow1/2 flip--
Calls
4 calls:
Slowest
13.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
12.0ms
(- (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)))

series229.0ms

Calls
4 calls:
Slowest
70.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
64.0ms
(sqrt (fma -4 (* c a) (* b b)))
51.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
44.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify500.0ms

Calls
30 calls:
Slowest
45.0ms
(sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b)))))
45.0ms
(* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b)))))
42.0ms
(* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b)))))
39.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))
39.0ms
(sqrt (sqrt (fma -4 (* c a) (* b b))))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.1b

localize96.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma -4 (* c a) (* b b)))
26.1b
(sqrt (fma -4 (* c a) (* b b)))
22.0b
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- b))
0.6b
(fma -4 (* c a) (* b b))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square pow1/2 fma-udef
Calls
4 calls:
Slowest
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))
0.0ms
(fma -4 (* c a) (* b b))

series436.0ms

Calls
4 calls:
Slowest
302.0ms
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- b))
53.0ms
(sqrt (fma -4 (* c a) (* b b)))
45.0ms
(sqrt (fma -4 (* c a) (* b b)))
35.0ms
(fma -4 (* c a) (* b b))

simplify1.2s

Calls
20 calls:
Slowest
463.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
243.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
92.0ms
(- (pow b 2) (* 4 (* a c)))
89.0ms
(- (pow b 2) (* 4 (* a c)))
65.0ms
(- (pow b 2) (* 4 (* a c)))

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.8b

regimes389.0ms

Accuracy

89.2% (0.9b remaining)

Error of 13.0b against oracle of 12.0b and baseline of 20.7b

bsearch90.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.0s8680×body80valid
534.0ms2865×body80nan