Details

Time bar (total: 19.7s)

sample167.0ms

Algorithm
intervals
Results
53.0ms138×body160valid
41.0ms301×body80nan
33.0ms557×pre80true
17.0ms118×body80valid

simplify136.0ms

Calls
1 calls:
Slowest
136.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize28.0ms

Local error

Found 4 expressions with local error:

28.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.3b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.2b
(fma c (* -4 a) (* b b))
0.1b
(sqrt (fma c (* -4 a) (* b b)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×fma-neg sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×div-sub div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg flip3-- pow1/2 fma-udef flip-- associate-/l/
Calls
4 calls:
Slowest
24.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
13.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series235.0ms

Calls
4 calls:
Slowest
67.0ms
(sqrt (fma c (* -4 a) (* b b)))
62.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
57.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
49.0ms
(fma c (* -4 a) (* b b))

simplify637.0ms

Calls
26 calls:
Slowest
83.0ms
(- (pow b 2) (* 4 (* a c)))
67.0ms
(- (pow b 2) (* 4 (* a c)))
62.0ms
(- (pow b 2) (* 4 (* a c)))
49.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
46.0ms
(sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))

prune1.0s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 26.1b

localize10.0ms

Local error

Found 4 expressions with local error:

28.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
28.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
28.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.6b
(cbrt (* (* (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
18×fma-neg
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×sqrt-prod
7×cbrt-div
5×frac-times associate-*l/
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×sub-neg flip3-- associate-*r/ flip--
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
32.0ms
(cbrt (* (* (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))
9.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
6.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
6.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)

series306.0ms

Calls
4 calls:
Slowest
128.0ms
(cbrt (* (* (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))
63.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
61.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
53.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify4.5s

Calls
36 calls:
Slowest
652.0ms
(cbrt (* (* (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
626.0ms
(cbrt (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))
611.0ms
(cbrt (* (* (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
611.0ms
(cbrt (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
569.0ms
(cbrt (* (* (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))

prune1.4s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 25.6b

localize12.0ms

Local error

Found 4 expressions with local error:

28.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.3b
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
0.2b
(fma c (* -4 a) (* b b))
0.1b
(sqrt (fma c (* -4 a) (* b b)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube fma-neg add-exp-log sqrt-prod
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×div-inv
1×frac-times rem-sqrt-square sub-neg flip3-- pow1/2 pow-prod-down associate-*l/ prod-exp associate-*r/ un-div-inv *-commutative cbrt-unprod fma-udef flip--
Calls
4 calls:
Slowest
26.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
12.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series235.0ms

Calls
4 calls:
Slowest
73.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
73.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
57.0ms
(sqrt (fma c (* -4 a) (* b b)))
32.0ms
(fma c (* -4 a) (* b b))

simplify1.5s

Calls
34 calls:
Slowest
330.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
190.0ms
(* (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
158.0ms
(* (- (sqrt (fma c (* -4 a) (* b b))) b) (/ 1 a))
156.0ms
(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (log (/ 1 a)))
91.0ms
(- (pow b 2) (* 4 (* a c)))

prune1.2s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 25.6b

localize24.0ms

Local error

Found 4 expressions with local error:

28.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.6b
(cbrt (/ 1 a))
0.6b
(cbrt (/ 1 a))
0.6b
(cbrt (/ 1 a))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
9×add-sqr-sqrt *-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
3×cbrt-div pow1/3 sqrt-prod div-inv
1×sub-neg flip3-- flip--
Calls
4 calls:
Slowest
12.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(cbrt (/ 1 a))
1.0ms
(cbrt (/ 1 a))
1.0ms
(cbrt (/ 1 a))

series941.0ms

Calls
4 calls:
Slowest
304.0ms
(cbrt (/ 1 a))
302.0ms
(cbrt (/ 1 a))
263.0ms
(cbrt (/ 1 a))
71.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify345.0ms

Calls
32 calls:
Slowest
43.0ms
(* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b)))))
31.0ms
(sqrt (sqrt (fma c (* -4 a) (* b b))))
22.0ms
(sqrt (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))))
22.0ms
(sqrt (sqrt (fma c (* -4 a) (* b b))))
19.0ms
(pow (/ 1 a) 1/3)

prune1.0s

Pruning

42 alts after pruning (42 fresh and 0 done)

Merged error: 25.5b

regimes1.1s

Accuracy

0% (2.9b remaining)

Error of 28.6b against oracle of 25.7b and baseline of 28.6b

bsearch5.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.6s8687×body80nan
1.3s4458×body160valid
1.1s16687×pre80true
431.0ms3542×body80valid