Details

Time bar (total: 20.1s)

sample153.0ms

Algorithm
intervals
Results
40.0ms31×body2560valid
32.0ms183×body80valid
30.0ms35×body1280valid
14.0ms18×body640valid
11.0ms64×body80nan
3.0ms6×body320valid
1.0ms1×body5120valid
1.0ms3×body160valid

simplify177.0ms

Calls
1 calls:
Slowest
177.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize19.0ms

Local error

Found 4 expressions with local error:

23.1b
(sqrt (fma c (* -4 a) (* b b)))
0.8b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.0b
(fma c (* -4 a) (* b b))

rewrite32.0ms

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
23.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
6.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series243.0ms

Calls
4 calls:
Slowest
68.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
64.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
59.0ms
(sqrt (fma c (* -4 a) (* b b)))
52.0ms
(fma c (* -4 a) (* b b))

simplify717.0ms

Calls
26 calls:
Slowest
91.0ms
(- (pow b 2) (* 4 (* a c)))
69.0ms
(- (pow b 2) (* 4 (* a c)))
63.0ms
(- (pow b 2) (* 4 (* a c)))
46.0ms
(sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
45.0ms
(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))

prune973.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.8b

localize10.0ms

Local error

Found 4 expressions with local error:

23.1b
(sqrt (fma c (* -4 a) (* b b)))
0.8b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
0.1b
(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×associate-/r* *-un-lft-identity add-cube-cbrt
6×fma-neg sqrt-prod
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u div-inv add-log-exp
3×associate-/r/
2×clear-num frac-2neg
1×rem-sqrt-square rec-exp sub-neg flip3-- pow1/2 pow-flip flip-- inv-pow
Calls
4 calls:
Slowest
12.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms
(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))

series356.0ms

Calls
4 calls:
Slowest
141.0ms
(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
114.0ms
(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
51.0ms
(sqrt (fma c (* -4 a) (* b b)))
51.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify647.0ms

Calls
31 calls:
Slowest
68.0ms
(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
67.0ms
(sqrt (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
62.0ms
(cbrt (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
57.0ms
(sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
47.0ms
(/ 1 (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))

prune928.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.1b

localize9.0ms

Local error

Found 4 expressions with local error:

23.1b
(sqrt (fma c (* -4 a) (* b b)))
0.8b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(* (/ 1 a) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
0.0b
(fma c (* -4 a) (* b b))

rewrite19.0ms

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/ *-commutative cbrt-unprod fma-udef flip--
Calls
4 calls:
Slowest
9.0ms
(* (/ 1 a) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
8.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series236.0ms

Calls
4 calls:
Slowest
88.0ms
(* (/ 1 a) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
59.0ms
(sqrt (fma c (* -4 a) (* b b)))
53.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
36.0ms
(fma c (* -4 a) (* b b))

simplify1.5s

Calls
33 calls:
Slowest
304.0ms
(* (/ 1 a) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
186.0ms
(+ (log (/ 1 a)) (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
171.0ms
(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (* (* (/ (- (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)))
133.0ms
(* 1 (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
94.0ms
(- (pow b 2) (* 4 (* a c)))

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.1b

localize26.0ms

Local error

Found 4 expressions with local error:

23.1b
(sqrt (fma c (* -4 a) (* b b)))
6.2b
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
0.1b
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
0.0b
(fma c (* -4 a) (* b b))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
17×*-un-lft-identity
16×prod-diff
15×add-cube-cbrt
13×div-inv
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u associate-/l*
3×sqrt-prod
1×rem-sqrt-square clear-num sub-neg frac-2neg flip3-- distribute-rgt-out-- pow1/2 diff-log frac-sub fma-udef flip-- distribute-lft-out-- sub-div difference-of-squares associate-/l/
Calls
4 calls:
Slowest
25.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
7.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series215.0ms

Calls
4 calls:
Slowest
65.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
55.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
54.0ms
(sqrt (fma c (* -4 a) (* b b)))
41.0ms
(fma c (* -4 a) (* b b))

simplify6.7s

Calls
64 calls:
Slowest
448.0ms
(fma 1 (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (- (* (/ 1 a) (/ b 2))))
417.0ms
(fma (/ (sqrt (fma c (* -4 a) (* b b))) 2) (/ 1 a) (- (* (/ 1 a) (/ b 2))))
363.0ms
(fma (* (cbrt (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)) (cbrt (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a))) (cbrt (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)) (- (* (/ 1 a) (/ b 2))))
361.0ms
(fma 1 (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (- (* (/ (/ b 2) a) 1)))
308.0ms
(fma (sqrt (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)) (sqrt (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)) (- (* (/ 1 a) (/ b 2))))

prune966.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 13.1b

regimes442.0ms

Accuracy

81.5% (3.9b remaining)

Error of 16.4b against oracle of 12.5b and baseline of 33.7b

bsearch186.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.7s1086×body2560valid
873.0ms5809×body80valid
742.0ms924×body1280valid
456.0ms2848×body80nan
223.0ms460×body640valid
89.0ms96×body5120valid
80.0ms222×body320valid
52.0ms108×body160valid