Details

Time bar (total: 2.6m)

sample128.0ms

Algorithm
intervals
Results
28.0ms189×body80valid
25.0ms30×body2560valid
19.0ms30×body1280valid
13.0ms4×body320valid
11.0ms79×body80nan
11.0ms19×body640valid
2.0ms3×body5120valid
2.0ms5×body160valid

simplify557.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
557.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize23.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma b b (* (* a c) -4)))
1.1b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.5b
(fma b b (* (* a c) -4))
0.1b
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
Slowest
22.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
8.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
1.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series529.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
187.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
141.0ms
(sqrt (fma b b (* (* a c) -4)))
130.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
71.0ms
(fma b b (* (* a c) -4))

simplify15.1s

Counts
225 → 191
Calls
225 calls:
Slowest
436.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
238.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
226.0ms
(- b (* 2 (/ (* a c) b)))
217.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
169.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) 1)

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize46.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma b b (* (* a c) -4)))
1.1b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.5b
(fma b b (* (* a c) -4))
0.2b
(/ 1 (/ a (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
693×times-frac
452×add-sqr-sqrt
377×*-un-lft-identity
303×add-cube-cbrt
74×difference-of-squares
71×associate-/r*
52×sqrt-prod
37×distribute-lft-out--
25×add-exp-log
18×prod-diff
17×div-inv
15×div-exp
13×add-cbrt-cube
6×pow1 cbrt-undiv fma-neg add-log-exp
5×associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp 1-exp associate-/l*
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef pow-flip flip-- inv-pow
Counts
4 → 384
Calls
4 calls:
Slowest
29.0ms
(/ 1 (/ a (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)))
16.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
8.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series517.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
189.0ms
(/ 1 (/ a (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)))
123.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
117.0ms
(sqrt (fma b b (* (* a c) -4)))
88.0ms
(fma b b (* (* a c) -4))

simplify1.8m

Counts
573 → 396
Calls
573 calls:
Slowest
782.0ms
(/ 1 (/ (sqrt a) (/ (- (sqrt (sqrt (fma b b (* (* a c) -4)))) (sqrt b)) (cbrt 2))))
744.0ms
(/ (sqrt 1) (/ (sqrt a) (/ (- (sqrt (fma b b (* (* a c) -4))) b) (cbrt 2))))
668.0ms
(/ (sqrt 1) (/ 1 (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2)))))
652.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (sqrt a) (/ (+ (sqrt (sqrt (fma b b (* (* a c) -4)))) (sqrt b)) (* (cbrt 2) (cbrt 2)))))
597.0ms
(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (/ (sqrt (- (sqrt (fma b b (* (* a c) -4))) b)) (* (cbrt 2) (cbrt 2)))))

prune5.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.7b

localize41.0ms

Local error

Found 3 expressions with local error:

19.5b
(sqrt (fma c (* a -4) (* b b)))
1.1b
(- (sqrt (fma c (* a -4) (* b b))) b)
0.2b
(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
30×*-un-lft-identity
26×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r*
10×times-frac
8×add-cbrt-cube add-exp-log
6×pow1 fma-neg associate-*l*
5×add-log-exp
4×difference-of-squares
3×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
2×frac-times associate-*l/ prod-exp cbrt-unprod distribute-lft-out-- unswap-sqr
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log div-exp pow-prod-down associate-*r/ *-commutative div-inv
Counts
3 → 100
Calls
3 calls:
Slowest
52.0ms
(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))
26.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
3.0ms
(sqrt (fma c (* a -4) (* b b)))

series332.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
119.0ms
(sqrt (fma c (* a -4) (* b b)))
106.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
106.0ms
(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))

simplify4.9s

Counts
93 → 109
Calls
93 calls:
Slowest
631.0ms
(* (- (* (sqrt (fma c (* a -4) (* b b))) (sqrt (fma c (* a -4) (* b b)))) (* b b)) 1/2)
311.0ms
(* (+ (* (sqrt (fma c (* a -4) (* b b))) (sqrt (fma c (* a -4) (* b b)))) (+ (* b b) (* (sqrt (fma c (* a -4) (* b b))) b))) a)
233.0ms
(* (- (pow (sqrt (fma c (* a -4) (* b b))) 3) (pow b 3)) (/ 1/2 a))
220.0ms
(* (* (* (- (sqrt (fma c (* a -4) (* b b))) b) (- (sqrt (fma c (* a -4) (* b b))) b)) (- (sqrt (fma c (* a -4) (* b b))) b)) (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)))
210.0ms
(* (- (pow (sqrt (fma c (* a -4) (* b b))) 3) (pow b 3)) 1/2)

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

localize33.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma c (* a -4) (* b b)))
19.5b
(sqrt (fma c (* a -4) (* b b)))
1.1b
(- (sqrt (fma c (* a -4) (* b b))) b)
1.1b
(- (sqrt (fma c (* a -4) (* b b))) b)

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
Slowest
16.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
16.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
11.0ms
(sqrt (fma c (* a -4) (* b b)))
3.0ms
(sqrt (fma c (* a -4) (* b b)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(sqrt (fma c (* a -4) (* b b)))
114.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
112.0ms
(sqrt (fma c (* a -4) (* b b)))
100.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)

simplify3.8s

Counts
116 → 128
Calls
116 calls:
Slowest
137.0ms
(fma (* (cbrt (sqrt (fma c (* a -4) (* b b)))) (cbrt (sqrt (fma c (* a -4) (* b b))))) (cbrt (sqrt (fma c (* a -4) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
109.0ms
(fma (* (cbrt (sqrt (fma c (* a -4) (* b b)))) (cbrt (sqrt (fma c (* a -4) (* b b))))) (cbrt (sqrt (fma c (* a -4) (* b b)))) (- (* b 1)))
102.0ms
(fma (* (cbrt (sqrt (fma c (* a -4) (* b b)))) (cbrt (sqrt (fma c (* a -4) (* b b))))) (cbrt (sqrt (fma c (* a -4) (* b b)))) (- (* b 1)))
100.0ms
(fma (* (cbrt (sqrt (fma c (* a -4) (* b b)))) (cbrt (sqrt (fma c (* a -4) (* b b))))) (cbrt (sqrt (fma c (* a -4) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
97.0ms
(/ (exp (sqrt (fma c (* a -4) (* b b)))) (exp b))

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

regimes500.0ms

Accuracy

80.6% (5.5b remaining)

Error of 10.8b against oracle of 5.4b and baseline of 33.5b

bsearch848.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s5825×body80valid
944.0ms1090×body2560valid
738.0ms926×body1280valid
482.0ms2868×body80nan
369.0ms477×body640valid
147.0ms238×body320valid
137.0ms107×body5120valid
31.0ms123×body160valid