Details

Time bar (total: 57.3s)

sample89.0ms

Algorithm
intervals
Results
20.0ms27×body1280valid
20.0ms37×body2560valid
16.0ms186×body80valid
9.0ms92×body80nan
5.0ms14×body640valid
2.0ms9×body320valid
1.0ms2×body5120valid
1.0ms4×body160valid

simplify146.0ms

Calls
1 calls:
Slowest
145.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize39.0ms

Local error

Found 4 expressions with local error:

21.1b
(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)

rewrite55.0ms

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/
Calls
4 calls:
Slowest
32.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
15.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series463.0ms

Calls
4 calls:
Slowest
171.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
124.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
91.0ms
(sqrt (fma b b (* (* a c) -4)))
77.0ms
(fma b b (* (* a c) -4))

simplify15.4s

Calls
225 calls:
Slowest
372.0ms
(/ (/ (* (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)))
235.0ms
(/ (* (* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (* (* a a) a))
228.0ms
(- b (* 2 (/ (* a c) b)))
184.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
176.0ms
(/ (/ (* (* (- (sqrt (fma b b (* (* a c) -4))) b) (- (sqrt (fma b b (* (* a c) -4))) b)) (- (sqrt (fma b b (* (* a c) -4))) b)) (* (* 2 2) 2)) (* (* a a) a))

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize26.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (fma (* a c) -4 (* b b)))
1.1b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.4b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)

rewrite40.0ms

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/
Calls
4 calls:
Slowest
19.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
15.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series484.0ms

Calls
4 calls:
Slowest
162.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
133.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
116.0ms
(sqrt (fma (* a c) -4 (* b b)))
72.0ms
(fma (* a c) -4 (* b b))

simplify16.0s

Calls
225 calls:
Slowest
746.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
243.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
198.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
189.0ms
(/ (* (* (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)) (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)) (* (* a a) a))
179.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) 1) (* (cbrt a) (cbrt a)))

prune2.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.6b

localize19.0ms

Local error

Found 3 expressions with local error:

21.1b
(sqrt (fma (* -4 c) a (* b b)))
1.1b
(- (sqrt (fma (* -4 c) a (* b b))) b)
0.2b
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))

rewrite67.0ms

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
Calls
3 calls:
Slowest
55.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))
9.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
1.0ms
(sqrt (fma (* -4 c) a (* b b)))

series332.0ms

Calls
3 calls:
Slowest
137.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))
103.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
92.0ms
(sqrt (fma (* -4 c) a (* b b)))

simplify5.1s

Calls
93 calls:
Slowest
638.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) 1/2)
353.0ms
(* (+ (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (+ (* b b) (* (sqrt (fma (* -4 c) a (* b b))) b))) a)
255.0ms
(* (- (pow (sqrt (fma (* -4 c) a (* b b))) 3) (pow b 3)) (/ 1/2 a))
206.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) (/ 1/2 a))
196.0ms
(* (* (* (- (sqrt (fma (* -4 c) a (* b b))) b) (- (sqrt (fma (* -4 c) a (* b b))) b)) (- (sqrt (fma (* -4 c) a (* b b))) b)) (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)))

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

localize28.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (fma (* -4 c) a (* b b)))
21.1b
(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)

rewrite26.0ms

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--
Calls
4 calls:
Slowest
13.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
7.0ms
(- (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)))

series462.0ms

Calls
4 calls:
Slowest
124.0ms
(sqrt (fma (* -4 c) a (* b b)))
119.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
111.0ms
(sqrt (fma (* -4 c) a (* b b)))
109.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)

simplify4.5s

Calls
116 calls:
Slowest
147.0ms
(fma (* (cbrt (sqrt (fma (* -4 c) a (* b b)))) (cbrt (sqrt (fma (* -4 c) a (* b b))))) (cbrt (sqrt (fma (* -4 c) a (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
127.0ms
(fma (* (cbrt (sqrt (fma (* -4 c) a (* b b)))) (cbrt (sqrt (fma (* -4 c) a (* b b))))) (cbrt (sqrt (fma (* -4 c) a (* b b)))) (- (* b 1)))
117.0ms
(fma (* (cbrt (sqrt (fma (* -4 c) a (* b b)))) (cbrt (sqrt (fma (* -4 c) a (* b b))))) (cbrt (sqrt (fma (* -4 c) a (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
112.0ms
(fma (* (cbrt (sqrt (fma (* -4 c) a (* b b)))) (cbrt (sqrt (fma (* -4 c) a (* b b))))) (cbrt (sqrt (fma (* -4 c) a (* b b)))) (- (* b 1)))
102.0ms
(fma (* (cbrt (sqrt (fma (* -4 c) a (* b b)))) (cbrt (sqrt (fma (* -4 c) a (* b b))))) (cbrt (sqrt (fma (* -4 c) a (* b b)))) (- (* (sqrt b) (sqrt b))))

prune1.8s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.5b

regimes401.0ms

Accuracy

87.2% (3.5b remaining)

Error of 9.1b against oracle of 5.6b and baseline of 33.2b

bsearch406.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.3s5882×body80valid
1.3s911×body1280valid
1.2s1060×body2560valid
463.0ms2867×body80nan
262.0ms419×body640valid
128.0ms121×body5120valid
127.0ms228×body320valid
29.0ms104×body160valid