Details

Time bar (total: 1.1m)

sample166.0ms

Algorithm
intervals
Results
39.0ms141×body160valid
33.0ms241×body80nan
29.0ms497×pre80true
16.0ms115×body80valid

simplify139.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
138.0ms
(/ (+ (- 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

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

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
25.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
22.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(fma c (* -4 a) (* b b))

series414.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
114.0ms
(sqrt (fma c (* -4 a) (* b b)))
112.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
73.0ms
(fma c (* -4 a) (* b b))

simplify14.9s

Counts
225 → 191
Calls
225 calls:
Slowest
453.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
224.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
213.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
199.0ms
(/ (* (* (/ (- (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)) (* (* a a) a))
173.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) 1)

prune2.4s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 25.9b

localize33.0ms

Local error

Found 4 expressions with local error:

28.1b
(- (sqrt (fma b b (* (* a -4) c))) b)
0.3b
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
0.1b
(sqrt (fma b b (* (* a -4) c)))
0.0b
(fma b b (* (* a -4) c))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r*
10×times-frac
9×add-cbrt-cube add-exp-log
7×pow1
6×fma-neg associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×flip3-- 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 fma-udef div-inv
Counts
4 → 111
Calls
4 calls:
Slowest
53.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
15.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
3.0ms
(sqrt (fma b b (* (* a -4) c)))
0.0ms
(fma b b (* (* a -4) c))

series444.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
112.0ms
(sqrt (fma b b (* (* a -4) c)))
112.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
51.0ms
(fma b b (* (* a -4) c))

simplify5.9s

Counts
96 → 123
Calls
96 calls:
Slowest
489.0ms
(* (- (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (* b b)) 1/2)
300.0ms
(* (- (pow (sqrt (fma b b (* (* a -4) c))) 3) (pow b 3)) (/ 1/2 a))
261.0ms
(- b (* 2 (/ (* a c) b)))
243.0ms
(* (- (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (* b b)) (/ 1/2 a))
242.0ms
(* (- (pow (sqrt (fma b b (* (* a -4) c))) 3) (pow b 3)) 1/2)

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* -2 (* a c)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a))
0.2b
(* (+ (sqrt (fma b b (* (* a -4) c))) b) a)
0.2b
(+ (sqrt (fma b b (* (* a -4) c))) b)
0.1b
(sqrt (fma b b (* (* a -4) c)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
27×add-cbrt-cube add-exp-log
13×*-un-lft-identity
12×add-sqr-sqrt
10×prod-exp cbrt-unprod
9×add-cube-cbrt
7×pow1
6×cbrt-undiv fma-def div-exp sqrt-prod add-log-exp
4×expm1-log1p-u associate-*l* associate-*l/ insert-posit16 log1p-expm1-u
3×flip3-+ associate-*r* flip-+
2×associate-/r/ distribute-lft-out
1×+-commutative rem-sqrt-square clear-num associate-/r* sum-log frac-2neg sqrt-pow1 times-frac pow1/2 pow-prod-down *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 91
Calls
4 calls:
Slowest
35.0ms
(* (+ (sqrt (fma b b (* (* a -4) c))) b) a)
27.0ms
(/ (* -2 (* a c)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a))
12.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
2.0ms
(sqrt (fma b b (* (* a -4) c)))

series577.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
218.0ms
(/ (* -2 (* a c)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a))
137.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
111.0ms
(sqrt (fma b b (* (* a -4) c)))
111.0ms
(* (+ (sqrt (fma b b (* (* a -4) c))) b) a)

simplify13.9s

Counts
51 → 103
Calls
51 calls:
Slowest
1.7s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* c c) c))) (* (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) a) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)))
1.6s
(/ (* (* (* -2 -2) -2) (* (* (* a c) (* a c)) (* a c))) (* (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) a) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)))
1.6s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) a) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)))
1.6s
(/ (* (* (* -2 -2) -2) (* (* (* a c) (* a c)) (* a c))) (* (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)) (* (* a a) a)))
1.4s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)) (* (* a a) a)))

prune988.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* -2 (* a c)) (* (+ b (sqrt (fma b b (* (* a -4) c)))) a))
0.2b
(* (+ b (sqrt (fma b b (* (* a -4) c)))) a)
0.2b
(+ b (sqrt (fma b b (* (* a -4) c))))
0.1b
(sqrt (fma b b (* (* a -4) c)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
27×add-cbrt-cube add-exp-log
12×*-un-lft-identity
11×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×add-cube-cbrt
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u associate-*l* associate-*l/ insert-posit16 log1p-expm1-u
3×fma-def flip3-+ associate-*r* sqrt-prod flip-+
2×associate-/r/ distribute-lft-out
1×+-commutative rem-sqrt-square clear-num associate-/r* sum-log frac-2neg sqrt-pow1 times-frac pow1/2 pow-prod-down *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 88
Calls
4 calls:
Slowest
39.0ms
(/ (* -2 (* a c)) (* (+ b (sqrt (fma b b (* (* a -4) c)))) a))
16.0ms
(* (+ b (sqrt (fma b b (* (* a -4) c)))) a)
5.0ms
(+ b (sqrt (fma b b (* (* a -4) c))))
1.0ms
(sqrt (fma b b (* (* a -4) c)))

series590.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
231.0ms
(/ (* -2 (* a c)) (* (+ b (sqrt (fma b b (* (* a -4) c)))) a))
151.0ms
(* (+ b (sqrt (fma b b (* (* a -4) c)))) a)
118.0ms
(+ b (sqrt (fma b b (* (* a -4) c))))
88.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify15.0s

Counts
48 → 100
Calls
48 calls:
Slowest
2.0s
(/ (* (* (* -2 -2) -2) (* (* (* a c) (* a c)) (* a c))) (* (* (* (+ b (sqrt (fma b b (* (* a -4) c)))) a) (* (+ b (sqrt (fma b b (* (* a -4) c)))) a)) (* (+ b (sqrt (fma b b (* (* a -4) c)))) a)))
2.0s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (+ b (sqrt (fma b b (* (* a -4) c)))) a) (* (+ b (sqrt (fma b b (* (* a -4) c)))) a)) (* (+ b (sqrt (fma b b (* (* a -4) c)))) a)))
1.7s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (+ b (sqrt (fma b b (* (* a -4) c)))) (+ b (sqrt (fma b b (* (* a -4) c))))) (+ b (sqrt (fma b b (* (* a -4) c))))) (* (* a a) a)))
1.7s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* c c) c))) (* (* (* (+ b (sqrt (fma b b (* (* a -4) c)))) a) (* (+ b (sqrt (fma b b (* (* a -4) c)))) a)) (* (+ b (sqrt (fma b b (* (* a -4) c)))) a)))
1.6s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* c c) c))) (* (* (* (+ b (sqrt (fma b b (* (* a -4) c)))) (+ b (sqrt (fma b b (* (* a -4) c))))) (+ b (sqrt (fma b b (* (* a -4) c))))) (* (* a a) a)))

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes200.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.8s4468×body160valid
1.3s8591×body80nan
1.0s16591×pre80true
954.0ms3532×body80valid