Details

Time bar (total: 55.6s)

sample151.0ms

Algorithm
intervals
Results
55.0ms34×body2560valid
29.0ms194×body80valid
26.0ms36×body1280valid
15.0ms108×body80nan
6.0ms8×body640valid
2.0ms3×body320valid
1.0ms1×body5120valid
0.0ms1×body160valid

simplify136.0ms

Counts
1 → 1
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

localize32.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (fma b b (* (* a c) -4)))
0.5b
(fma b b (* (* a c) -4))
0.4b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.1b
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite59.0ms

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
35.0ms
(/ (/ (- (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))

series495.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
131.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
116.0ms
(sqrt (fma b b (* (* a c) -4)))
86.0ms
(fma b b (* (* a c) -4))

simplify15.5s

Counts
225 → 191
Calls
225 calls:
Slowest
451.0ms
(/ (/ (* (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)))
262.0ms
(- b (* 2 (/ (* a c) b)))
250.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
229.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
189.0ms
(/ (* (* (/ (- (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))

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize21.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (fma (* -4 c) a (* b b)))
0.4b
(- (sqrt (fma (* -4 c) a (* b b))) b)
0.2b
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))
0.0b
(fma (* -4 c) a (* b b))

rewrite56.0ms

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
38.0ms
(* (- (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)))
0.0ms
(fma (* -4 c) a (* b b))

series393.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(sqrt (fma (* -4 c) a (* b b)))
105.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))
96.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
68.0ms
(fma (* -4 c) a (* b b))

simplify5.5s

Counts
96 → 123
Calls
96 calls:
Slowest
622.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) 1/2)
350.0ms
(* (+ (* (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)
277.0ms
(* (- (pow (sqrt (fma (* -4 c) a (* b b))) 3) (pow b 3)) (/ 1/2 a))
214.0ms
(* (* (* (- (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)))
183.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) (/ 1/2 a))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize21.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (fma (* -4 c) a (* b b)))
0.4b
(- (sqrt (fma (* -4 c) a (* b b))) b)
0.1b
(/ (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2) a)
0.0b
(fma (* -4 c) a (* b b))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff
16×sqrt-prod
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* times-frac
2×cbrt-undiv flip3-- div-exp associate-*l/ flip-- difference-of-squares associate-/l/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log prod-exp cbrt-unprod fma-udef div-inv associate-/l* distribute-lft-out--
Counts
4 → 95
Calls
4 calls:
Slowest
38.0ms
(/ (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2) a)
18.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
2.0ms
(sqrt (fma (* -4 c) a (* b b)))
0.0ms
(fma (* -4 c) a (* b b))

series429.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
122.0ms
(sqrt (fma (* -4 c) a (* b b)))
106.0ms
(/ (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2) a)
75.0ms
(fma (* -4 c) a (* b b))

simplify4.3s

Counts
79 → 107
Calls
79 calls:
Slowest
631.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) 1/2)
275.0ms
(/ (* (* (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2) (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2)) (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2)) (* (* a a) a))
217.0ms
(/ (* (* (* (- (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))
202.0ms
(* (- (pow (sqrt (fma (* -4 c) a (* b b))) 3) (pow b 3)) 1/2)
138.0ms
(- (log (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2)) (log a))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize49.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (fma (* -4 c) a (* b b)))
0.4b
(- (sqrt (fma (* -4 c) a (* b b))) b)
0.2b
(/ 1 (/ a (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2)))
0.1b
(/ a (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
42×times-frac
41×*-un-lft-identity
39×add-cube-cbrt
30×add-exp-log
18×add-cbrt-cube prod-diff
16×sqrt-prod
14×div-exp
11×associate-/r/
10×associate-/r* associate-*l/
7×cbrt-undiv
6×pow1 flip3-- fma-neg div-inv flip-- associate-/l* add-log-exp
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u
3×rec-exp 1-exp
2×clear-num frac-2neg cbrt-unprod difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log pow-flip distribute-lft-out-- inv-pow
Counts
4 → 151
Calls
4 calls:
Slowest
24.0ms
(/ a (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2))
23.0ms
(/ 1 (/ a (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2)))
18.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
2.0ms
(sqrt (fma (* -4 c) a (* b b)))

series659.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
269.0ms
(/ a (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2))
177.0ms
(/ 1 (/ a (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2)))
127.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
86.0ms
(sqrt (fma (* -4 c) a (* b b)))

simplify15.6s

Counts
154 → 163
Calls
154 calls:
Slowest
559.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ a (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2))) (cbrt (/ a (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2)))))
491.0ms
(/ (sqrt 1) (/ a (* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) 1/2)))
418.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ a (* (- (pow (sqrt (fma (* -4 c) a (* b b))) 3) (pow b 3)) 1/2)))
412.0ms
(/ 1 (/ a (* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) 1/2)))
402.0ms
(/ (* (* 1 1) 1) (/ (* (* a a) a) (* (* (* (- (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))))

prune2.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

regimes336.0ms

Accuracy

81.9% (5.0b remaining)

Error of 10.6b against oracle of 5.6b and baseline of 33.4b

bsearch162.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.1s5846×body80valid
976.0ms1027×body2560valid
832.0ms2890×body80nan
703.0ms888×body1280valid
274.0ms468×body640valid
136.0ms107×body5120valid
93.0ms233×body320valid
31.0ms122×body160valid