Details

Time bar (total: 1.0m)

sample150.0ms

Algorithm
intervals
Results
47.0ms193×body80valid
30.0ms33×body2560valid
26.0ms36×body1280valid
15.0ms99×body80nan
7.0ms11×body640valid
4.0ms10×body320valid
4.0ms3×body5120valid
1.0ms2×body160valid

simplify164.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
164.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize40.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (fma b b (* (* a c) -4)))
0.7b
(- (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)

rewrite57.0ms

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
32.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
16.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
3.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series412.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
119.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
101.0ms
(sqrt (fma b b (* (* a c) -4)))
57.0ms
(fma b b (* (* a c) -4))

simplify15.9s

Counts
225 → 191
Calls
225 calls:
Slowest
415.0ms
(/ (/ (* (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)))
309.0ms
(- b (* 2 (/ (* a c) b)))
214.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
206.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
198.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) 1)

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize23.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (fma (* a c) -4 (* b b)))
0.7b
(- (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)

rewrite33.0ms

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
21.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
7.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series509.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
195.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
122.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
98.0ms
(sqrt (fma (* a c) -4 (* b b)))
93.0ms
(fma (* a c) -4 (* b b))

simplify15.9s

Counts
225 → 191
Calls
225 calls:
Slowest
424.0ms
(/ (/ (* (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)))
220.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
216.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
168.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) 1) (* (cbrt a) (cbrt a)))
168.0ms
(- (log (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)) (log a))

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize39.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (fma (* a c) -4 (* b b)))
0.7b
(- (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) (* a 2))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff sqrt-prod
9×add-cbrt-cube add-exp-log
6×times-frac fma-neg associate-/l* add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod fma-udef div-inv
Counts
4 → 102
Calls
4 calls:
Slowest
37.0ms
(/ (- (sqrt (fma (* a c) -4 (* b b))) b) (* a 2))
15.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series478.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(/ (- (sqrt (fma (* a c) -4 (* b b))) b) (* a 2))
121.0ms
(sqrt (fma (* a c) -4 (* b b)))
103.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
83.0ms
(fma (* a c) -4 (* b b))

simplify5.6s

Counts
87 → 114
Calls
87 calls:
Slowest
535.0ms
(- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (* b b))
473.0ms
(fma (sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b))))) (sqrt (cbrt (fma (* a c) -4 (* b b)))) (- (* (sqrt b) (sqrt b))))
399.0ms
(- (pow (sqrt (fma (* a c) -4 (* b b))) 3) (pow b 3))
227.0ms
(/ (* (* (- (sqrt (fma (* a c) -4 (* b b))) b) (- (sqrt (fma (* a c) -4 (* b b))) b)) (- (sqrt (fma (* a c) -4 (* b b))) b)) (* (* (* a 2) (* a 2)) (* a 2)))
214.0ms
(/ (* (* (- (sqrt (fma (* a c) -4 (* b b))) b) (- (sqrt (fma (* a c) -4 (* b b))) b)) (- (sqrt (fma (* a c) -4 (* b b))) b)) (* (* (* a a) a) (* (* 2 2) 2)))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize31.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (fma b b (* (* a c) -4)))
0.7b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.5b
(fma b b (* (* a c) -4))
0.2b
(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
46×*-un-lft-identity
36×add-cube-cbrt
34×times-frac
26×add-exp-log
22×associate-*l*
19×sqrt-prod
18×prod-diff
16×add-cbrt-cube
13×associate-*r*
8×div-exp prod-exp difference-of-squares
7×pow1
6×fma-neg add-log-exp unswap-sqr
4×expm1-log1p-u cbrt-undiv cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out--
2×rec-exp 1-exp div-inv
1×frac-times rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log pow-prod-down associate-*l/ associate-*r/ un-div-inv *-commutative fma-udef flip--
Counts
4 → 138
Calls
4 calls:
Slowest
25.0ms
(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
7.0ms
(- (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))

series469.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
135.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
108.0ms
(sqrt (fma b b (* (* a c) -4)))
74.0ms
(fma b b (* (* a c) -4))

simplify8.5s

Counts
126 → 150
Calls
126 calls:
Slowest
375.0ms
(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
287.0ms
(+ (- (log (- (sqrt (fma b b (* (* a c) -4))) b)) (log 2)) (- 0 (log a)))
281.0ms
(* (/ (* (* (- (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)) (/ (* (* 1 1) 1) (* (* a a) a)))
271.0ms
(+ (log (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (- 0 (log a)))
265.0ms
(- b (* 2 (/ (* a c) b)))

prune1.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.9b

regimes487.0ms

Accuracy

83.8% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 33.4b

bsearch291.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.5s1073×body2560valid
972.0ms5886×body80valid
745.0ms914×body1280valid
446.0ms3031×body80nan
299.0ms434×body640valid
112.0ms220×body320valid
102.0ms115×body5120valid
25.0ms100×body160valid