Details

Time bar (total: 1.1m)

sample149.0ms

Algorithm
intervals
Results
49.0ms209×body80valid
29.0ms28×body2560valid
23.0ms28×body1280valid
15.0ms99×body80nan
8.0ms13×body640valid
2.0ms4×body320valid
1.0ms1×body5120valid
0.0ms1×body160valid

simplify141.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
141.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize25.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (fma b b (* (* a c) -4)))
1.5b
(fma b b (* (* a c) -4))
0.2b
(/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)
0.2b
(- (sqrt (fma b b (* (* a c) -4))) b)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
Slowest
25.0ms
(/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)
15.0ms
(- (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))

series442.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)
121.0ms
(sqrt (fma b b (* (* a c) -4)))
117.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
75.0ms
(fma b b (* (* a c) -4))

simplify6.7s

Counts
111 → 126
Calls
111 calls:
Slowest
527.0ms
(- (* (sqrt (fma b b (* (* a c) -4))) (sqrt (fma b b (* (* a c) -4)))) (* b b))
490.0ms
(/ (+ (sqrt (sqrt (fma b b (* (* a c) -4)))) (sqrt b)) (sqrt 2))
389.0ms
(- (pow (sqrt (fma b b (* (* a c) -4))) 3) (pow b 3))
266.0ms
(/ (* (* (- (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))
231.0ms
(- b (* 2 (/ (* a c) b)))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize29.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (fma a (* -4 c) (* b b)))
0.2b
(/ (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0) 2)
0.2b
(- (sqrt (fma a (* -4 c) (* b b))) b)
0.1b
(/ (/ (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0) 2) a)

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
167×*-un-lft-identity
132×times-frac
90×add-sqr-sqrt
85×add-cube-cbrt
32×distribute-lft-out
24×associate-/l*
18×prod-diff
17×distribute-lft-out--
16×sqrt-prod
11×add-cbrt-cube add-exp-log
6×associate-/r* fma-neg div-inv add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u
3×div-sub associate-/l/
2×clear-num frac-2neg associate-+l- difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
4 → 197
Calls
4 calls:
Slowest
106.0ms
(/ (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0) 2)
72.0ms
(/ (/ (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0) 2) a)
8.0ms
(- (sqrt (fma a (* -4 c) (* b b))) b)
1.0ms
(sqrt (fma a (* -4 c) (* b b)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(/ (/ (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0) 2) a)
142.0ms
(- (sqrt (fma a (* -4 c) (* b b))) b)
122.0ms
(/ (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0) 2)
86.0ms
(sqrt (fma a (* -4 c) (* b b)))

simplify19.7s

Counts
243 → 209
Calls
243 calls:
Slowest
544.0ms
(/ (/ (* (cbrt (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0)) (cbrt (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
427.0ms
(+ (pow (- (sqrt (fma a (* -4 c) (* b b))) b) 3) (pow 0 3))
345.0ms
(/ (* (* (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0) (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0)) (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0)) (* (* 2 2) 2))
318.0ms
(- (* (- (sqrt (fma a (* -4 c) (* b b))) b) (- (sqrt (fma a (* -4 c) (* b b))) b)) (* 0 0))
239.0ms
(/ (/ (* (cbrt (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0)) (cbrt (+ (- (sqrt (fma a (* -4 c) (* b b))) b) 0))) (sqrt 2)) (* (cbrt a) (cbrt a)))

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize49.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (fma a (* c -4) (* b b)))
0.4b
(/ (- (sqrt (fma a (* c -4) (* b b))) b) (* a 2))
0.2b
(- (sqrt (fma a (* c -4) (* b b))) b)
0.0b
(fma a (* c -4) (* b b))

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)
3.0ms
(sqrt (fma a (* c -4) (* b b)))
0.0ms
(fma a (* c -4) (* b b))

series502.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
196.0ms
(/ (- (sqrt (fma a (* c -4) (* b b))) b) (* a 2))
120.0ms
(sqrt (fma a (* c -4) (* b b)))
118.0ms
(- (sqrt (fma a (* c -4) (* b b))) b)
68.0ms
(fma a (* c -4) (* b b))

simplify4.8s

Counts
87 → 114
Calls
87 calls:
Slowest
649.0ms
(- (* (sqrt (fma a (* c -4) (* b b))) (sqrt (fma a (* c -4) (* b b)))) (* b b))
326.0ms
(- (pow (sqrt (fma a (* c -4) (* b b))) 3) (pow b 3))
252.0ms
(/ (* (* (- (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)))
229.0ms
(/ (* (* (- (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)))
150.0ms
(- (log (- (sqrt (fma a (* c -4) (* b b))) b)) (+ (log a) (log 2)))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize28.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (fma a (* c -4) (* b b)))
0.3b
(/ (* a 2) (- (sqrt (fma a (* c -4) (* b b))) b))
0.2b
(/ 1 (/ (* a 2) (- (sqrt (fma a (* c -4) (* b b))) b)))
0.2b
(- (sqrt (fma a (* c -4) (* b b))) b)

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
66×times-frac
56×*-un-lft-identity
42×add-cube-cbrt
30×add-exp-log
22×sqrt-prod
18×associate-/r* add-cbrt-cube prod-diff
14×div-exp difference-of-squares
11×associate-/r/
7×cbrt-undiv distribute-lft-out--
6×pow1 flip3-- fma-neg div-inv flip-- add-log-exp
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u associate-/l*
3×rec-exp 1-exp
2×clear-num frac-2neg cbrt-unprod
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log pow-flip inv-pow
Counts
4 → 169
Calls
4 calls:
Slowest
34.0ms
(/ 1 (/ (* a 2) (- (sqrt (fma a (* c -4) (* b b))) b)))
28.0ms
(/ (* a 2) (- (sqrt (fma a (* c -4) (* b b))) b))
15.0ms
(- (sqrt (fma a (* c -4) (* b b))) b)
1.0ms
(sqrt (fma a (* c -4) (* b b)))

series723.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
284.0ms
(/ (* a 2) (- (sqrt (fma a (* c -4) (* b b))) b))
183.0ms
(/ 1 (/ (* a 2) (- (sqrt (fma a (* c -4) (* b b))) b)))
130.0ms
(sqrt (fma a (* c -4) (* b b)))
125.0ms
(- (sqrt (fma a (* c -4) (* b b))) b)

simplify17.5s

Counts
185 → 181
Calls
185 calls:
Slowest
616.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ a (+ (sqrt (sqrt (fma a (* c -4) (* b b)))) (sqrt b))))
581.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* a 2) (- (pow (sqrt (fma a (* c -4) (* b b))) 3) (pow b 3))))
450.0ms
(/ 1 (/ (* a 2) (- (sqrt (fma a (* c -4) (* b b))) b)))
448.0ms
(/ (sqrt 1) (/ (* a 2) (- (pow (sqrt (fma a (* c -4) (* b b))) 3) (pow b 3))))
447.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* a 2) (- (* (sqrt (fma a (* c -4) (* b b))) (sqrt (fma a (* c -4) (* b b)))) (* b b))))

prune2.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.8b

regimes342.0ms

Accuracy

96.8% (0.9b remaining)

Error of 6.6b against oracle of 5.7b and baseline of 32.9b

bsearch366.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.4s1074×body2560valid
888.0ms5900×body80valid
825.0ms881×body1280valid
421.0ms2889×body80nan
298.0ms467×body640valid
144.0ms221×body320valid
91.0ms95×body5120valid
29.0ms113×body160valid