Details

Time bar (total: 42.9s)

sample215.0ms

Algorithm
intervals
Results
74.0ms36×body1280valid
26.0ms34×body2560valid
25.0ms195×body80valid
16.0ms108×body80nan
5.0ms8×body640valid
1.0ms3×body320valid
1.0ms1×body5120valid

simplify109.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
108.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize36.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (- (* b_2 b_2) (* a c)))
0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
Slowest
81.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
69.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))
14.0ms
(- (* b_2 b_2) (* a c))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
116.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
114.0ms
(sqrt (- (* b_2 b_2) (* a c)))
51.0ms
(- (* b_2 b_2) (* a c))

simplify4.1s

Counts
73 → 100
Calls
73 calls:
Slowest
372.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
333.0ms
(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))
309.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
229.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
213.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize45.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (- (* b_2 b_2) (* a c)))
0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
123×add-sqr-sqrt
96×*-un-lft-identity
70×add-cube-cbrt
26×difference-of-squares
24×associate-/r*
16×sqrt-prod
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1
5×div-inv
4×insert-posit16
3×cbrt-undiv associate-/l*
2×rec-exp sub-neg sqrt-div diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-flip inv-pow
Counts
4 → 166
Calls
4 calls:
Slowest
48.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
30.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
104.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
91.0ms
(sqrt (- (* b_2 b_2) (* a c)))
53.0ms
(- (* b_2 b_2) (* a c))

simplify19.5s

Counts
204 → 178
Calls
204 calls:
Slowest
514.0ms
(/ (* (* 1 1) 1) (/ (* (* a a) a) (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
398.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))
395.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (* (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))))
365.0ms
(/ (* (* 1 1) 1) (* (* (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
355.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize38.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (- (* b_2 b_2) (* a c)))
0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
18×*-un-lft-identity
13×associate-*r* add-exp-log add-cube-cbrt
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1
6×associate-*l*
5×flip3-- sqrt-prod flip--
4×prod-exp insert-posit16 difference-of-squares
3×unswap-sqr
2×frac-times sub-neg sqrt-div diff-log div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
Slowest
169.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
59.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
110.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
101.0ms
(sqrt (- (* b_2 b_2) (* a c)))
68.0ms
(- (* b_2 b_2) (* a c))

simplify5.7s

Counts
62 → 101
Calls
62 calls:
Slowest
550.0ms
(* (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
505.0ms
(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) 1)
424.0ms
(* (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (sqrt (/ 1 a)))
423.0ms
(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) 1)
292.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))

prune859.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

localize40.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (- (* b_2 b_2) (* a c)))
18.8b
(sqrt (- (* b_2 b_2) (* a c)))
0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (* b_2 b_2) (* a c))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 58
Calls
4 calls:
Slowest
10.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
78.0ms
(sqrt (- (* b_2 b_2) (* a c)))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))
64.0ms
(- (* b_2 b_2) (* a c))
59.0ms
(- (* b_2 b_2) (* a c))

simplify2.4s

Counts
28 → 70
Calls
28 calls:
Slowest
328.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
307.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
250.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
202.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
192.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune794.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.3b

regimes306.0ms

Accuracy

81.9% (5.0b remaining)

Error of 10.6b against oracle of 5.6b and baseline of 33.5b

bsearch124.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
976.0ms887×body1280valid
831.0ms1028×body2560valid
773.0ms5843×body80valid
324.0ms2884×body80nan
287.0ms471×body640valid
109.0ms107×body5120valid
76.0ms232×body320valid
27.0ms123×body160valid