Details

Time bar (total: 20.6s)

sample516.0ms

Algorithm
intervals
Results
191.0ms194×body80valid
37.0ms8×body640valid
35.0ms32×body2560valid
21.0ms27×body1280valid
16.0ms95×body80nan
7.0ms5×body5120valid
4.0ms7×body320valid
2.0ms7×body160valid

simplify818.0ms

Calls
1 calls:
Slowest
817.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize39.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
2.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt add-log-exp
4×pow1 flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×sqrt-prod associate-/l*
2×sub-neg sqrt-div associate-/l/
1×rem-sqrt-square clear-num frac-2neg pow1/2 diff-log div-sub div-inv
Calls
4 calls:
Slowest
70.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
29.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))
6.0ms
(- (* b_2 b_2) (* a c))

series213.0ms

Calls
4 calls:
Slowest
70.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))
48.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
26.0ms
(- (* b_2 b_2) (* a c))

simplify2.3s

Calls
24 calls:
Slowest
425.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
378.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
322.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
207.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
153.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune635.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

localize1.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
2.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt add-log-exp
4×pow1 flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×sqrt-prod associate-/l*
2×sub-neg sqrt-div associate-/l/
1×rem-sqrt-square clear-num frac-2neg pow1/2 diff-log div-sub div-inv
Calls
4 calls:
Slowest
44.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
14.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series216.0ms

Calls
4 calls:
Slowest
82.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
65.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
36.0ms
(sqrt (- (* b_2 b_2) (* a c)))
33.0ms
(- (* b_2 b_2) (* a c))

simplify2.3s

Calls
24 calls:
Slowest
394.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
390.0ms
(- (* (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) (* b_2 b_2)) (* (* a c) (* a c))))
275.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
185.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune781.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

localize11.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
2.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b
(- (* b_2 b_2) (* a c))
0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log add-log-exp
5×flip3-- flip--
4×associate-*r* insert-posit16
3×associate-*l* sqrt-prod
2×frac-times sub-neg sqrt-div associate-*l/
1×rem-sqrt-square pow1/2 diff-log pow-prod-down prod-exp associate-*r/ un-div-inv *-commutative cbrt-unprod div-inv
Calls
4 calls:
Slowest
61.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
25.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series188.0ms

Calls
4 calls:
Slowest
65.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))
45.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0ms
(- (* b_2 b_2) (* a c))

simplify4.2s

Calls
34 calls:
Slowest
524.0ms
(* (* (* (- (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)))
513.0ms
(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) 1)
464.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
410.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
311.0ms
(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) (/ 1 a))

prune640.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.4b

localize21.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
13.1b
(/ (- 0 (* a c)) a)
1.1b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b
(- (* b_2 b_2) (* a c))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×flip3-- sqrt-prod flip-- associate-/l*
2×sqrt-div associate-/l/
1×+-commutative rem-sqrt-square clear-num sub-neg frac-2neg flip3-+ pow1/2 diff-log div-sub distribute-frac-neg flip-+ div-inv sub0-neg
Calls
4 calls:
Slowest
10.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms
(/ (- 0 (* a c)) a)
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))
3.0ms
(- (* b_2 b_2) (* a c))

series144.0ms

Calls
4 calls:
Slowest
63.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
36.0ms
(sqrt (- (* b_2 b_2) (* a c)))
36.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(/ (- 0 (* a c)) a)

simplify2.1s

Calls
25 calls:
Slowest
421.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
311.0ms
(- (pow 0 3) (pow (* a c) 3))
305.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
229.0ms
(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
196.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune814.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.4b

regimes275.0ms

Accuracy

95.2% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 29.1b

bsearch305.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s5801×body80valid
895.0ms1119×body2560valid
624.0ms876×body1280valid
307.0ms2891×body80nan
229.0ms470×body640valid
96.0ms118×body5120valid
95.0ms216×body320valid
28.0ms128×body160valid