Details

Time bar (total: 19.9s)

sample205.0ms

Algorithm
intervals
Results
76.0ms203×body80valid
22.0ms31×body2560valid
13.0ms21×body1280valid
12.0ms95×body80nan
10.0ms21×body640valid
2.0ms4×body320valid
1.0ms1×body5120valid
0.0ms2×body160valid

simplify165.0ms

Calls
1 calls:
Slowest
164.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize72.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite87.0ms

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
48.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
25.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))
3.0ms
(- (* b_2 b_2) (* a c))

series342.0ms

Calls
4 calls:
Slowest
134.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))
74.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
45.0ms
(- (* b_2 b_2) (* a c))

simplify2.1s

Calls
24 calls:
Slowest
424.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
357.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
328.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
183.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
135.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune698.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize6.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(- (* b_2 b_2) (* a c))
0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite53.0ms

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
34.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
13.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0ms
(sqrt (- (* b_2 b_2) (* a c)))
2.0ms
(- (* b_2 b_2) (* a c))

series427.0ms

Calls
4 calls:
Slowest
129.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
126.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
105.0ms
(sqrt (- (* b_2 b_2) (* a c)))
67.0ms
(- (* b_2 b_2) (* a c))

simplify3.7s

Calls
34 calls:
Slowest
463.0ms
(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) 1)
414.0ms
(* (* (* (- (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)))
356.0ms
(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) (/ 1 a))
348.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
313.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune763.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.5b

localize2.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite80.0ms

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)
26.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))
5.0ms
(- (* b_2 b_2) (* a c))

series380.0ms

Calls
4 calls:
Slowest
152.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
94.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))
60.0ms
(- (* b_2 b_2) (* a c))

simplify2.2s

Calls
24 calls:
Slowest
427.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
399.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
342.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
261.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
163.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune986.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.5b

localize10.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (- (* b_2 b_2) (* a c)))
14.3b
(/ (- 0 (* a c)) a)
0.7b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(- (* b_2 b_2) (* a c))

rewrite17.0ms

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
9.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0ms
(/ (- 0 (* a c)) a)
2.0ms
(sqrt (- (* b_2 b_2) (* a c)))
2.0ms
(- (* b_2 b_2) (* a c))

series246.0ms

Calls
4 calls:
Slowest
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))
84.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
62.0ms
(- (* b_2 b_2) (* a c))
11.0ms
(/ (- 0 (* a c)) a)

simplify2.1s

Calls
25 calls:
Slowest
398.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
354.0ms
(- (pow 0 3) (pow (* a c) 3))
325.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
241.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
222.0ms
(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))

prune773.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.5b

regimes291.0ms

Accuracy

95.7% (1.1b remaining)

Error of 6.3b against oracle of 5.3b and baseline of 29.8b

bsearch294.0ms

end18.0ms

sample3.9s

Algorithm
intervals
Results
1.4s5885×body80valid
901.0ms1037×body2560valid
601.0ms887×body1280valid
380.0ms2915×body80nan
203.0ms460×body640valid
79.0ms242×body320valid
78.0ms95×body5120valid
24.0ms109×body160valid