Details

Time bar (total: 35.2s)

sample192.0ms

Algorithm
intervals
Results
46.0ms99×body80nan
25.0ms33×body2560valid
24.0ms193×body80valid
21.0ms36×body1280valid
5.0ms11×body640valid
4.0ms10×body320valid
2.0ms3×body5120valid
1.0ms2×body160valid

simplify87.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
86.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize39.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (- (* b_2 b_2) (* a c)))
0.7b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite318.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u 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 → 122
Calls
4 calls:
Slowest
181.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
91.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0ms
(sqrt (- (* b_2 b_2) (* a c)))
15.0ms
(- (* b_2 b_2) (* a c))

series366.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(sqrt (- (* b_2 b_2) (* a c)))
102.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
84.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
39.0ms
(- (* b_2 b_2) (* a c))

simplify5.8s

Counts
116 → 134
Calls
116 calls:
Slowest
503.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
376.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
357.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
272.0ms
(/ (* (* (- (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))
236.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize28.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (- (* b_2 b_2) (* a c)))
13.1b
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.3b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b
(- (* b_2 b_2) (* a c))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log add-cube-cbrt
8×add-log-exp
6×fma-def times-frac sqrt-prod associate-/l*
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×distribute-lft-neg-in cbrt-undiv neg-mul-1 distribute-rgt-neg-in flip3-+ flip3-- sqrt-div div-exp associate-*r/ associate-/r/ flip-+ flip--
1×neg-sub0 +-commutative rem-sqrt-square clear-num associate-/r* sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff prod-exp distribute-frac-neg cbrt-unprod div-inv distribute-lft-out
Counts
4 → 90
Calls
4 calls:
Slowest
49.0ms
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
29.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series433.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
99.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
87.0ms
(sqrt (- (* b_2 b_2) (* a c)))
64.0ms
(- (* b_2 b_2) (* a c))

simplify7.2s

Counts
53 → 102
Calls
53 calls:
Slowest
2.0s
(/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (* 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))))
1.3s
(/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (* 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))))
443.0ms
(+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (- (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2)))
408.0ms
(- (log (- (* a c))) (+ (log a) (log (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
399.0ms
(- (log (- (* a c))) (log (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

localize26.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (- (* b_2 b_2) (* a c)))
1.3b
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
0.4b
(- (* b_2 b_2) (* a c))
0.1b
(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt
12×times-frac
8×add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1 distribute-lft-out
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u
3×fma-def sqrt-prod associate-/l*
2×flip3-+ flip3-- sqrt-div associate-/r/ flip-+ flip--
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-exp prod-diff div-inv
Counts
4 → 89
Calls
4 calls:
Slowest
52.0ms
(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
24.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
20.0ms
(sqrt (- (* b_2 b_2) (* a c)))
16.0ms
(- (* b_2 b_2) (* a c))

series451.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
232.0ms
(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
84.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))
59.0ms
(- (* b_2 b_2) (* a c))

simplify3.5s

Counts
60 → 101
Calls
60 calls:
Slowest
619.0ms
(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
340.0ms
(/ (* (* c c) c) (* (* (+ b_2 (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))))))
328.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
297.0ms
(+ (* b_2 b_2) (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 (sqrt (- (* b_2 b_2) (* a c))))))
239.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.8b

localize39.0ms

Local error

Found 4 expressions with local error:

21.1b
(sqrt (- (* b_2 b_2) (* a c)))
0.7b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b
(- (* b_2 b_2) (* a c))
0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
32×*-un-lft-identity
27×add-cube-cbrt
19×prod-diff
17×sqrt-prod
13×associate-*r* add-exp-log
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u 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 → 123
Calls
4 calls:
Slowest
137.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
49.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
26.0ms
(sqrt (- (* b_2 b_2) (* a c)))
10.0ms
(- (* b_2 b_2) (* a c))

series376.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
113.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
85.0ms
(sqrt (- (* b_2 b_2) (* a c)))
41.0ms
(- (* b_2 b_2) (* a c))

simplify6.6s

Counts
105 → 135
Calls
105 calls:
Slowest
522.0ms
(* (* (* (- (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)))
384.0ms
(* (+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (+ (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
320.0ms
(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) (/ 1 a))
298.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
292.0ms
(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) (/ 1 a))

prune1.3s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.8b

regimes480.0ms

Accuracy

92.8% (1.7b remaining)

Error of 7.4b against oracle of 5.7b and baseline of 29.0b

bsearch252.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
862.0ms1075×body2560valid
816.0ms5888×body80valid
562.0ms915×body1280valid
504.0ms223×body320valid
429.0ms3026×body80nan
206.0ms434×body640valid
106.0ms115×body5120valid
20.0ms95×body160valid