Details

Time bar (total: 2.5m)

sample263.0ms

Algorithm
intervals
Results
33.0ms35×body2560valid
32.0ms191×body80valid
28.0ms37×body1280valid
16.0ms106×body80nan
9.0ms16×body640valid
2.0ms4×body320valid
1.0ms4×body160valid
1.0ms1×body5120valid

simplify124.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
123.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize38.0ms

Local error

Found 4 expressions with local error:

19.8b
(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)

rewrite222.0ms

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
126.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
55.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))
15.0ms
(- (* b_2 b_2) (* a c))

series351.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
102.0ms
(sqrt (- (* b_2 b_2) (* a c)))
89.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
53.0ms
(- (* b_2 b_2) (* a c))

simplify6.3s

Counts
116 → 134
Calls
116 calls:
Slowest
608.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
441.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
349.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
313.0ms
(/ (* (* (- (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))
298.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize33.0ms

Local error

Found 4 expressions with local error:

19.8b
(sqrt (- (* b_2 b_2) (* a c)))
7.4b
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
0.6b
(- (* b_2 b_2) (* a c))
0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
481×times-frac
378×add-sqr-sqrt
366×*-un-lft-identity
358×add-cube-cbrt
287×prod-diff
143×sqrt-prod
39×div-inv
23×fma-neg
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- sqrt-div insert-posit16 log1p-expm1-u flip-- distribute-lft-out--
3×associate-/r*
2×sub-neg diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-exp frac-sub sub-div
Counts
4 → 415
Calls
4 calls:
Slowest
68.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
17.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
15.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
107.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))
59.0ms
(- (* b_2 b_2) (* a c))

simplify2.0m

Counts
687 → 427
Calls
687 calls:
Slowest
735.0ms
(fma (- (/ (cbrt b_2) (cbrt a))) (/ (* (cbrt b_2) (cbrt b_2)) (* (cbrt a) (cbrt a))) (* (/ (cbrt b_2) (cbrt a)) (/ (* (cbrt b_2) (cbrt b_2)) (* (cbrt a) (cbrt a)))))
655.0ms
(fma (/ (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (* (cbrt a) (cbrt a))) (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (cbrt a)) (- (* (/ (sqrt b_2) (sqrt a)) (/ (sqrt b_2) (sqrt a)))))
589.0ms
(fma (sqrt (/ (sqrt (- (* b_2 b_2) (* a c))) a)) (sqrt (/ (sqrt (- (* b_2 b_2) (* a c))) a)) (- (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))
583.0ms
(fma (/ 1 1) (/ (sqrt (- (* b_2 b_2) (* a c))) a) (- (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))
545.0ms
(fma (- (/ b_2 (cbrt a))) (/ 1 (* (cbrt a) (cbrt a))) (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a)))))

prune4.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.9b

localize32.0ms

Local error

Found 3 expressions with local error:

23.5b
(fma (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a) (- (/ b_2 a)))
19.8b
(sqrt (- (* b_2 b_2) (* a c)))
0.6b
(- (* b_2 b_2) (* a c))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-log-exp
4×pow1 *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u add-cbrt-cube add-exp-log sqrt-prod insert-posit16 log1p-expm1-u
2×flip3-- sqrt-div flip--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff fma-udef
Counts
3 → 46
Calls
3 calls:
Slowest
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
16.0ms
(- (* b_2 b_2) (* a c))
1.0ms
(fma (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a) (- (/ b_2 a)))

series256.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
130.0ms
(fma (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a) (- (/ b_2 a)))
83.0ms
(sqrt (- (* b_2 b_2) (* a c)))
43.0ms
(- (* b_2 b_2) (* a c))

simplify1.5s

Counts
19 → 55
Calls
19 calls:
Slowest
341.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
254.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
235.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
170.0ms
(/ (exp (* b_2 b_2)) (exp (* a c)))
130.0ms
(- (* 1/2 (/ c b_2)) (* 2 (/ b_2 a)))

prune651.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.9b

localize47.0ms

Local error

Found 4 expressions with local error:

19.8b
(sqrt (- (* b_2 b_2) (* a c)))
17.1b
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.9b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(- (* b_2 b_2) (* a c))

rewrite146.0ms

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
60.0ms
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
50.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
16.0ms
(- (* b_2 b_2) (* a c))

series428.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
209.0ms
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
91.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))
47.0ms
(- (* b_2 b_2) (* a c))

simplify7.6s

Counts
53 → 102
Calls
53 calls:
Slowest
2.1s
(/ (* (* (- (* 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))))
1.5s
(/ (* (* (- (* 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))))
520.0ms
(+ (* (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)))
430.0ms
(- (log (- (* a c))) (log (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
355.0ms
(- (log (- (* a c))) (+ (log a) (log (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))

prune886.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.9b

regimes285.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.9b against oracle of 5.9b and baseline of 29.1b

bsearch242.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.4s5819×body80valid
913.0ms1071×body2560valid
722.0ms2833×body80nan
704.0ms940×body1280valid
231.0ms422×body640valid
139.0ms93×body5120valid
119.0ms234×body320valid
33.0ms130×body160valid