Details

Time bar (total: 2.5m)

sample462.0ms

Algorithm
intervals
Results
71.0ms24×body1280valid
27.0ms38×body2560valid
25.0ms184×body80valid
9.0ms96×body80nan
8.0ms17×body640valid
2.0ms3×body5120valid
2.0ms7×body320valid
1.0ms5×body160valid

simplify465.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
464.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize37.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b_2 b_2) (* a c)))
1.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b
(- (* b_2 b_2) (* a c))
0.3b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite148.0ms

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
66.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
50.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series363.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
108.0ms
(sqrt (- (* b_2 b_2) (* a c)))
103.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
38.0ms
(- (* b_2 b_2) (* a c))

simplify5.8s

Counts
116 → 134
Calls
116 calls:
Slowest
558.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
347.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
321.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
273.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
256.0ms
(/ (* (* (- (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))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize31.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b_2 b_2) (* a c)))
1.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b
(- (* b_2 b_2) (* a c))
0.3b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite194.0ms

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
111.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
55.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
104.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
96.0ms
(sqrt (- (* b_2 b_2) (* a c)))
50.0ms
(- (* b_2 b_2) (* a c))

simplify5.8s

Counts
116 → 134
Calls
116 calls:
Slowest
444.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
343.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
287.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
270.0ms
(/ (* (* (- (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))
269.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize32.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b_2 b_2) (* a c)))
1.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b
(- (* b_2 b_2) (* a c))
0.3b
(/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))

rewrite181.0ms

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×associate-/r* add-cbrt-cube add-exp-log
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 121
Calls
4 calls:
Slowest
79.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
65.0ms
(/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))
15.0ms
(- (* b_2 b_2) (* a c))

series497.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
247.0ms
(/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
107.0ms
(sqrt (- (* b_2 b_2) (* a c)))
92.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
51.0ms
(- (* b_2 b_2) (* a c))

simplify5.3s

Counts
117 → 133
Calls
117 calls:
Slowest
353.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
294.0ms
(+ (* (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)))
254.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
225.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
181.0ms
(/ (* (* 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)))

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.5b

localize20.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b_2 b_2) (* a c)))
8.5b
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
1.2b
(- (* b_2 b_2) (* a c))
0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)

rewrite130.0ms

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
54.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
27.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
19.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
118.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
96.0ms
(sqrt (- (* b_2 b_2) (* a c)))
49.0ms
(- (* b_2 b_2) (* a c))

simplify2.0m

Counts
687 → 427
Calls
687 calls:
Slowest
810.0ms
(fma (/ (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c))))) (* (cbrt a) (cbrt a))) (/ (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) (- (* (/ b_2 (sqrt a)) (/ 1 (sqrt a)))))
641.0ms
(fma (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt a)) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt a)) (- (* (cbrt (/ b_2 a)) (* (cbrt (/ b_2 a)) (cbrt (/ b_2 a))))))
590.0ms
(fma (/ 1 1) (/ (sqrt (- (* b_2 b_2) (* a c))) a) (- (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))
570.0ms
(fma (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt a)) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt a)) (- (* (/ b_2 a) (/ 1 1))))
544.0ms
(fma (- (/ b_2 (cbrt a))) (/ 1 (* (cbrt a) (cbrt a))) (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a)))))

prune4.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.5b

regimes818.0ms

Accuracy

83.4% (4.7b remaining)

Error of 10.1b against oracle of 5.4b and baseline of 33.9b

bsearch169.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.1s913×body1280valid
868.0ms5840×body80valid
820.0ms1088×body2560valid
395.0ms2878×body80nan
234.0ms441×body640valid
104.0ms125×body5120valid
83.0ms239×body320valid
31.0ms139×body160valid