Details

Time bar (total: 9.2m)

sample194.0ms

Algorithm
intervals
Results
46.0ms30×body2560valid
20.0ms189×body80valid
12.0ms32×body1280valid
8.0ms99×body80nan
5.0ms15×body640valid
1.0ms4×body320valid
1.0ms5×body160valid
1.0ms1×body5120valid

simplify208.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
208.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize27.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (- (* b_2 b_2) (* a c)))
1.3b
(- (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)

rewrite234.0ms

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
110.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
75.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
31.0ms
(sqrt (- (* b_2 b_2) (* a c)))
14.0ms
(- (* b_2 b_2) (* a c))

series481.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
130.0ms
(sqrt (- (* b_2 b_2) (* a c)))
128.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms
(- (* b_2 b_2) (* a c))

simplify6.1s

Counts
116 → 134
Calls
116 calls:
Slowest
534.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
368.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
354.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
293.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
283.0ms
(/ (* (* (- (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))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize19.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (- (* b_2 b_2) (* a c)))
5.7b
(- (/ (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)

rewrite150.0ms

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
94.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
18.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
16.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
109.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))
61.0ms
(- (* b_2 b_2) (* a c))

simplify2.0m

Counts
687 → 427
Calls
687 calls:
Slowest
775.0ms
(fma (- (/ b_2 (cbrt a))) (/ 1 (* (cbrt a) (cbrt a))) (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a)))))
721.0ms
(fma (/ (sqrt 1) (* (cbrt a) (cbrt a))) (/ (sqrt (- (* b_2 b_2) (* a c))) (cbrt a)) (- (* (/ b_2 a) 1)))
674.0ms
(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) (cbrt a)) (/ (sqrt b_2) (* (cbrt a) (cbrt a))))))
544.0ms
(fma (- (/ b_2 (cbrt a))) (/ 1 (* (cbrt a) (cbrt a))) (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a)))))
540.0ms
(fma (/ 1 1) (/ (sqrt (- (* b_2 b_2) (* a c))) a) (- (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))

prune4.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize47.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (- (* b_2 b_2) (* a c)))
9.3b
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
0.6b
(- (* b_2 b_2) (* a c))
0.2b
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))

rewrite251.0ms

Algorithm
rewrite-expression-head
Rules
2630×times-frac
1567×add-sqr-sqrt
1530×*-un-lft-identity
1517×add-cube-cbrt
1002×prod-diff
421×sqrt-prod
139×div-inv
107×associate-/r/
94×sqrt-div
78×fma-neg
49×flip3-- flip--
24×associate-/r*
15×add-exp-log
14×difference-of-squares
9×add-cbrt-cube
8×add-log-exp
7×div-exp
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/l* distribute-lft-out--
2×rec-exp sub-neg diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 frac-sub pow-flip inv-pow
Counts
4 → 1269
Calls
4 calls:
Slowest
142.0ms
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
25.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series386.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
118.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
90.0ms
(sqrt (- (* b_2 b_2) (* a c)))
42.0ms
(- (* b_2 b_2) (* a c))

simplify6.7m

Counts
2312 → 1281
Calls
2312 calls:
Slowest
832.0ms
(fma (- (/ b_2 (cbrt a))) (/ 1 (* (cbrt a) (cbrt a))) (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a)))))
805.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))))) (/ (cbrt 1) (/ a (sqrt (cbrt (- (* b_2 b_2) (* a c)))))) (- (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))
744.0ms
(fma (/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (/ (sqrt 1) (/ (cbrt a) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (- (* (sqrt (/ b_2 a)) (sqrt (/ b_2 a)))))
720.0ms
(fma (/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (/ (sqrt 1) (/ (cbrt a) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (- (* (sqrt (/ b_2 a)) (sqrt (/ b_2 a)))))
702.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (/ a (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3))))) (/ (cbrt 1) (sqrt (+ (* (* b_2 b_2) (* b_2 b_2)) (+ (* (* a c) (* a c)) (* (* b_2 b_2) (* a c)))))) (- (* (/ (cbrt b_2) a) (/ (* (cbrt b_2) (cbrt b_2)) 1))))

prune8.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (- (* b_2 b_2) (* a c)))
11.0b
(- (* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c)))) (/ b_2 a))
0.6b
(- (* b_2 b_2) (* a c))
0.2b
(* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
23×*-un-lft-identity
22×times-frac
21×add-cube-cbrt
14×prod-diff
13×associate-*l* add-exp-log
10×sqrt-div
9×add-cbrt-cube sqrt-prod
8×add-log-exp
7×pow1 flip3-- flip--
6×associate-*r* unswap-sqr
5×frac-sub
4×expm1-log1p-u frac-times prod-exp associate-*r/ insert-posit16 log1p-expm1-u
3×associate-*l/
2×sub-neg fma-neg diff-log div-exp cbrt-unprod div-inv
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down *-commutative sub-div
Counts
4 → 118
Calls
4 calls:
Slowest
32.0ms
(- (* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c)))) (/ b_2 a))
27.0ms
(* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series266.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(- (* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c)))) (/ b_2 a))
80.0ms
(* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))
36.0ms
(- (* b_2 b_2) (* a c))

simplify7.3s

Counts
104 → 130
Calls
104 calls:
Slowest
413.0ms
(* (sqrt (+ (* (* b_2 b_2) (* b_2 b_2)) (+ (* (* a c) (* a c)) (* (* b_2 b_2) (* a c))))) a)
369.0ms
(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (* (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (- (* b_2 b_2) (* a c)))))
290.0ms
(fma (- (/ b_2 (cbrt a))) (/ 1 (* (cbrt a) (cbrt a))) (* (/ b_2 (cbrt a)) (/ 1 (* (cbrt a) (cbrt a)))))
253.0ms
(- (* (* (/ 1 a) (sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))) a) (* (sqrt (+ (* b_2 b_2) (* a c))) b_2))
223.0ms
(- (* (* 1 (sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))) a) (* (* a (sqrt (+ (* b_2 b_2) (* a c)))) b_2))

prune799.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

regimes208.0ms

Accuracy

83.5% (4.7b remaining)

Error of 9.9b against oracle of 5.2b and baseline of 33.8b

bsearch112.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
579.0ms5825×body80valid
480.0ms1123×body2560valid
387.0ms461×body640valid
321.0ms876×body1280valid
238.0ms2896×body80nan
89.0ms109×body5120valid
41.0ms209×body320valid
16.0ms124×body160valid