Details

Time bar (total: 6.1m)

sample50.0ms

Algorithm
intervals
Results
17.0ms54×body1280valid
9.0ms35×body640valid
9.0ms137×body80valid
4.0ms20×body320valid
1.0ms10×body160valid

simplify78.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
78.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize25.0ms

Local error

Found 3 expressions with local error:

3.1b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
1284×*-un-lft-identity
984×times-frac
841×add-sqr-sqrt
612×prod-diff
521×add-cube-cbrt
251×distribute-lft-out
158×difference-of-squares
110×associate-/r/
90×distribute-lft-out--
77×difference-of-sqr-1
55×div-inv
37×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×add-log-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 753
Calls
3 calls:
Slowest
75.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
17.0ms
(/ (+ x 1) (- x 1))
8.0ms
(/ x (+ x 1))

series164.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
110.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
31.0ms
(/ (+ x 1) (- x 1))
23.0ms
(/ x (+ x 1))

simplify5.5m

Counts
1423 → 762
Calls
1423 calls:
Slowest
893.0ms
(fma (/ (sqrt x) (sqrt (+ x 1))) (/ (sqrt x) (sqrt (+ x 1))) (- (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))))
855.0ms
(fma (/ (sqrt x) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt x) (cbrt (+ x 1))) (- (* (/ (cbrt (+ x 1)) (- x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1))))
850.0ms
(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))))
827.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
805.0ms
(fma (/ 1 1) (/ x (+ x 1)) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))

prune4.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

28.5b
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))
14.3b
(/ x (- (* x x) (* 1 1)))
14.3b
(/ (+ x 1) (- (* x x) (* 1 1)))
0.1b
(* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
45×times-frac
38×add-sqr-sqrt
33×add-cube-cbrt
22×associate-*r*
13×add-cbrt-cube add-exp-log difference-of-squares
10×distribute-lft-out
8×associate-/r*
7×associate-/l*
6×pow1 associate-/r/
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-+ flip3-- div-exp flip-+ div-inv flip--
2×frac-times clear-num frac-2neg associate-*l/ prod-exp cbrt-unprod unswap-sqr associate-/l/
1×pow-prod-down associate-*r/ *-commutative fma-udef
Counts
4 → 139
Calls
4 calls:
Slowest
42.0ms
(* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))
19.0ms
(/ (+ x 1) (- (* x x) (* 1 1)))
15.0ms
(/ x (- (* x x) (* 1 1)))
0.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))

series250.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))
51.0ms
(/ x (- (* x x) (* 1 1)))
32.0ms
(* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))
27.0ms
(/ (+ x 1) (- (* x x) (* 1 1)))

simplify18.3s

Counts
184 → 151
Calls
184 calls:
Slowest
793.0ms
(* (- (* x x) (* 1 1)) (/ (+ x 1) (- (* x x) (* 1 1))))
693.0ms
(* (+ x 1) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (+ x 1)))
634.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- (* x x) (* 1 1)) (- (* x x) (* 1 1))) (- (* x x) (* 1 1))))
568.0ms
(* (* (fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))) (fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))) (fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))))
402.0ms
(* (/ x (- (* x x) (* 1 1))) (- x 1))

prune871.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

3.2b
(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1))))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 53
Calls
4 calls:
Slowest
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
0.0ms
(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1))))

series836.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
236.0ms
(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1))))
202.0ms
(cbrt x)
199.0ms
(cbrt x)
199.0ms
(cbrt x)

simplify2.9s

Counts
71 → 65
Calls
71 calls:
Slowest
346.0ms
(* (* (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1)))) (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1))))) (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1)))))
221.0ms
(exp (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1)))))
200.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
160.0ms
(+ (* 3 x) (+ (pow x 3) (+ (pow x 2) 1)))
157.0ms
(* (cbrt (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1))))) (cbrt (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1))))))

prune475.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

5.8b
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))
0.5b
(/ -1 (* x x))
0.1b
(/ (/ -1 x) (* x x))
0.0b
(+ (/ -1 x) (/ (/ -1 x) (* x x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
43×times-frac
29×*-un-lft-identity
27×add-sqr-sqrt add-cube-cbrt
21×add-cbrt-cube add-exp-log
16×associate-/l*
13×fma-def
8×cbrt-undiv div-exp
6×add-log-exp
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×prod-exp cbrt-unprod
2×clear-num associate-/r* frac-2neg
1×+-commutative sum-log flip3-+ frac-add flip-+ fma-udef distribute-lft-out associate-/l/
Counts
4 → 113
Calls
4 calls:
Slowest
18.0ms
(+ (/ -1 x) (/ (/ -1 x) (* x x)))
9.0ms
(/ (/ -1 x) (* x x))
6.0ms
(/ -1 (* x x))
0.0ms
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))

series152.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
53.0ms
(+ (/ -1 x) (/ (/ -1 x) (* x x)))
41.0ms
(/ (/ -1 x) (* x x))
30.0ms
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))
28.0ms
(/ -1 (* x x))

simplify6.4s

Counts
132 → 125
Calls
132 calls:
Slowest
442.0ms
(exp (fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x))))
272.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) x) (* (* x x) x)))
248.0ms
(* (* (fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x))) (fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))) (fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x))))
230.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) (* x x)) (* x x)))
224.0ms
(* (* (/ (/ -1 x) (* x x)) (/ (/ -1 x) (* x x))) (/ (/ -1 x) (* x x)))

prune610.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes62.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.1b

bsearch121.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
528.0ms1693×body1280valid
319.0ms4120×body80valid
303.0ms1261×body640valid
97.0ms617×body320valid
55.0ms309×body160valid