Details

Time bar (total: 1.4m)

sample79.0ms

Algorithm
intervals
Results
38.0ms41×body640valid
16.0ms54×body1280valid
11.0ms127×body80valid
4.0ms24×body320valid
1.0ms10×body160valid

simplify65.0ms

Calls
1 calls:
Slowest
65.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize25.0ms

Local error

Found 3 expressions with local error:

2.4b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
90×prod-diff
75×add-sqr-sqrt
72×*-un-lft-identity
70×add-cube-cbrt
64×times-frac
48×associate-/r/
24×div-inv
18×flip3-+ flip-+
8×flip3-- flip--
6×associate-/r* fma-neg
5×add-cbrt-cube add-exp-log add-log-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l*
2×clear-num frac-2neg difference-of-squares associate-/l/
1×cbrt-undiv sub-neg diff-log div-exp frac-sub distribute-lft-out--
Calls
3 calls:
Slowest
29.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
4.0ms
(/ (+ x 1) (- x 1))
1.0ms
(/ x (+ x 1))

series168.0ms

Calls
3 calls:
Slowest
96.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
38.0ms
(/ (+ x 1) (- x 1))
34.0ms
(/ x (+ x 1))

simplify49.3s

Calls
235 calls:
Slowest
873.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (/ 1 (- x 1)) (+ x 1))))
862.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
715.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
714.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
698.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (sqrt (/ (+ x 1) (- x 1))) (sqrt (/ (+ x 1) (- x 1))))))

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))
0.0b
(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
0.0b
(* (/ x (+ x 1)) (/ x (+ x 1)))
0.0b
(/ (- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))) (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
34×times-frac
30×add-sqr-sqrt add-cube-cbrt
21×associate-*r* associate-*l*
20×add-cbrt-cube add-exp-log
18×frac-sub
14×frac-times pow1 associate-*l/ associate-*r/
11×associate-/r/ associate-/l/
6×add-log-exp difference-of-squares
5×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv distribute-lft-out
4×expm1-log1p-u associate-/r* flip3-- insert-posit16 log1p-expm1-u flip-- associate-/l*
3×flip3-+ flip-+
2×pow2 pow-plus pow-prod-down *-commutative pow-prod-up
1×clear-num sub-neg frac-2neg fma-neg diff-log div-sub prod-diff frac-add
Calls
4 calls:
Slowest
30.0ms
(/ (- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))) (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
9.0ms
(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
8.0ms
(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))
8.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))

series489.0ms

Calls
4 calls:
Slowest
254.0ms
(/ (- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))) (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
157.0ms
(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))
43.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))
36.0ms
(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))

simplify25.8s

Calls
157 calls:
Slowest
776.0ms
(- (* (* x x) (- x 1)) (* (* (+ x 1) (+ x 1)) (* (/ (+ x 1) (- x 1)) (+ x 1))))
751.0ms
(- (* (* x x) (- x 1)) (* (* (+ x 1) (+ x 1)) (* (+ x 1) (/ (+ x 1) (- x 1)))))
705.0ms
(- (* (* x x) (- x 1)) (* (* (+ x 1) (+ x 1)) (* (/ (+ x 1) (- x 1)) (+ x 1))))
682.0ms
(- (* (* x x) (- x 1)) (* (* (+ x 1) (+ x 1)) (* (+ x 1) (/ (+ x 1) (- x 1)))))
632.0ms
(sqrt (- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))))

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

7.5b
(fma (/ (/ -1 (* x x)) x) 3 (/ -1 (* x x)))
0.2b
(/ -1 (* x x))
0.2b
(/ -1 (* x x))
0.1b
(/ (/ -1 (* x x)) x)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
5×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 div-inv associate-/l* add-log-exp
3×clear-num frac-2neg
2×associate-/r*
1×fma-udef associate-/l/
Calls
4 calls:
Slowest
4.0ms
(/ (/ -1 (* x x)) x)
0.0ms
(/ -1 (* x x))
0.0ms
(/ -1 (* x x))
0.0ms
(fma (/ (/ -1 (* x x)) x) 3 (/ -1 (* x x)))

series222.0ms

Calls
4 calls:
Slowest
117.0ms
(fma (/ (/ -1 (* x x)) x) 3 (/ -1 (* x x)))
45.0ms
(/ (/ -1 (* x x)) x)
33.0ms
(/ -1 (* x x))
26.0ms
(/ -1 (* x x))

simplify485.0ms

Calls
14 calls:
Slowest
136.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
97.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
96.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
17.0ms
(/ -1 (pow x 3))
17.0ms
(* (cbrt (/ -1 (* x x))) (cbrt (/ -1 (* x x))))

prune564.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

7.4b
(fma (/ (log (exp (/ -1 (* x x)))) x) 3 (/ -1 (* x x)))
1.8b
(log (exp (/ -1 (* x x))))
0.2b
(/ -1 (* x x))
0.2b
(/ -1 (* x x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1 log-pow
4×expm1-log1p-u exp-prod add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×log-prod div-inv
2×clear-num associate-/r* frac-2neg
1×rem-log-exp fma-udef
Calls
4 calls:
Slowest
3.0ms
(log (exp (/ -1 (* x x))))
1.0ms
(fma (/ (log (exp (/ -1 (* x x)))) x) 3 (/ -1 (* x x)))
0.0ms
(/ -1 (* x x))
0.0ms
(/ -1 (* x x))

series210.0ms

Calls
4 calls:
Slowest
118.0ms
(fma (/ (log (exp (/ -1 (* x x)))) x) 3 (/ -1 (* x x)))
35.0ms
(log (exp (/ -1 (* x x))))
31.0ms
(/ -1 (* x x))
26.0ms
(/ -1 (* x x))

simplify522.0ms

Calls
19 calls:
Slowest
146.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
104.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
99.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
17.0ms
(/ -1 (pow x 2))
15.0ms
(/ -1 (pow x 2))

prune727.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.0b

bsearch174.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
807.0ms1215×body640valid
712.0ms1714×body1280valid
431.0ms4141×body80valid
191.0ms628×body320valid
44.0ms302×body160valid