Details

Time bar (total: 35.0s)

sample81.0ms

Algorithm
intervals
Results
27.0ms58×body640valid
17.0ms136×body80valid
13.0ms21×body1280valid
9.0ms25×body320valid
4.0ms17×body160valid

simplify98.0ms

Calls
1 calls:
Slowest
97.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize17.0ms

Local error

Found 3 expressions with local error:

2.2b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))
0.0b
(/ 1 (- x 1))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
48×prod-diff
43×*-un-lft-identity
30×add-sqr-sqrt
29×div-inv
26×associate-+l+ add-cube-cbrt
20×associate-/r/
10×flip3-+ flip-+ add-log-exp
8×distribute-lft-out--
6×fma-def fma-neg distribute-lft-out
4×pow1 add-exp-log
3×expm1-log1p-u associate-/r* flip3-- add-cbrt-cube frac-add insert-posit16 log1p-expm1-u flip--
2×sum-log sub-neg diff-log frac-sub difference-of-squares
1×+-commutative rec-exp clear-num frac-2neg associate-+l- pow-flip inv-pow
Calls
3 calls:
Slowest
43.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
10.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
1.0ms
(/ 1 (- x 1))

series70.0ms

Calls
3 calls:
Slowest
51.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
12.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
6.0ms
(/ 1 (- x 1))

simplify11.6s

Calls
118 calls:
Slowest
459.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (- x 1)) (* (+ (/ 1 (+ x 1)) (/ 2 x)) 1))
413.0ms
(* (* (+ x 1) x) (- x 1))
364.0ms
(fma (/ 1 (+ (pow x 3) (pow 1 3))) (+ (* x x) (- (* 1 1) (* x 1))) (- (* (/ 2 x) 1)))
340.0ms
(* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (- x 1))
335.0ms
(fma (/ 1 (+ (pow x 3) (pow 1 3))) (+ (* x x) (- (* 1 1) (* x 1))) (- (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

12.8b
(fma (/ 1 (fma x x -1)) (- x 1) (- (/ 2 x)))
7.9b
(+ (fma (/ 1 (fma x x -1)) (- x 1) (- (/ 2 x))) (/ 1 (- x 1)))
0.6b
(/ 1 (fma x x -1))
0.0b
(/ 1 (- x 1))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
7×add-sqr-sqrt add-cube-cbrt
6×pow1 associate-/r* add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×fma-def div-inv
2×rec-exp clear-num frac-2neg associate-/r/ fma-udef pow-flip distribute-lft-out inv-pow
1×+-commutative associate-+l+ sum-log flip3-+ flip3-- flip-+ flip--
Calls
4 calls:
Slowest
5.0ms
(+ (fma (/ 1 (fma x x -1)) (- x 1) (- (/ 2 x))) (/ 1 (- x 1)))
1.0ms
(/ 1 (- x 1))
1.0ms
(/ 1 (fma x x -1))
0.0ms
(fma (/ 1 (fma x x -1)) (- x 1) (- (/ 2 x)))

series110.0ms

Calls
4 calls:
Slowest
59.0ms
(+ (fma (/ 1 (fma x x -1)) (- x 1) (- (/ 2 x))) (/ 1 (- x 1)))
21.0ms
(/ 1 (fma x x -1))
19.0ms
(fma (/ 1 (fma x x -1)) (- x 1) (- (/ 2 x)))
10.0ms
(/ 1 (- x 1))

simplify2.9s

Calls
28 calls:
Slowest
401.0ms
(* (exp (fma (/ 1 (fma x x -1)) (- x 1) (- (/ 2 x)))) (exp (/ 1 (- x 1))))
280.0ms
(+ (fma (/ 1 (fma x x -1)) (- x 1) (- (/ 2 x))) (/ 1 (- x 1)))
235.0ms
(+ (fma (/ 1 (fma x x -1)) (- x 1) (- (/ 2 x))) (/ 1 (- x 1)))
231.0ms
(- (+ (* 2 x) (+ (* 2 (pow x 3)) (* 2 (/ 1 x)))))
230.0ms
(sqrt (fma (/ 1 (fma x x -1)) (- x 1) (- (/ 2 x))))

prune832.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

3.2b
(+ (/ 1 (- x 1)) (/ 1 (+ x 1)))
2.2b
(+ (/ -2 x) (+ (/ 1 (- x 1)) (/ 1 (+ x 1))))
0.0b
(/ 1 (- x 1))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
14×distribute-lft-out
11×div-inv
10×fma-def add-log-exp
6×add-sqr-sqrt associate-/r/ add-cube-cbrt
5×frac-add
4×pow1 sum-log add-exp-log flip-+
3×expm1-log1p-u associate-/r* flip3-+ add-cbrt-cube insert-posit16 log1p-expm1-u flip--
2×+-commutative flip3--
1×rec-exp associate-+r+ clear-num frac-2neg pow-flip inv-pow
Calls
3 calls:
Slowest
19.0ms
(+ (/ -2 x) (+ (/ 1 (- x 1)) (/ 1 (+ x 1))))
11.0ms
(+ (/ 1 (- x 1)) (/ 1 (+ x 1)))
1.0ms
(/ 1 (- x 1))

series92.0ms

Calls
3 calls:
Slowest
58.0ms
(+ (/ -2 x) (+ (/ 1 (- x 1)) (/ 1 (+ x 1))))
21.0ms
(+ (/ 1 (- x 1)) (/ 1 (+ x 1)))
13.0ms
(/ 1 (- x 1))

simplify4.5s

Calls
44 calls:
Slowest
548.0ms
(+ (* 1 (+ x 1)) (* (- x 1) 1))
512.0ms
(+ (* -2 (* (- x 1) (+ x 1))) (* x (+ (* 1 (+ x 1)) (* (- x 1) 1))))
382.0ms
(* x (* (- x 1) (+ x 1)))
329.0ms
(+ (* -2 (- (/ 1 (- x 1)) (/ 1 (+ x 1)))) (* x (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (/ 1 (+ x 1)) (/ 1 (+ x 1))))))
293.0ms
(* x (+ (* (/ 1 (- x 1)) (/ 1 (- x 1))) (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 1 (- x 1)) (/ 1 (+ x 1))))))

prune848.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

17.5b
(+ (fma -2 (+ (* x x) -1) (* x x)) (* x x))
16.3b
(fma -2 (+ (* x x) -1) (* x x))
9.3b
(fma (- (* x x) x) x (- (* x x) x))
0.0b
(/ (+ (fma -2 (+ (* x x) -1) (* x x)) (* x x)) (fma (- (* x x) x) x (- (* x x) x)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×associate-/r* fma-def fma-udef associate-/l*
2×flip3-+ flip-+ associate-/l/
1×cbrt-undiv +-commutative associate-+l+ clear-num sum-log frac-2neg div-exp div-inv
Calls
4 calls:
Slowest
23.0ms
(/ (+ (fma -2 (+ (* x x) -1) (* x x)) (* x x)) (fma (- (* x x) x) x (- (* x x) x)))
4.0ms
(+ (fma -2 (+ (* x x) -1) (* x x)) (* x x))
0.0ms
(fma -2 (+ (* x x) -1) (* x x))
0.0ms
(fma (- (* x x) x) x (- (* x x) x))

series268.0ms

Calls
4 calls:
Slowest
90.0ms
(/ (+ (fma -2 (+ (* x x) -1) (* x x)) (* x x)) (fma (- (* x x) x) x (- (* x x) x)))
61.0ms
(+ (fma -2 (+ (* x x) -1) (* x x)) (* x x))
60.0ms
(fma (- (* x x) x) x (- (* x x) x))
57.0ms
(fma -2 (+ (* x x) -1) (* x x))

simplify9.5s

Calls
43 calls:
Slowest
611.0ms
(/ (sqrt (+ (fma -2 (+ (* x x) -1) (* x x)) (* x x))) (cbrt (fma (- (* x x) x) x (- (* x x) x))))
418.0ms
(* -2 (+ (* x x) -1))
386.0ms
(sqrt (+ (fma -2 (+ (* x x) -1) (* x x)) (* x x)))
380.0ms
(/ (* (cbrt (+ (fma -2 (+ (* x x) -1) (* x x)) (* x x))) (cbrt (+ (fma -2 (+ (* x x) -1) (* x x)) (* x x)))) 1)
374.0ms
(* (cbrt (fma -2 (+ (* x x) -1) (* x x))) (cbrt (fma -2 (+ (* x x) -1) (* x x))))

prune682.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

98.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 7.9b

bsearch64.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
558.0ms921×body320valid
556.0ms1889×body640valid
409.0ms4149×body80valid
272.0ms564×body1280valid
90.0ms479×body160valid