Details

Time bar (total: 2.9m)

sample79.0ms

Algorithm
intervals
Results
30.0ms64×body640valid
17.0ms132×body80valid
10.0ms18×body1280valid
9.0ms27×body320valid
3.0ms15×body160valid

simplify112.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
112.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.0b

localize19.0ms

Local error

Found 4 expressions with local error:

2.4b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))
0.0b
(/ 1 (- x 1))
0.0b
(/ 1 (+ x 1))

rewrite330.0ms

Algorithm
rewrite-expression-head
Rules
743×*-un-lft-identity
715×times-frac
544×add-sqr-sqrt
494×add-cube-cbrt
468×prod-diff
236×associate-+l+
99×distribute-lft-out
72×div-inv
58×associate-/r/
29×flip3-+ flip-+
22×distribute-lft-out--
20×difference-of-squares
18×fma-neg
13×fma-def
12×add-exp-log
11×associate-/r* add-log-exp
8×add-cbrt-cube
6×pow1 associate-/l*
4×expm1-log1p-u difference-of-sqr-1 div-exp insert-posit16 log1p-expm1-u
3×flip3-- frac-add flip--
2×cbrt-undiv rec-exp clear-num sum-log sub-neg frac-2neg diff-log 1-exp frac-sub pow-flip inv-pow
1×+-commutative associate-+l-
Counts
4 → 648
Calls
4 calls:
Slowest
213.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
66.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
8.0ms
(/ 1 (- x 1))
8.0ms
(/ 1 (+ x 1))

series186.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
102.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
32.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
26.0ms
(/ 1 (- x 1))
24.0ms
(/ 1 (+ x 1))

simplify2.0m

Counts
879 → 660
Calls
879 calls:
Slowest
588.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
570.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
528.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (- x 1)) (* (+ (/ 1 (+ x 1)) (/ 2 x)) 1))
522.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
515.0ms
(fma (* (cbrt (/ 1 (+ x 1))) (cbrt (/ 1 (+ x 1)))) (cbrt (/ 1 (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

60.7b
(fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))
2.4b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (/ 1 (- x 1))))
0.6b
(cbrt (/ 2 x))
0.6b
(cbrt (/ 2 x))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
365×*-un-lft-identity
347×times-frac
266×add-sqr-sqrt
249×add-cube-cbrt
236×associate-+l+
234×prod-diff
55×distribute-lft-out
40×div-inv
26×cbrt-prod associate-/r/
17×flip3-+ flip-+
16×add-log-exp
13×fma-def
10×distribute-lft-out--
6×sum-log frac-add difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×cbrt-div flip3-- pow1/3 diff-log frac-sub flip--
1×+-commutative associate-+r+ sub-neg associate-+l- fma-udef
Counts
4 → 344
Calls
4 calls:
Slowest
156.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (/ 1 (- x 1))))
1.0ms
(cbrt (/ 2 x))
1.0ms
(cbrt (/ 2 x))
0.0ms
(fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
752.0ms
(fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))
248.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (/ 1 (- x 1))))
216.0ms
(cbrt (/ 2 x))
208.0ms
(cbrt (/ 2 x))

simplify37.7s

Counts
313 → 356
Calls
313 calls:
Slowest
539.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (+ (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (/ 1 (- x 1)))))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (+ (pow (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) 3) (pow (/ 1 (- x 1)) 3))))
504.0ms
(fma (/ 1 (+ (pow x 3) (pow 1 3))) (+ (* x x) (- (* 1 1) (* x 1))) (- (* (/ 1 x) 2)))
457.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt 1) (cbrt (+ x 1))) (- (* (/ (cbrt 2) (sqrt x)) (/ (* (cbrt 2) (cbrt 2)) (sqrt x)))))
339.0ms
(+ (* (- (* 1 x) (* (+ x 1) 2)) (+ (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (/ 1 (- x 1)))))) (* (* (+ x 1) x) (+ (pow (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) 3) (pow (/ 1 (- x 1)) 3))))
331.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

30.7b
(fma (- x (fma x 2 2)) (- x 1) (fma x x x))
0.1b
(* (fma x x -1) x)
0.0b
(- x (fma x 2 2))
0.0b
(/ (fma (- x (fma x 2 2)) (- x 1) (fma x x x)) (* (fma x x -1) x))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
11×add-cbrt-cube add-exp-log
9×prod-diff
6×pow1 add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×times-frac fma-neg associate-*r* associate-*l* associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod fma-udef
1×clear-num associate-/r* sub-neg frac-2neg flip3-- diff-log pow-prod-down *-commutative div-inv flip-- associate--r+ distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 86
Calls
4 calls:
Slowest
6.0ms
(/ (fma (- x (fma x 2 2)) (- x 1) (fma x x x)) (* (fma x x -1) x))
5.0ms
(* (fma x x -1) x)
5.0ms
(- x (fma x 2 2))
0.0ms
(fma (- x (fma x 2 2)) (- x 1) (fma x x x))

series572.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
255.0ms
(/ (fma (- x (fma x 2 2)) (- x 1) (fma x x x)) (* (fma x x -1) x))
181.0ms
(fma (- x (fma x 2 2)) (- x 1) (fma x x x))
78.0ms
(* (fma x x -1) x)
57.0ms
(- x (fma x 2 2))

simplify5.7s

Counts
57 → 98
Calls
57 calls:
Slowest
431.0ms
(/ (cbrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x))) x)
430.0ms
(/ (sqrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x))) x)
422.0ms
(* (cbrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x))) (cbrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x))))
402.0ms
(/ (fma (- x (fma x 2 2)) (- x 1) (fma x x x)) x)
396.0ms
(sqrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x)))

prune695.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ 2 (* (fma x x -1) x))
0.1b
(* (fma x x -1) x)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
4×pow1
3×times-frac associate-*r* associate-*l* associate-/l*
2×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
1×clear-num associate-/r* frac-2neg pow-prod-down *-commutative div-inv unswap-sqr
Counts
2 → 45
Calls
2 calls:
Slowest
9.0ms
(* (fma x x -1) x)
6.0ms
(/ 2 (* (fma x x -1) x))

series129.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
81.0ms
(* (fma x x -1) x)
47.0ms
(/ 2 (* (fma x x -1) x))

simplify1.5s

Counts
27 → 51
Calls
27 calls:
Slowest
276.0ms
(* (* (* (fma x x -1) (fma x x -1)) (fma x x -1)) (* (* x x) x))
164.0ms
(- (+ (* 2 x) (+ (* 2 (pow x 3)) (* 2 (/ 1 x)))))
145.0ms
(- (log 2) (log (* (fma x x -1) x)))
142.0ms
(+ (* 2 (/ 1 (pow x 7))) (+ (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (pow x 5)))))
142.0ms
(+ (* 2 (/ 1 (pow x 7))) (+ (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (pow x 5)))))

prune251.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes26.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
838.0ms1826×body640valid
370.0ms4127×body80valid
241.0ms987×body320valid
236.0ms598×body1280valid
82.0ms462×body160valid