Details

Time bar (total: 3.6m)

sample68.0ms

Algorithm
intervals
Results
19.0ms53×body640valid
14.0ms139×body80valid
12.0ms26×body1280valid
7.0ms25×body320valid
3.0ms13×body160valid

simplify93.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
93.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize24.0ms

Local error

Found 3 expressions with local error:

1.4b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))
0.0b
(/ 1 (+ x 1))

rewrite300.0ms

Algorithm
rewrite-expression-head
Rules
718×*-un-lft-identity
694×times-frac
515×add-sqr-sqrt
481×add-cube-cbrt
468×prod-diff
236×associate-+l+
99×distribute-lft-out
71×div-inv
56×associate-/r/
29×flip3-+ flip-+
18×fma-neg distribute-lft-out--
13×fma-def
12×difference-of-squares
10×add-log-exp
7×add-exp-log
5×add-cbrt-cube
4×pow1 associate-/r*
3×expm1-log1p-u frac-add insert-posit16 log1p-expm1-u associate-/l*
2×sum-log sub-neg flip3-- diff-log div-exp frac-sub flip--
1×cbrt-undiv +-commutative rec-exp clear-num frac-2neg 1-exp associate-+l- pow-flip inv-pow
Counts
3 → 596
Calls
3 calls:
Slowest
203.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
72.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
8.0ms
(/ 1 (+ x 1))

series204.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
139.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
43.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
22.0ms
(/ 1 (+ x 1))

simplify2.0m

Counts
819 → 605
Calls
819 calls:
Slowest
852.0ms
(fma (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
652.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (+ x 1)) (- (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))))
599.0ms
(fma (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
542.0ms
(fma 1 (/ 1 (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
532.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ 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

localize47.0ms

Local error

Found 4 expressions with local error:

60.5b
(fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x)))))
1.4b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
353×*-un-lft-identity
329×times-frac
254×add-sqr-sqrt
237×add-cube-cbrt
236×associate-+l+
234×prod-diff
55×distribute-lft-out
38×div-inv
26×associate-/r/
17×flip3-+ flip-+
16×add-log-exp
13×fma-def
10×distribute-lft-out--
6×cbrt-prod sum-log frac-add difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×flip3-- pow1/3 diff-log frac-sub flip--
1×+-commutative associate-+r+ sub-neg associate-+l- fma-udef
Counts
4 → 322
Calls
4 calls:
Slowest
155.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
0.0ms
(fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
788.0ms
(fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x)))))
248.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
189.0ms
(cbrt x)
184.0ms
(cbrt x)

simplify37.0s

Counts
291 → 334
Calls
291 calls:
Slowest
613.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (+ (* (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (+ (pow (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) 3) (pow (/ 1 (- x 1)) 3))))
444.0ms
(+ (* (- (* 1 x) (* (+ x 1) 2)) (+ (* (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))) (* (* (+ x 1) x) (+ (pow (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) 3) (pow (/ 1 (- x 1)) 3))))
438.0ms
(fma (/ (sqrt 1) (sqrt (+ x 1))) (/ (sqrt 1) (sqrt (+ x 1))) (- (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))))
374.0ms
(* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (+ (* (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))))
336.0ms
(+ (* (- (pow (/ 1 (+ x 1)) 3) (pow (/ 2 x) 3)) (- (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))) (* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (- (* (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x)))))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))))

prune3.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

60.5b
(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
1.4b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
353×*-un-lft-identity
329×times-frac
254×add-sqr-sqrt
237×add-cube-cbrt
236×associate-+l+
234×prod-diff
55×distribute-lft-out
38×div-inv
26×associate-/r/
17×flip3-+ flip-+
16×add-log-exp
13×fma-def
10×distribute-lft-out--
6×cbrt-prod sum-log frac-add difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×flip3-- pow1/3 diff-log frac-sub flip--
1×+-commutative associate-+r+ sub-neg associate-+l- fma-udef
Counts
4 → 322
Calls
4 calls:
Slowest
152.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
1.0ms
(cbrt x)
1.0ms
(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
1.0ms
(cbrt x)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
675.0ms
(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
209.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
195.0ms
(cbrt x)
193.0ms
(cbrt x)

simplify37.6s

Counts
291 → 334
Calls
291 calls:
Slowest
579.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (+ (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (+ (pow (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) 3) (pow (/ 1 (- x 1)) 3))))
447.0ms
(+ (* (- (* 1 x) (* (+ x 1) 2)) (+ (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))) (* (* (+ x 1) x) (+ (pow (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) 3) (pow (/ 1 (- x 1)) 3))))
361.0ms
(* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (+ (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))))
360.0ms
(+ (* (- (pow (/ 1 (+ x 1)) 3) (pow (/ 2 x) 3)) (- (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))) (* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (- (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))))
329.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

29.2b
(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))

rewrite20.0ms

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
8.0ms
(* (fma x x -1) x)
6.0ms
(/ (fma (- x (fma x 2 2)) (- x 1) (fma x x x)) (* (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))

series545.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
247.0ms
(/ (fma (- x (fma x 2 2)) (- x 1) (fma x x x)) (* (fma x x -1) x))
171.0ms
(fma (- x (fma x 2 2)) (- x 1) (fma x x x))
74.0ms
(* (fma x x -1) x)
52.0ms
(- x (fma x 2 2))

simplify5.3s

Counts
57 → 98
Calls
57 calls:
Slowest
409.0ms
(/ (cbrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x))) x)
407.0ms
(/ (sqrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x))) x)
401.0ms
(* (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))))
379.0ms
(/ (fma (- x (fma x 2 2)) (- x 1) (fma x x x)) x)
375.0ms
(sqrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x)))

prune657.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes18.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
847.0ms1882×body640valid
364.0ms4089×body80valid
219.0ms591×body1280valid
213.0ms960×body320valid
92.0ms480×body160valid