Details

Time bar (total: 1.1m)

sample79.0ms

Algorithm
intervals
Results
29.0ms55×body1280valid
16.0ms39×body640valid
14.0ms129×body80valid
7.0ms23×body320valid
2.0ms10×body160valid

simplify362.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize12.0ms

Local error

Found 3 expressions with local error:

3.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite163.0ms

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
82.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
34.0ms
(/ (+ x 1) (- x 1))
10.0ms
(/ x (+ x 1))

series197.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
121.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
40.0ms
(/ (+ x 1) (- x 1))
37.0ms
(/ x (+ x 1))

simplify1.0s

Counts
762 → 762

prune8.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

3.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
3.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
3.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.1b
(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))

rewrite641.0ms

Algorithm
rewrite-expression-head
Rules
3664×*-un-lft-identity
2832×times-frac
2392×add-sqr-sqrt
1836×prod-diff
1492×add-cube-cbrt
717×distribute-lft-out
444×difference-of-squares
318×associate-/r/
255×distribute-lft-out--
216×difference-of-sqr-1
159×div-inv
105×flip3-+ flip3-- flip-+ flip--
81×frac-times
63×cbrt-div
54×fma-neg
51×frac-sub
27×associate-*l/
15×associate-*r/
10×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×sub-neg diff-log
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 2053
Calls
4 calls:
Slowest
354.0ms
(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
79.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
57.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
54.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
95.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
91.0ms
(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
85.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.4s

Counts
2065 → 2065

prune28.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize131.0ms

Local error

Found 4 expressions with local error:

3.6b
(- (/ x (+ 1 x)) (/ (+ 1 x) (+ x -1)))
3.5b
(- (* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (/ x (+ 1 x))) (* (* (/ (+ 1 x) (+ x -1)) (/ (+ 1 x) (+ x -1))) (/ (+ 1 x) (+ x -1))))
3.5b
(- (* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (/ x (+ 1 x))) (* (* (/ (+ 1 x) (+ x -1)) (/ (+ 1 x) (+ x -1))) (/ (+ 1 x) (+ x -1))))
0.5b
(cbrt (* (fma (/ x (+ 1 x)) (/ x (+ 1 x)) (* (/ (+ 1 x) (+ x -1)) (+ (/ (+ 1 x) (+ x -1)) (/ x (+ 1 x))))) (* (+ (/ x (+ 1 x)) (/ (+ 1 x) (+ x -1))) (fma (/ x (+ 1 x)) (/ x (+ 1 x)) (* (/ (+ 1 x) (+ x -1)) (+ (/ (+ 1 x) (+ x -1)) (/ x (+ 1 x))))))))

rewrite532.0ms

Algorithm
rewrite-expression-head
Rules
932×*-un-lft-identity
704×times-frac
484×add-sqr-sqrt
470×prod-diff
400×add-cube-cbrt
255×distribute-lft-out
143×associate-*l/
140×frac-times
99×frac-sub
90×associate-/r/
87×associate-*r/
72×difference-of-sqr--1
46×flip3-+ flip-+
45×div-inv
20×fma-neg
10×add-log-exp
9×distribute-lft-out--
4×expm1-log1p-u pow1 add-cbrt-cube pow3 add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
3×cbrt-div sub-neg flip3-- diff-log flip--
2×difference-cubes
1×cbrt-prod pow1/3 frac-add
Counts
4 → 664
Calls
4 calls:
Slowest
146.0ms
(- (* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (/ x (+ 1 x))) (* (* (/ (+ 1 x) (+ x -1)) (/ (+ 1 x) (+ x -1))) (/ (+ 1 x) (+ x -1))))
132.0ms
(- (* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (/ x (+ 1 x))) (* (* (/ (+ 1 x) (+ x -1)) (/ (+ 1 x) (+ x -1))) (/ (+ 1 x) (+ x -1))))
129.0ms
(cbrt (* (fma (/ x (+ 1 x)) (/ x (+ 1 x)) (* (/ (+ 1 x) (+ x -1)) (+ (/ (+ 1 x) (+ x -1)) (/ x (+ 1 x))))) (* (+ (/ x (+ 1 x)) (/ (+ 1 x) (+ x -1))) (fma (/ x (+ 1 x)) (/ x (+ 1 x)) (* (/ (+ 1 x) (+ x -1)) (+ (/ (+ 1 x) (+ x -1)) (/ x (+ 1 x))))))))
82.0ms
(- (/ x (+ 1 x)) (/ (+ 1 x) (+ x -1)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
390.0ms
(cbrt (* (fma (/ x (+ 1 x)) (/ x (+ 1 x)) (* (/ (+ 1 x) (+ x -1)) (+ (/ (+ 1 x) (+ x -1)) (/ x (+ 1 x))))) (* (+ (/ x (+ 1 x)) (/ (+ 1 x) (+ x -1))) (fma (/ x (+ 1 x)) (/ x (+ 1 x)) (* (/ (+ 1 x) (+ x -1)) (+ (/ (+ 1 x) (+ x -1)) (/ x (+ 1 x))))))))
278.0ms
(- (* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (/ x (+ 1 x))) (* (* (/ (+ 1 x) (+ x -1)) (/ (+ 1 x) (+ x -1))) (/ (+ 1 x) (+ x -1))))
259.0ms
(- (* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (/ x (+ 1 x))) (* (* (/ (+ 1 x) (+ x -1)) (/ (+ 1 x) (+ x -1))) (/ (+ 1 x) (+ x -1))))
109.0ms
(- (/ x (+ 1 x)) (/ (+ 1 x) (+ x -1)))

simplify1.8s

Counts
676 → 676

prune15.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

7.5b
(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))
0.4b
(/ 1 (* x x))
0.1b
(/ 3 (* x (* x x)))
0.0b
(* x (* x x))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
26×pow1
23×*-un-lft-identity add-cbrt-cube
11×add-sqr-sqrt
10×add-cube-cbrt
9×times-frac prod-exp add-log-exp
8×distribute-lft-out
7×div-exp cbrt-unprod
6×fma-def pow-prod-up div-inv pow-flip associate-/l*
5×cbrt-undiv
4×expm1-log1p-u pow-prod-down frac-add insert-posit16 log1p-expm1-u
3×sum-log associate-*l*
2×pow2 rec-exp clear-num associate-/r* frac-2neg flip3-+ pow-plus distribute-rgt-out 1-exp pow-sqr flip-+
1×+-commutative associate-+l+ cube-unmult associate-*r* *-commutative inv-pow unswap-sqr
Counts
4 → 117
Calls
4 calls:
Slowest
178.0ms
(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))
14.0ms
(* x (* x x))
12.0ms
(/ 3 (* x (* x x)))
9.0ms
(/ 1 (* x x))

series161.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
53.0ms
(* x (* x x))
52.0ms
(/ 3 (* x (* x x)))
34.0ms
(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))
22.0ms
(/ 1 (* x x))

simplify2.5s

Counts
129 → 129

prune954.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch172.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
787.0ms1699×body1280valid
497.0ms1260×body640valid
438.0ms4121×body80valid
148.0ms635×body320valid
85.0ms285×body160valid