Details

sample86.0ms

Algorithm

intervals

Results

47.0ms	136×	body	80	valid
14.0ms	50×	body	1280	valid
11.0ms	45×	body	640	valid
3.0ms	17×	body	320	valid
1.0ms	8×	body	160	valid

simplify67.0ms

Calls

1 calls:

Slowest

67.0ms

(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite188.0ms

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`

Calls

3 calls:

Slowest

113.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
20.0ms	(/ (+ x 1) (- x 1))
9.0ms	(/ x (+ x 1))

series182.0ms

Calls

3 calls:

Slowest

103.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
42.0ms	(/ x (+ x 1))
37.0ms	(/ (+ x 1) (- x 1))

simplify5.0m

Calls

1382 calls:

Slowest

773.0ms	(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
756.0ms	(fma (- (/ (+ x 1) (cbrt (- x 1)))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1))))))
746.0ms	(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
731.0ms	(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
730.0ms	(fma (- (/ (cbrt (+ x 1)) (cbrt (- x 1)))) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (/ (cbrt (+ x 1)) (cbrt (- x 1))) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (- x 1)) (cbrt (- x 1))))))

prune4.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

19.8b	(- (/ x (+ x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (- x 1) (cbrt (+ x 1)))))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

2618×	`times-frac`
1913×	`*-un-lft-identity`
1437×	`add-sqr-sqrt`
1080×	`prod-diff`
909×	`add-cube-cbrt`
518×	`cbrt-prod`
312×	`distribute-lft-out`
260×	`difference-of-squares`
176×	`associate-/r/`
127×	`distribute-lft-out--`
126×	`difference-of-sqr-1`
97×	`div-inv`
82×	`flip3-+` `flip-+`
42×	`cbrt-div`
18×	`fma-neg`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Calls

4 calls:

Slowest

58.0ms	(- (/ x (+ x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (- x 1) (cbrt (+ x 1)))))
2.0ms	(cbrt (+ x 1))
2.0ms	(cbrt (+ x 1))
2.0ms	(cbrt (+ x 1))

series191.0ms

Calls

4 calls:

Slowest

83.0ms	(- (/ x (+ x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (- x 1) (cbrt (+ x 1)))))
38.0ms	(cbrt (+ x 1))
37.0ms	(cbrt (+ x 1))
33.0ms	(cbrt (+ x 1))