Details

sample52.0ms

Algorithm

intervals

Results

17.0ms	49×	body	640	valid
12.0ms	145×	body	80	valid
12.0ms	47×	body	320	valid
3.0ms	15×	body	160	valid

simplify18.0ms

Calls

1 calls:

Slowest

17.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
90×	`frac-sub`
77×	`add-sqr-sqrt`
70×	`associate-/r*`
60×	`associate-/l*`
53×	`add-cube-cbrt`
36×	`times-frac`
20×	`clear-num` `frac-2neg`
16×	`distribute-lft-out`
10×	`distribute-lft-out--`
9×	`difference-of-squares`
6×	`add-exp-log`
5×	`div-inv`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1`
2×	`div-exp` `associate-/r/` `insert-posit16`
1×	`cbrt-undiv` `rec-exp` `sub-neg` `flip3-+` `flip3--` `diff-log` `1-exp` `flip-+` `pow-flip` `flip--` `inv-pow`

Calls

2 calls:

Slowest

50.0ms	(- (/ 1 (+ x 1)) (/ 1 x))
16.0ms	(/ 1 (+ x 1))

series56.0ms

Calls

2 calls:

Slowest

33.0ms	(- (/ 1 (+ x 1)) (/ 1 x))
23.0ms	(/ 1 (+ x 1))

simplify20.7s

Calls

257 calls:

Slowest

629.0ms	(- (* (- 1) (cbrt x)) (* (- (+ x 1)) (/ 1 (* (cbrt x) (cbrt x)))))
618.0ms	(- (* (/ 1 (sqrt (+ x 1))) (- x)) (* (sqrt (+ x 1)) (- 1)))
536.0ms	(/ (* (* 1 1) 1) (* (* (+ x 1) (+ x 1)) (+ x 1)))
484.0ms	(- (* (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt x)) (* (cbrt (+ x 1)) (/ 1 (* (cbrt x) (cbrt x)))))
405.0ms	(- (* (/ 1 (sqrt (+ x 1))) (cbrt x)) (* (sqrt (+ x 1)) (/ 1 (* (cbrt x) (cbrt x)))))

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ -1 (+ x (* x x)))
0.0b	(+ x (* x x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`distribute-rgt-out`
20×	`associate-r` `distribute-lft-out`
15×	`associate-/r` `associate-l*` `distribute-rgt1-in`
10×	`*-commutative`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+` `insert-posit16`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Calls

2 calls:

Slowest

18.0ms	(/ -1 (+ x (* x x)))
9.0ms	(+ x (* x x))

series100.0ms

Calls

2 calls:

Slowest

67.0ms	(+ x (* x x))
33.0ms	(/ -1 (+ x (* x x)))

simplify3.7s

Calls

128 calls:

Slowest

312.0ms	(- (/ 1 (pow x 3)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 2))))
295.0ms	(- (/ 1 (pow x 3)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 2))))
284.0ms	(+ (* x x) (- (* (* x x) (* x x)) (* x (* x x))))
179.0ms	(/ (* (* -1 -1) -1) (* (* (+ x (* x x)) (+ x (* x x))) (+ x (* x x))))
108.0ms	(* (exp x) (exp (* x x)))

prune704.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
80×	`*-un-lft-identity`
52×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`associate-/l*`
14×	`distribute-lft-out`
9×	`associate-/l/`
7×	`associate-/r*`
6×	`add-cbrt-cube` `add-exp-log` `div-inv`
3×	`cbrt-undiv` `div-exp`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`pow1` `flip3-+` `flip-+` `insert-posit16` `add-log-exp`

Calls

1 calls:

Slowest

20.0ms

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

series19.0ms

Calls

1 calls:

Slowest

19.0ms

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

simplify6.3s

Calls

134 calls:

Slowest

847.0ms	(/ (* (* (/ -1 x) (/ -1 x)) (/ -1 x)) (* (* (+ x 1) (+ x 1)) (+ x 1)))
416.0ms	(/ (/ (* (cbrt -1) (cbrt -1)) (* (cbrt x) (cbrt x))) (* (cbrt (+ x 1)) (cbrt (+ x 1))))
287.0ms	(- (/ 1 (pow x 3)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 2))))
243.0ms	(- (/ 1 (pow x 3)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 2))))
217.0ms	(/ (/ (* (cbrt -1) (cbrt -1)) (sqrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1))))

prune688.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

29.6b	(cbrt (/ (/ -1 (* x x)) (* (+ x 1) (* x (* (+ x 1) (+ x 1))))))
0.4b	(/ -1 (* x x))
0.1b	(/ (/ -1 (* x x)) (* (+ x 1) (* x (* (+ x 1) (+ x 1)))))
0.1b	(* x (* (+ x 1) (+ x 1)))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

9159×	`times-frac`
7509×	`add-sqr-sqrt`
6624×	`associate-r`
5611×	`*-un-lft-identity`
3997×	`add-cube-cbrt`
2382×	`cbrt-prod`
2207×	`unswap-sqr`
2007×	`associate-l`
1707×	`swap-sqr`
803×	`*-commutative`
706×	`distribute-lft-out`
141×	`associate-/r*`
121×	`cbrt-div`
107×	`associate-/l*`
101×	`div-inv`
86×	`associate-*r/`
68×	`add-cbrt-cube` `add-exp-log`
60×	`frac-times` `flip3-+` `flip-+`
52×	`associate-/r/`
42×	`associate-/l/`
26×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
9×	`pow1`
8×	`distribute-rgt-in` `distribute-lft-in`
5×	`clear-num` `frac-2neg`
4×	`+-commutative` `insert-posit16` `add-log-exp`
3×	`pow-prod-down`
1×	`pow1/3`

Calls

4 calls:

Slowest

1.1s	(cbrt (/ (/ -1 (* x x)) (* (+ x 1) (* x (* (+ x 1) (+ x 1))))))
703.0ms	(/ (/ -1 (* x x)) (* (+ x 1) (* x (* (+ x 1) (+ x 1)))))
97.0ms	(* x (* (+ x 1) (+ x 1)))
9.0ms	(/ -1 (* x x))

series198.0ms

Calls

4 calls:

Slowest

64.0ms	(cbrt (/ (/ -1 (* x x)) (* (+ x 1) (* x (* (+ x 1) (+ x 1))))))
58.0ms	(/ -1 (* x x))
53.0ms	(/ (/ -1 (* x x)) (* (+ x 1) (* x (* (+ x 1) (+ x 1)))))
22.0ms	(* x (* (+ x 1) (+ x 1)))