Details

sample263.0ms

Algorithm

intervals

Results

117.0ms	251×	body	10240	exit
86.0ms	103×	body	1280	valid
33.0ms	73×	body	640	valid
11.0ms	42×	body	320	valid
3.0ms	19×	body	160	valid
2.0ms	19×	body	80	valid

simplify74.0ms

Calls

1 calls:

Slowest

74.0ms

(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.7b

localize31.0ms

Local error

Found 3 expressions with local error:

5.1b	(- (exp x) (exp (- x)))
2.2b	(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
0.0b	(+ (exp x) (exp (- x)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
20×	`times-frac`
14×	`add-cube-cbrt`
7×	`distribute-lft-out` `add-log-exp`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
4×	`associate-/r*`
3×	`pow1` `insert-posit16`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `tanh-undef` `div-inv`

Calls

3 calls:

Slowest

72.0ms	(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
20.0ms	(- (exp x) (exp (- x)))
9.0ms	(+ (exp x) (exp (- x)))

series193.0ms

Calls

3 calls:

Slowest

105.0ms	(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
53.0ms	(- (exp x) (exp (- x)))
35.0ms	(+ (exp x) (exp (- x)))

simplify4.3s

Calls

69 calls:

Slowest

404.0ms	(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
357.0ms	(- (pow (exp x) 3) (pow (exp (- x)) 3))
278.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
255.0ms	(+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))
255.0ms	(/ (- (exp x) (exp (* -1 x))) (+ (exp (* -1 x)) (exp x)))

prune631.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b

(tanh x)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `tanh-def` `add-log-exp`

Calls

1 calls:

Slowest

2.0ms

(tanh x)

series121.0ms

Calls

1 calls:

Slowest

121.0ms

(tanh x)

simplify717.0ms

Calls

3 calls:

Slowest

363.0ms	(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
255.0ms	(/ (- (exp x) (exp (* -1 x))) (+ (exp (* -1 x)) (exp x)))
98.0ms	(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))

prune144.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) -1/3)
0.1b	(* (pow x 5) 2/15)
0.1b	(* (* (* x x) -1/3) x)
0.0b	(+ (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

88×	`associate-l`
67×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
29×	`unswap-sqr`
23×	`add-exp-log`
21×	`add-cube-cbrt`
20×	`pow1` `add-cbrt-cube`
18×	`associate-r` `distribute-lft-out`
12×	`prod-exp`
10×	`pow-prod-down` `cbrt-unprod`
9×	`swap-sqr` `*-commutative` `add-log-exp`
4×	`unpow-prod-down` `insert-posit16`
3×	`sum-log`
2×	`+-commutative` `associate-+l+` `sqr-pow`
1×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+`

Calls

4 calls:

Slowest

1.1s	(+ (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15))
95.0ms	(* (* (* x x) -1/3) x)
28.0ms	(* (* x x) -1/3)
10.0ms	(* (pow x 5) 2/15)

series256.0ms

Calls

4 calls:

Slowest

103.0ms	(+ (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15))
64.0ms	(* (pow x 5) 2/15)
52.0ms	(* (* (* x x) -1/3) x)
36.0ms	(* (* x x) -1/3)

simplify11.0s

Calls

118 calls:

Slowest

680.0ms	(* (* (* (* (* x x) -1/3) (* (* x x) -1/3)) (* (* x x) -1/3)) (* (* x x) x))
656.0ms	(+ (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15))
638.0ms	(+ (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15))
627.0ms	(+ (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15))
575.0ms	(+ (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15))

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

39.4b	(/ (+ (pow (+ (* (* (* x x) -1/3) x) x) 3) (pow (* (pow x 5) 2/15) 3)) (+ (* (+ (* (* (* x x) -1/3) x) x) (+ (* (* (* x x) -1/3) x) x)) (- (* (* (pow x 5) 2/15) (* (pow x 5) 2/15)) (* (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15)))))
0.2b	(* (* x x) -1/3)
0.2b	(* (* x x) -1/3)
0.2b	(* (* x x) -1/3)

rewrite25.2s

Algorithm

rewrite-expression-head

Rules

37829×	`*-un-lft-identity`
33313×	`associate-l`
21452×	`distribute-lft-out`
5616×	`times-frac`
5292×	`distribute-lft-out--`
4720×	`unpow-prod-down` `cube-prod`
472×	`pow-unpow` `sum-cubes`
225×	`add-sqr-sqrt`
189×	`add-cube-cbrt`
117×	`associate-/r*`
48×	`associate-/l*`
21×	`add-cbrt-cube` `add-exp-log` `unswap-sqr`
19×	`pow1`
18×	`associate-r` `associate-/r/`
16×	`frac-add`
14×	`flip3-+` `flip-+`
12×	`swap-sqr`
9×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
8×	`frac-times` `flip3--` `flip--`
4×	`associate-l/` `associate-r/` `insert-posit16` `add-log-exp`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Calls

4 calls:

Slowest

24.1s	(/ (+ (pow (+ (* (* (* x x) -1/3) x) x) 3) (pow (* (pow x 5) 2/15) 3)) (+ (* (+ (* (* (* x x) -1/3) x) x) (+ (* (* (* x x) -1/3) x) x)) (- (* (* (pow x 5) 2/15) (* (pow x 5) 2/15)) (* (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15)))))
38.0ms	(* (* x x) -1/3)
37.0ms	(* (* x x) -1/3)
27.0ms	(* (* x x) -1/3)

series402.0ms

Calls

4 calls:

Slowest

296.0ms	(/ (+ (pow (+ (* (* (* x x) -1/3) x) x) 3) (pow (* (pow x 5) 2/15) 3)) (+ (* (+ (* (* (* x x) -1/3) x) x) (+ (* (* (* x x) -1/3) x) x)) (- (* (* (pow x 5) 2/15) (* (pow x 5) 2/15)) (* (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15)))))
42.0ms	(* (* x x) -1/3)
35.0ms	(* (* x x) -1/3)
28.0ms	(* (* x x) -1/3)