Details

sample201.0ms

Algorithm

halfpoints

Results

simplify184.0ms

Calls

1 calls:

Slowest

184.0ms

(re (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (cos y) (exp x) (/ (cos y) (exp x)))
0.0b	(/ (cos y) (exp x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-exp-log`
4×	`add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `fma-udef` `div-inv`

Calls

2 calls:

Slowest

14.0ms	(/ (cos y) (exp x))
0.0ms	(fma (cos y) (exp x) (/ (cos y) (exp x)))

series170.0ms

Calls

2 calls:

Slowest

112.0ms	(fma (cos y) (exp x) (/ (cos y) (exp x)))
58.0ms	(/ (cos y) (exp x))

simplify1.3s

Calls

32 calls:

Slowest

791.0ms	(/ (* (* (cos y) (cos y)) (cos y)) (* (* (exp x) (exp x)) (exp x)))
116.0ms	(- 1 (+ (* 1/2 (pow y 2)) x))
51.0ms	(- (+ (pow x 2) 2) (pow y 2))
37.0ms	(/ (* (cbrt (cos y)) (cbrt (cos y))) (* (cbrt (exp x)) (cbrt (exp x))))
30.0ms	(/ (* (cbrt (cos y)) (cbrt (cos y))) (sqrt (exp x)))

prune565.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (cos y) (exp x))
0.0b	(+ (* (cos y) (exp x)) (/ (cos y) (exp x)))
0.0b	(/ (cos y) (exp x))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`fma-def`
9×	`times-frac` `add-exp-log`
7×	`add-cbrt-cube` `associate-l`
6×	`associate-r`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `associate-/r` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `associate-/l`
2×	`div-exp` `prod-exp` `*-commutative` `div-inv` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `pow-prod-down` `cbrt-unprod` `flip-+`

Calls

3 calls:

Slowest

70.0ms	(+ (* (cos y) (exp x)) (/ (cos y) (exp x)))
22.0ms	(* (cos y) (exp x))
17.0ms	(/ (cos y) (exp x))

series166.0ms

Calls

3 calls:

Slowest

77.0ms	(+ (* (cos y) (exp x)) (/ (cos y) (exp x)))
49.0ms	(/ (cos y) (exp x))
40.0ms	(* (cos y) (exp x))

simplify1.6s

Calls

61 calls:

Slowest

376.0ms	(/ (* (* (cos y) (cos y)) (cos y)) (* (* (exp x) (exp x)) (exp x)))
292.0ms	(* (* (* (cos y) (cos y)) (cos y)) (* (* (exp x) (exp x)) (exp x)))
230.0ms	(* (exp (* (cos y) (exp x))) (exp (/ (cos y) (exp x))))
141.0ms	(- 1 (+ (* 1/2 (pow y 2)) x))
67.0ms	(- (+ x 1) (* 1/2 (pow y 2)))

prune867.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (exp x))
0.0b	(+ (exp x) (/ 1 (exp x)))
0.0b	(* (cos y) (+ (exp x) (/ 1 (exp x))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
10×	`add-exp-log`
9×	`times-frac`
7×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-r` `add-log-exp`
4×	`div-exp` `pow-flip` `distribute-lft-out`
3×	`expm1-log1p-u` `+-commutative` `exp-prod` `associate-/r` `fma-def` `associate-l` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `flip3-+` `1-exp` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`

Calls

3 calls:

Slowest

67.0ms	(* (cos y) (+ (exp x) (/ 1 (exp x))))
11.0ms	(+ (exp x) (/ 1 (exp x)))
10.0ms	(/ 1 (exp x))

series121.0ms

Calls

3 calls:

Slowest

76.0ms	(* (cos y) (+ (exp x) (/ 1 (exp x))))
33.0ms	(+ (exp x) (/ 1 (exp x)))
12.0ms	(/ 1 (exp x))

simplify1.6s

Calls

64 calls:

Slowest

198.0ms	(* (* (* (cos y) (cos y)) (cos y)) (* (* (+ (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x)))) (+ (exp x) (/ 1 (exp x)))))
194.0ms	(+ (* (exp x) (exp x)) (- (* (/ 1 (exp x)) (/ 1 (exp x))) (* (exp x) (/ 1 (exp x)))))
119.0ms	(/ (* (* 1 1) 1) (* (* (exp x) (exp x)) (exp x)))
83.0ms	(* (+ (exp x) (/ 1 (exp x))) (cos y))
80.0ms	(- (+ (* 1/2 (pow x 2)) 1) x)

prune970.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

17.2b	(- (* (/ 1 (exp x)) (/ 1 (exp x))) (* (exp x) (/ 1 (exp x))))
0.1b	(pow (exp x) 3)
0.0b	(pow (/ 1 (exp x)) 3)
0.0b	(* (exp x) (exp x))

rewrite472.0ms

Algorithm

rewrite-expression-head

Rules

3201×	`add-sqr-sqrt`
2436×	`*-un-lft-identity`
1962×	`add-cube-cbrt`
1942×	`times-frac`
1320×	`prod-diff`
1224×	`frac-sub`
1175×	`associate-/l*`
1090×	`associate-r`
1077×	`associate-*r/`
1048×	`associate-/r*`
972×	`frac-times`
500×	`associate-l`
481×	`clear-num`
472×	`unswap-sqr`
390×	`swap-sqr`
370×	`un-div-inv`
347×	`frac-2neg`
218×	`div-inv`
127×	`associate-*l/`
92×	`*-commutative`
60×	`difference-of-squares`
55×	`fma-neg`
49×	`sub-div`
30×	`distribute-rgt-out--`
24×	`exp-prod`
16×	`unpow-prod-down` `cube-prod`
15×	`add-exp-log`
14×	`pow1`
10×	`pow-pow` `add-cbrt-cube`
9×	`cube-div` `pow-exp`
8×	`distribute-lft-out--`
6×	`pow-unpow` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `pow-flip`
3×	`rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `rec-exp` `1-exp` `unpow3` `sqr-pow`
1×	`pow2` `cbrt-undiv` `sub-neg` `pow-plus` `flip3--` `diff-log` `cbrt-unprod` `flip--` `inv-pow`

Calls

4 calls:

Slowest

262.0ms	(- (* (/ 1 (exp x)) (/ 1 (exp x))) (* (exp x) (/ 1 (exp x))))
13.0ms	(* (exp x) (exp x))
7.0ms	(pow (/ 1 (exp x)) 3)
6.0ms	(pow (exp x) 3)

series163.0ms

Calls

4 calls:

Slowest

52.0ms	(- (* (/ 1 (exp x)) (/ 1 (exp x))) (* (exp x) (/ 1 (exp x))))
49.0ms	(pow (/ 1 (exp x)) 3)
38.0ms	(pow (exp x) 3)
23.0ms	(* (exp x) (exp x))