Details

sample113.0ms

Algorithm

intervals

Results

55.0ms	816×	body	80	nan
21.0ms	256×	body	80	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.0b	(/ (sqrt (- 1.0 (* x x))) x)
0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

rewrite481.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
33×	`times-frac`
32×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
20×	`sqrt-prod`
8×	`log-prod` `distribute-lft-out`
7×	`add-exp-log` `associate-/l*`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`div-inv` `difference-of-squares`
4×	`sqrt-div`
3×	`log-div` `associate-/r*`
2×	`distribute-rgt-out` `flip3--` `flip3-+` `frac-add` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log` `log-pow`

Counts

4 → 98

Calls

4 calls:

6.0ms	(sqrt (- 1.0 (* x x)))
397.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
14.0ms	(/ (sqrt (- 1.0 (* x x))) x)
60.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series710.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (- 1.0 (* x x)))
317.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
204.0ms	(/ (sqrt (- 1.0 (* x x))) x)
125.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify42.0ms

Counts: 110 → 110

prune329.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (cbrt (pow (sqrt (- 1.0 (* x x))) 3)) x)
0.0b	(+ (/ 1.0 x) (/ (cbrt (pow (sqrt (- 1.0 (* x x))) 3)) x))
0.0b	(cbrt (pow (sqrt (- 1.0 (* x x))) 3))
0.0b	(pow (sqrt (- 1.0 (* x x))) 3)

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

100×	`cbrt-prod`
76×	`add-sqr-sqrt`
75×	`times-frac`
72×	`*-un-lft-identity`
64×	`add-cube-cbrt`
48×	`sqrt-prod`
42×	`unpow-prod-down` `cube-prod`
23×	`associate-/l*`
12×	`difference-of-squares`
7×	`add-exp-log`
6×	`pow1` `cube-div` `cube-mult` `sqrt-div` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
4×	`cbrt-div` `distribute-lft-out`
3×	`pow-unpow` `flip3--` `pow-pow` `associate-/r*` `flip--` `div-inv`
2×	`associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `distribute-rgt-out` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `div-exp` `frac-add` `pow-exp` `clear-num` `sum-log` `sqrt-pow2` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 193

Calls

4 calls:

49.0ms	(/ (cbrt (pow (sqrt (- 1.0 (* x x))) 3)) x)
96.0ms	(+ (/ 1.0 x) (/ (cbrt (pow (sqrt (- 1.0 (* x x))) 3)) x))
8.0ms	(cbrt (pow (sqrt (- 1.0 (* x x))) 3))
9.0ms	(pow (sqrt (- 1.0 (* x x))) 3)

series646.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (cbrt (pow (sqrt (- 1.0 (* x x))) 3)) x)
130.0ms	(+ (/ 1.0 x) (/ (cbrt (pow (sqrt (- 1.0 (* x x))) 3)) x))
72.0ms	(cbrt (pow (sqrt (- 1.0 (* x x))) 3))
251.0ms	(pow (sqrt (- 1.0 (* x x))) 3)

simplify83.0ms

Counts: 205 → 205

prune662.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

simplify107.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.7s	23585×	body	80	nan
890.0ms	8000×	body	80	valid