Details

sample141.0ms

Algorithm

intervals

Results

47.0ms	500×	body	80	nan
45.0ms	244×	body	160	nan
25.0ms	256×	body	80	valid

simplify160.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

159.0ms

(log (+ x (sqrt (- (* x x) 1))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize26.0ms

Local error

Found 2 expressions with local error:

27.8b	(sqrt (- (* x x) 1))
0.0b	(+ x (sqrt (- (* x x) 1)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity` `sqrt-prod`
5×	`add-sqr-sqrt`
4×	`add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `difference-of-sqr-1` `flip-+` `flip--` `distribute-lft-out`

Counts

2 → 32

Calls

2 calls:

Slowest

20.0ms	(+ x (sqrt (- (* x x) 1)))
16.0ms	(sqrt (- (* x x) 1))

series112.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

72.0ms	(+ x (sqrt (- (* x x) 1)))
40.0ms	(sqrt (- (* x x) 1))

simplify5.9s

Counts

45 → 38

Calls

45 calls:

Slowest

432.0ms	(+ (* x x) (- (* (sqrt (- (* x x) 1)) (sqrt (- (* x x) 1))) (* x (sqrt (- (* x x) 1)))))
370.0ms	(* (* (sqrt (- (* x x) 1)) (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))
369.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
285.0ms	(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
275.0ms	(- (* x x) (* (sqrt (- (* x x) 1)) (sqrt (- (* x x) 1))))

prune320.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 2 expressions with local error:

0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.0b	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
11×	`*-un-lft-identity`
10×	`associate-r`
7×	`associate-l`
6×	`pow1` `add-cube-cbrt`
4×	`frac-times` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `insert-posit16` `difference-of-squares`
1×	`+-commutative` `sum-log` `sqrt-unprod` `difference-of-sqr-1` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 56

Calls

2 calls:

Slowest

35.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
4.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

series627.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

506.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
121.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify6.4s

Counts

70 → 62

Calls

70 calls:

Slowest

488.0ms	(+ (pow x 3) (pow (* (sqrt (+ x 1)) (sqrt (- x 1))) 3))
438.0ms	(* (* (* (sqrt (+ x 1)) (sqrt (- x 1))) (* (sqrt (+ x 1)) (sqrt (- x 1)))) (* (sqrt (+ x 1)) (sqrt (- x 1))))
425.0ms	(* (* (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))) (+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))) (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
319.0ms	(- (* x x) (* (* (sqrt (+ x 1)) (sqrt (- x 1))) (* (sqrt (+ x 1)) (sqrt (- x 1)))))
296.0ms	(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))

prune495.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.4s	7775×	body	160	nan
1.3s	16657×	body	80	nan
1.3s	8000×	body	80	valid