Details

sample85.0ms

Algorithm

intervals

Results

26.0ms	219×	body	160	nan
24.0ms	484×	body	80	nan
18.0ms	256×	body	80	valid

simplify116.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

116.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize18.0ms

Local error

Found 2 expressions with local error:

29.0b	(sqrt (- (* x x) 1))
0.0b	(log (+ x (sqrt (- (* x x) 1))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

Slowest

11.0ms	(log (+ x (sqrt (- (* x x) 1))))
8.0ms	(sqrt (- (* x x) 1))

series221.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

172.0ms	(log (+ x (sqrt (- (* x x) 1))))
49.0ms	(sqrt (- (* x x) 1))

simplify6.9s

Counts

52 → 41

Calls

52 calls:

Slowest

455.0ms	(log (+ (* x x) (- (* (sqrt (- (* x x) 1)) (sqrt (- (* x x) 1))) (* x (sqrt (- (* x x) 1))))))
452.0ms	(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
448.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
370.0ms	(* (* (sqrt (- (* x x) 1)) (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))
332.0ms	(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))

prune349.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 59

Calls

2 calls:

Slowest

48.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
6.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

series286.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

184.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
102.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify6.5s

Counts

76 → 65

Calls

76 calls:

Slowest

610.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
559.0ms	(log (+ (pow x 3) (pow (* (sqrt (+ x 1)) (sqrt (- x 1))) 3)))
370.0ms	(* (* (* (sqrt (+ x 1)) (sqrt (- x 1))) (* (sqrt (+ x 1)) (sqrt (- x 1)))) (* (sqrt (+ x 1)) (sqrt (- x 1))))
362.0ms	(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
338.0ms	(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))

prune664.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
36×	`sqrt-prod`
28×	`sqrt-div`
24×	`*-un-lft-identity`
20×	`associate-r`
14×	`pow1` `associate-l` `add-cube-cbrt`
8×	`frac-times` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `unswap-sqr`
6×	`sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `flip--`
4×	`associate-l/` `associate-r/` `insert-posit16` `add-log-exp` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-unprod` `difference-of-sqr-1` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 120

Calls

4 calls:

Slowest

26.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
24.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
6.0ms	(sqrt (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
4.0ms	(sqrt (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

129.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
126.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
119.0ms	(sqrt (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
103.0ms	(sqrt (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

simplify12.2s

Counts

152 → 132

Calls

152 calls:

Slowest

494.0ms	(sqrt (+ (pow x 3) (pow (* (sqrt (+ x 1)) (sqrt (- x 1))) 3)))
445.0ms	(* (* (* (sqrt (+ x 1)) (sqrt (- x 1))) (* (sqrt (+ x 1)) (sqrt (- x 1)))) (* (sqrt (+ x 1)) (sqrt (- x 1))))
437.0ms	(+ (sqrt (sqrt -1)) (+ (* 1/8 (* (pow x 2) (sqrt (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (* x (sqrt (/ 1 (sqrt -1)))))))
420.0ms	(sqrt (+ (pow x 3) (pow (* (sqrt (+ x 1)) (sqrt (- x 1))) 3)))
401.0ms	(* (* (* (sqrt (+ x 1)) (sqrt (- x 1))) (* (sqrt (+ x 1)) (sqrt (- x 1)))) (* (sqrt (+ x 1)) (sqrt (- x 1))))

prune1.7s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.3s	7582×	body	160	nan
1.3s	8000×	body	80	valid
1.2s	16074×	body	80	nan