Details

sample152.0ms

Algorithm

intervals

Results

60.0ms	219×	body	160	nan
39.0ms	484×	body	80	nan
27.0ms	256×	body	80	valid

simplify617.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

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

12.0ms	(log (+ x (sqrt (- (* x x) 1))))
8.0ms	(sqrt (- (* x x) 1))

series180.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

135.0ms	(log (+ x (sqrt (- (* x x) 1))))
45.0ms	(sqrt (- (* x x) 1))

simplify702.0ms

Counts: 52 → 41

prune378.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize31.0ms

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)))))

rewrite32.0ms

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

23.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
7.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

series301.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

198.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
103.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify404.0ms

Counts: 76 → 65

prune488.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize34.0ms

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)))))

rewrite98.0ms

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

57.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
32.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
3.0ms	(sqrt (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
3.0ms	(sqrt (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

series479.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

146.0ms	(sqrt (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
127.0ms	(sqrt (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
105.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
100.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify905.0ms

Counts: 152 → 132

prune1.6s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.7s	16074×	body	80	nan
1.3s	7582×	body	160	nan
1.2s	8000×	body	80	valid