Details

sample79.0ms

Algorithm

intervals

Results

35.0ms	772×	body	80	nan
18.0ms	256×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	18
3	18
2	16
1	12
0	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
27×	`times-frac`
25×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
16×	`sqrt-prod`
8×	`log-prod`
7×	`associate-/l*`
5×	`add-exp-log`
4×	`add-cbrt-cube` `distribute-lft-out` `difference-of-squares`
3×	`pow1` `log-div` `associate-/r*` `div-inv`
2×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `distribute-rgt-out` `flip3--` `div-exp` `rem-log-exp` `frac-add` `log-pow` `flip-+` `flip--`

Counts

2 → 69

Calls

2 calls:

10.0ms	(/ (sqrt (- 1.0 (* x x))) x)
65.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series643.0ms

Counts

2 → 6

Calls

2 calls:

210.0ms	(/ (sqrt (- 1.0 (* x x))) x)
433.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
2	1907
1	463
0	205

prune438.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
57×	`times-frac`
50×	`sqrt-prod`
49×	`*-un-lft-identity` `add-cube-cbrt`
31×	`associate-r`
26×	`cbrt-prod`
12×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`associate-/l*`
8×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`log-div` `log-prod` `associate-/r` `associate-l*`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `flip3-+` `pow1/2` `pow1/3` `rem-log-exp` `pow-prod-down` `frac-add` `log-pow` `*-commutative` `flip-+`

Counts

4 → 144

Calls

4 calls:

2.0ms	(sqrt (cbrt (fma x (- x) 1.0)))
22.0ms	(* (fabs (cbrt (fma x (- x) 1.0))) (/ (sqrt (cbrt (fma x (- x) 1.0))) x))
9.0ms	(log (+ (/ 1.0 x) (* (fabs (cbrt (fma x (- x) 1.0))) (/ (sqrt (cbrt (fma x (- x) 1.0))) x))))
6.0ms	(/ (sqrt (cbrt (fma x (- x) 1.0))) x)

series1.7s

Counts

4 → 12

Calls

4 calls:

284.0ms	(sqrt (cbrt (fma x (- x) 1.0)))
396.0ms	(* (fabs (cbrt (fma x (- x) 1.0))) (/ (sqrt (cbrt (fma x (- x) 1.0))) x))
588.0ms	(log (+ (/ 1.0 x) (* (fabs (cbrt (fma x (- x) 1.0))) (/ (sqrt (cbrt (fma x (- x) 1.0))) x))))
420.0ms	(/ (sqrt (cbrt (fma x (- x) 1.0))) x)

simplify930.0ms

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
1	972
0	359

prune1.0s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.7s	23776×	body	80	nan
1.2s	8000×	body	80	valid