Details

sample127.0ms

Algorithm

intervals

Results

68.0ms	808×	body	80	nan
20.0ms	256×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

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

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
21×	`times-frac`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
13×	`fma-def`
8×	`log-prod` `distribute-lft-out`
5×	`pow1` `div-inv` `add-log-exp`
4×	`add-exp-log` `sqrt-prod`
3×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3-+` `distribute-rgt-out` `sqrt-div` `frac-add` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3--` `pow1/2` `rem-log-exp` `log-pow` `flip--` `difference-of-squares`

Counts

3 → 72

Calls

3 calls:

35.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
12.0ms	(sqrt (- 1.0 (* x x)))
56.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series709.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
95.0ms	(sqrt (- 1.0 (* x x)))
468.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
2	2015
1	473
0	186

prune557.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (- x) x 1.0))
0.0b	(sqrt (fma (- x) x 1.0))
0.1b	(sqrt (+ (/ 1.0 x) (/ (sqrt (fma (- x) x 1.0)) x)))
0.1b	(sqrt (+ (/ 1.0 x) (/ (sqrt (fma (- x) x 1.0)) x)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`times-frac` `sqrt-prod`
12×	`add-cube-cbrt` `hypot-def`
8×	`pow1` `distribute-lft-out`
6×	`sqrt-div`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`flip3-+` `distribute-rgt-out` `frac-add` `flip-+`

Counts

4 → 88

Calls

4 calls:

1.0ms	(sqrt (fma (- x) x 1.0))
1.0ms	(sqrt (fma (- x) x 1.0))
51.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (fma (- x) x 1.0)) x)))
81.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (fma (- x) x 1.0)) x)))

series896.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(sqrt (fma (- x) x 1.0))
102.0ms	(sqrt (fma (- x) x 1.0))
335.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (fma (- x) x 1.0)) x)))
327.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (fma (- x) x 1.0)) x)))

simplify955.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1548
1	417
0	173

prune657.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (fma (- x) x 1.0)) (sqrt x))
0.2b	(/ 1.0 (sqrt x))
0.2b	(/ 1 (sqrt x))
0.4b	(* (sqrt (/ 1 (sqrt x))) (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (fma (- x) x 1.0)) (sqrt x)))))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

138×	`sqrt-prod`
114×	`add-sqr-sqrt` `times-frac`
104×	`*-un-lft-identity`
82×	`add-cube-cbrt`
25×	`associate-l`
18×	`associate-/r*`
16×	`associate-r`
14×	`add-exp-log`
12×	`add-cbrt-cube` `associate-/l*` `unswap-sqr`
10×	`pow1` `sqrt-div`
9×	`distribute-lft-out`
6×	`div-inv`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-*r/` `pow-flip`
2×	`flip3-+` `frac-add` `flip-+`
1×	`rec-exp` `sqrt-undiv` `distribute-rgt-out` `sqrt-unprod` `1-exp` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 227

Calls

4 calls:

13.0ms	(/ (sqrt (fma (- x) x 1.0)) (sqrt x))
6.0ms	(/ 1.0 (sqrt x))
6.0ms	(/ 1 (sqrt x))
266.0ms	(* (sqrt (/ 1 (sqrt x))) (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (fma (- x) x 1.0)) (sqrt x)))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (sqrt (fma (- x) x 1.0)) (sqrt x))
52.0ms	(/ 1.0 (sqrt x))
29.0ms	(/ 1 (sqrt x))
317.0ms	(* (sqrt (/ 1 (sqrt x))) (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (fma (- x) x 1.0)) (sqrt x)))))

simplify1.5s

Counts

239 → 239

Iterations

Iter	Nodes
done	5001
2	3544
1	824
0	376

prune1.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes25.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.3s	24124×	body	80	nan
1.1s	8000×	body	80	valid