Details

sample152.0ms

Algorithm

intervals

Results

60.0ms	505×	body	80	nan
44.0ms	248×	body	160	nan
24.0ms	256×	body	80	valid

simplify19.2s

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize28.0ms

Local error

Found 4 expressions with local error:

29.9b	(sqrt (- (* x x) 1))
0.0b	(+ x (sqrt (- (* x x) 1)))
0.0b	(- (* x x) 1)
0.0b	(log (+ x (sqrt (- (* x x) 1))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
8×	`add-exp-log` `add-cube-cbrt` `add-log-exp`
6×	`pow1` `sqrt-prod`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`fma-def` `prod-diff`
2×	`log-div` `expm1-def` `flip3-+` `flip3--` `sqrt-div` `difference-of-sqr-1` `flip-+` `flip--` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `rem-log-exp` `prod-exp` `log-pow`

Counts

4 → 81

Calls

4 calls:

Slowest

21.0ms	(+ x (sqrt (- (* x x) 1)))
20.0ms	(sqrt (- (* x x) 1))
14.0ms	(log (+ x (sqrt (- (* x x) 1))))
8.0ms	(- (* x x) 1)

series372.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

210.0ms	(log (+ x (sqrt (- (* x x) 1))))
65.0ms	(+ x (sqrt (- (* x x) 1)))
53.0ms	(sqrt (- (* x x) 1))
44.0ms	(- (* x x) 1)

simplify2.2s

Counts: 93 → 93

prune874.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`sqrt-prod`
14×	`*-un-lft-identity`
12×	`sqrt-div`
10×	`associate-r`
9×	`add-cube-cbrt`
8×	`pow1`
7×	`associate-l`
6×	`add-exp-log`
5×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`expm1-log1p-u` `log-prod` `fma-def` `flip3--` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `difference-of-squares`
1×	`+-commutative` `sum-log` `sqrt-unprod` `difference-of-sqr-1` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 80

Calls

3 calls:

Slowest

45.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
9.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
9.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

series433.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

221.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
120.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
92.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify1.6s

Counts: 89 → 89

prune830.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 3 expressions with local error:

0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.1b	(fma (sqrt x) (sqrt x) (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.0b	(log (fma (sqrt x) (sqrt x) (* (sqrt (+ x 1)) (sqrt (- x 1)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`sqrt-prod`
13×	`*-un-lft-identity`
12×	`sqrt-div`
10×	`associate-r`
8×	`pow1` `add-cube-cbrt`
7×	`associate-l`
6×	`add-exp-log`
5×	`add-cbrt-cube`
4×	`frac-times` `unswap-sqr`
3×	`expm1-log1p-u` `log-prod` `flip3-+` `flip3--` `pow-prod-down` `flip-+` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `difference-of-squares`
1×	`sqrt-unprod` `difference-of-sqr-1` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 72

Calls

3 calls:

Slowest

25.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
1.0ms	(log (fma (sqrt x) (sqrt x) (* (sqrt (+ x 1)) (sqrt (- x 1)))))
0.0ms	(fma (sqrt x) (sqrt x) (* (sqrt (+ x 1)) (sqrt (- x 1))))

series622.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

315.0ms	(log (fma (sqrt x) (sqrt x) (* (sqrt (+ x 1)) (sqrt (- x 1)))))
196.0ms	(fma (sqrt x) (sqrt x) (* (sqrt (+ x 1)) (sqrt (- x 1))))
111.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify982.0ms

Counts: 81 → 81

prune853.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.7s	16542×	body	80	nan
1.4s	7691×	body	160	nan
781.0ms	8000×	body	80	valid