Details

sample106.0ms

Algorithm

intervals

Results

40.0ms	536×	body	80	nan
29.0ms	227×	body	160	nan
18.0ms	256×	body	80	valid

simplify5.9s

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize22.0ms

Local error

Found 3 expressions with local error:

30.1b	(sqrt (fma x x -1))
0.3b	(log (+ x (sqrt (fma x x -1))))
0.0b	(+ x (sqrt (fma x x -1)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `sqrt-prod` `insert-posit16` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

3 → 52

Calls

3 calls:

Slowest

10.0ms	(+ x (sqrt (fma x x -1)))
8.0ms	(log (+ x (sqrt (fma x x -1))))
3.0ms	(sqrt (fma x x -1))

series347.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

196.0ms	(log (+ x (sqrt (fma x x -1))))
80.0ms	(sqrt (fma x x -1))
71.0ms	(+ x (sqrt (fma x x -1)))

simplify765.0ms

Counts: 61 → 61

prune569.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (- (fma x 2 (/ -1/8 (* x (* x x)))) (/ 1/2 x)))
0.2b	(/ -1/8 (* x (* x x)))
0.1b	(* x (* x x))
0.0b	(- (fma x 2 (/ -1/8 (* x (* x x)))) (/ 1/2 x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
43×	`add-cube-cbrt`
39×	`prod-diff`
32×	`times-frac`
19×	`pow1` `add-exp-log`
18×	`add-cbrt-cube`
6×	`log-prod` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `difference-of-squares`
3×	`cbrt-undiv` `fma-neg` `div-exp` `associate-l` `pow-prod-down` `associate-/l*`
2×	`log-div` `flip3--` `flip--` `distribute-lft-out--`
1×	`pow2` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `cube-unmult` `rem-log-exp` `associate-r` `associate--l+` `pow-sqr` `log-pow` `-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

Slowest

20.0ms	(/ -1/8 (* x (* x x)))
17.0ms	(* x (* x x))
15.0ms	(log (- (fma x 2 (/ -1/8 (* x (* x x)))) (/ 1/2 x)))
7.0ms	(- (fma x 2 (/ -1/8 (* x (* x x)))) (/ 1/2 x))

series267.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

109.0ms	(log (- (fma x 2 (/ -1/8 (* x (* x x)))) (/ 1/2 x)))
59.0ms	(* x (* x x))
51.0ms	(/ -1/8 (* x (* x x)))
48.0ms	(- (fma x 2 (/ -1/8 (* x (* x x)))) (/ 1/2 x))

simplify870.0ms

Counts: 146 → 146

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ -1/4 (* x x))
0.5b	(/ 3/32 (* (* x x) (* x x)))
0.2b	(+ (log 2) (log x))
0.2b	(* (* x x) (* x x))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

120×	`pow1`
39×	`add-cbrt-cube` `add-exp-log`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
17×	`prod-exp` `cbrt-unprod`
15×	`*-un-lft-identity`
13×	`pow2`
11×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`cbrt-undiv` `div-exp`
6×	`log-prod` `times-frac` `associate-/l*`
5×	`log-pow`
4×	`expm1-log1p-u` `fma-def` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-+l+` `associate-+r+`
2×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`
1×	`+-commutative` `sum-log` `flip3-+` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

Slowest

30.0ms	(* (* x x) (* x x))
24.0ms	(/ 3/32 (* (* x x) (* x x)))
11.0ms	(+ (log 2) (log x))
6.0ms	(/ -1/4 (* x x))

series524.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

368.0ms	(+ (log 2) (log x))
69.0ms	(* (* x x) (* x x))
47.0ms	(/ 3/32 (* (* x x) (* x x)))
40.0ms	(/ -1/4 (* x x))

simplify1.4s

Counts: 160 → 160

prune1.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

30.1b	(sqrt (fma x x -1))
30.1b	(sqrt (fma x x -1))
0.2b	(sqrt (+ x (sqrt (fma x x -1))))
0.2b	(sqrt (+ x (sqrt (fma x x -1))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`sqrt-prod`
12×	`*-un-lft-identity`
8×	`pow1` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `sqrt-div` `add-exp-log` `hypot-def` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 74

Calls

4 calls:

Slowest

7.0ms	(sqrt (+ x (sqrt (fma x x -1))))
6.0ms	(sqrt (+ x (sqrt (fma x x -1))))
1.0ms	(sqrt (fma x x -1))
1.0ms	(sqrt (fma x x -1))

series373.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

117.0ms	(sqrt (+ x (sqrt (fma x x -1))))
99.0ms	(sqrt (+ x (sqrt (fma x x -1))))
79.0ms	(sqrt (fma x x -1))
78.0ms	(sqrt (fma x x -1))

simplify1.4s

Counts: 86 → 86

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	16390×	body	80	nan
1.3s	7858×	body	160	nan
706.0ms	8000×	body	80	valid