Details

sample182.0ms

Algorithm

intervals

Results

47.0ms	713×	body	80	nan
13.0ms	256×	body	80	valid

simplify33.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

32.0ms

(* (sqrt (- x 1)) (sqrt x))

prune481.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 1 expressions with local error:

0.5b	(* (sqrt (- x 1)) (sqrt x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`sqrt-prod`
10×	`associate-l`
8×	`*-un-lft-identity`
6×	`associate-r`
5×	`pow1` `add-cube-cbrt`
4×	`unswap-sqr`
3×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-*l/` `difference-of-squares`
1×	`flip3--` `sqrt-unprod` `difference-of-sqr-1` `prod-exp` `*-commutative` `cbrt-unprod` `insert-posit16` `flip--` `distribute-lft-out--` `add-log-exp`

Counts

1 → 37

Calls

1 calls:

Slowest

34.0ms

(* (sqrt (- x 1)) (sqrt x))

series106.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

106.0ms

(* (sqrt (- x 1)) (sqrt x))

simplify1.4s

Counts

35 → 40

Calls

35 calls:

Slowest

471.0ms	(* (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
303.0ms	(* (sqrt (- (pow x 3) (pow 1 3))) (sqrt x))
103.0ms	(- x (+ (* 1/8 (/ 1 x)) 1/2))
95.0ms	(* (sqrt (- (* x x) (* 1 1))) (sqrt x))
30.0ms	(+ (log (sqrt (- x 1))) (log (sqrt x)))

prune256.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

Calls

0 calls:

Slowest

series0.0ms

Counts

0 → 0

Calls

0 calls:

Slowest

simplify0.0ms

Counts

0 → 0

Calls

0 calls:

Slowest

prune5.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (sqrt (- x 1)) (sqrt x)))
0.5b	(cbrt (* (sqrt (- x 1)) (sqrt x)))
0.5b	(cbrt (* (sqrt (- x 1)) (sqrt x)))
0.5b	(* (sqrt (- x 1)) (sqrt x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`sqrt-prod`
11×	`*-un-lft-identity`
10×	`associate-l`
8×	`pow1` `sqrt-div` `associate-*l/` `add-cube-cbrt`
6×	`cbrt-div` `add-cbrt-cube` `associate-r` `add-exp-log`
4×	`flip3--` `insert-posit16` `flip--` `add-log-exp` `unswap-sqr`
3×	`cbrt-prod` `pow1/3` `pow-prod-down`
2×	`sqrt-pow1` `pow1/2` `difference-of-squares`
1×	`sqrt-unprod` `difference-of-sqr-1` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 73

Calls

4 calls:

Slowest

22.0ms	(* (sqrt (- x 1)) (sqrt x))
14.0ms	(cbrt (* (sqrt (- x 1)) (sqrt x)))
14.0ms	(cbrt (* (sqrt (- x 1)) (sqrt x)))
14.0ms	(cbrt (* (sqrt (- x 1)) (sqrt x)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

187.0ms	(cbrt (* (sqrt (- x 1)) (sqrt x)))
143.0ms	(cbrt (* (sqrt (- x 1)) (sqrt x)))
135.0ms	(cbrt (* (sqrt (- x 1)) (sqrt x)))
74.0ms	(* (sqrt (- x 1)) (sqrt x))

simplify4.0s

Counts

53 → 85

Calls

53 calls:

Slowest

388.0ms	(* (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
313.0ms	(* (sqrt (- (pow x 3) (pow 1 3))) (sqrt x))
308.0ms	(cbrt (* (sqrt (- (pow x 3) (pow 1 3))) (sqrt x)))
298.0ms	(cbrt (* (sqrt (- (pow x 3) (pow 1 3))) (sqrt x)))
293.0ms	(- (exp (* 1/6 (+ (log -1) (log x)))) (+ (* 1/6 (* x (exp (* 1/6 (+ (log -1) (log x)))))) (* 5/72 (* (pow x 2) (exp (* 1/6 (+ (log -1) (log x))))))))

prune997.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

27.7b	(sqrt (- (* x x) x))
0.0b	(- (* x x) x)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`flip3--` `add-cbrt-cube` `distribute-rgt-out--` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

2 → 33

Calls

2 calls:

Slowest

18.0ms	(- (* x x) x)
16.0ms	(sqrt (- (* x x) x))

series84.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

44.0ms	(- (* x x) x)
39.0ms	(sqrt (- (* x x) x))

simplify796.0ms

Counts

19 → 39

Calls

19 calls:

Slowest

292.0ms	(sqrt (- (* (* x x) (* x x)) (* x x)))
177.0ms	(sqrt (- (pow (* x x) 3) (pow x 3)))
112.0ms	(- x (+ (* 1/8 (/ 1 x)) 1/2))
82.0ms	(- (+ (* 1/8 (/ 1 x)) 1/2) x)
45.0ms	(/ (exp (* x x)) (exp x))

prune253.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes86.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.4s	23839×	body	80	nan
963.0ms	7992×	body	80	valid
1.0ms	8×	body	160	valid