Details

sample260.0ms

Algorithm

intervals

Results

98.0ms	703×	body	80	nan
73.0ms	255×	body	80	valid
0.0ms	1×	body	160	valid

simplify77.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

76.0ms

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

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 1 expressions with local error:

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

rewrite70.0ms

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×	`expm1-log1p-u` `flip3--` `sqrt-unprod` `difference-of-sqr-1` `prod-exp` `*-commutative` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `add-log-exp`

Counts

1 → 39

Calls

1 calls:

Slowest

67.0ms

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

series95.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

94.0ms

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

simplify2.1s

Counts

45 → 42

Calls

45 calls:

Slowest

286.0ms	(* (sqrt (- (pow x 3) (pow 1 3))) (sqrt x))
209.0ms	(* (* (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x))) (* (sqrt (- x 1)) (sqrt x)))
177.0ms	(* (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
135.0ms	(exp (* (sqrt (- x 1)) (sqrt x)))
81.0ms	(+ (log (sqrt (- x 1))) (log (sqrt x)))

prune275.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

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

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.4b	(* (sqrt (+ x -1)) (fabs (cbrt x)))
0.3b	(* (* (sqrt (+ x -1)) (fabs (cbrt x))) (sqrt (cbrt x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`associate-r` `add-cube-cbrt` `sqrt-prod`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`cbrt-prod` `associate-l`
6×	`associate-*l/`
4×	`expm1-log1p-u` `sqrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `pow1/3` `*-commutative` `flip-+` `unswap-sqr`
1×	`difference-of-sqr--1` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

Slowest

45.0ms	(* (* (sqrt (+ x -1)) (fabs (cbrt x))) (sqrt (cbrt x)))
15.0ms	(* (sqrt (+ x -1)) (fabs (cbrt x)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series715.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

271.0ms	(cbrt x)
247.0ms	(cbrt x)
153.0ms	(* (* (sqrt (+ x -1)) (fabs (cbrt x))) (sqrt (cbrt x)))
44.0ms	(* (sqrt (+ x -1)) (fabs (cbrt x)))

simplify5.8s

Counts

102 → 98

Calls

102 calls:

Slowest

735.0ms	(* (* (* (* (sqrt (+ x -1)) (fabs (cbrt x))) (* (sqrt (+ x -1)) (fabs (cbrt x)))) (* (sqrt (+ x -1)) (fabs (cbrt x)))) (* (* (sqrt (cbrt x)) (sqrt (cbrt x))) (sqrt (cbrt x))))
650.0ms	(* (* (* (* (sqrt (+ x -1)) (fabs (cbrt x))) (sqrt (cbrt x))) (* (* (sqrt (+ x -1)) (fabs (cbrt x))) (sqrt (cbrt x)))) (* (* (sqrt (+ x -1)) (fabs (cbrt x))) (sqrt (cbrt x))))
631.0ms	(* (* (sqrt (+ (pow x 3) (pow -1 3))) (fabs (cbrt x))) (sqrt (cbrt x)))
531.0ms	(* (sqrt (+ (pow x 3) (pow -1 3))) (fabs (cbrt x)))
374.0ms	(* (* (* (sqrt (+ x -1)) (fabs (cbrt x))) (* (sqrt (+ x -1)) (fabs (cbrt x)))) (* (sqrt (+ x -1)) (fabs (cbrt x))))

prune968.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 1 expressions with local error:

29.0b

(pow (* (- x 1) x) (/ 1 2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow-unpow`
9×	`times-frac`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-exp-log`
2×	`pow-pow` `pow-exp`
1×	`expm1-log1p-u` `pow-to-exp` `unpow-prod-down` `add-cbrt-cube` `pow-prod-down` `prod-exp` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `sqr-pow`

Counts

1 → 30

Calls

1 calls:

Slowest

19.0ms

(pow (* (- x 1) x) (/ 1 2))

series74.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

74.0ms

(pow (* (- x 1) x) (/ 1 2))

simplify7.3s

Counts

35 → 33

Calls

35 calls:

Slowest

669.0ms	(pow (* (- x 1) x) (/ (* (cbrt 1) (cbrt 1)) (sqrt 2)))
594.0ms	(pow (* (- x 1) x) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt 2) (cbrt 2))))
491.0ms	(* (* (pow (* (- x 1) x) (/ 1 2)) (pow (* (- x 1) x) (/ 1 2))) (pow (* (- x 1) x) (/ 1 2)))
392.0ms	(- (exp (* 1/2 (+ (log -1) (log x)))) (+ (* 1/2 (* x (exp (* 1/2 (+ (log -1) (log x)))))) (* 1/8 (* (pow x 2) (exp (* 1/2 (+ (log -1) (log x))))))))
326.0ms	(pow (* (- x 1) x) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))

prune171.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.4b remaining)

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

bsearch1.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.2s	23656×	body	80	nan
906.0ms	7992×	body	80	valid
1.0ms	8×	body	160	valid