Details

sample122.0ms

Algorithm

intervals

Results

69.0ms	67×	body	1280	valid
24.0ms	53×	body	640	valid
8.0ms	31×	body	320	valid
5.0ms	95×	body	80	valid
4.0ms	92×	body	80	nan
1.0ms	10×	body	160	valid

simplify7.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

7.0ms

(log (+ 1 x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize6.0ms

Local error

Found 1 expressions with local error:

3.1b	(log (+ 1 x))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log-prod` `*-un-lft-identity`
2×	`add-sqr-sqrt` `pow1` `log-div` `add-exp-log` `add-cube-cbrt`
1×	`flip3-+` `add-cbrt-cube` `rem-log-exp` `log-pow` `flip-+` `insert-posit16` `distribute-lft-out` `add-log-exp`

Counts

1 → 16

Calls

1 calls:

Slowest

3.0ms

(log (+ 1 x))

series36.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

36.0ms

(log (+ 1 x))

simplify1.0s

Counts

10 → 19

Calls

10 calls:

Slowest

444.0ms	(- (+ (/ 1 x) (log -1)) (+ (log (/ -1 x)) (* 1/2 (/ 1 (pow x 2)))))
243.0ms	(- (/ 1 x) (+ (log (/ 1 x)) (* 1/2 (/ 1 (pow x 2)))))
230.0ms	(- (+ x (* 1/3 (pow x 3))) (* 1/2 (pow x 2)))
54.0ms	(log (+ (pow 1 3) (pow x 3)))
20.0ms	(log (* (cbrt (+ 1 x)) (cbrt (+ 1 x))))

prune149.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(* x 1/3)
0.0b	(* (+ -1/2 (* x 1/3)) (* x x))
0.0b	(+ -1/2 (* x 1/3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`insert-posit16`
2×	`flip3-+` `associate-l/` `-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log`

Counts

3 → 53

Calls

3 calls:

Slowest

24.0ms	(* (+ -1/2 (* x 1/3)) (* x x))
5.0ms	(* x 1/3)
4.0ms	(+ -1/2 (* x 1/3))

series199.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

125.0ms	(* (+ -1/2 (* x 1/3)) (* x x))
57.0ms	(+ -1/2 (* x 1/3))
17.0ms	(* x 1/3)

simplify2.1s

Counts

31 → 62

Calls

31 calls:

Slowest

250.0ms	(* (* (* (+ -1/2 (* x 1/3)) (+ -1/2 (* x 1/3))) (+ -1/2 (* x 1/3))) (* (* (* x x) (* x x)) (* x x)))
238.0ms	(* (* (* (+ -1/2 (* x 1/3)) (+ -1/2 (* x 1/3))) (+ -1/2 (* x 1/3))) (* (* (* x x) x) (* (* x x) x)))
237.0ms	(- (* 1/3 (pow x 3)) (* 1/2 (pow x 2)))
235.0ms	(* (+ (pow -1/2 3) (pow (* x 1/3) 3)) (* x x))
215.0ms	(- (* 1/3 (pow x 3)) (* 1/2 (pow x 2)))

prune445.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

3.2b	(log (sqrt (+ 1 x)))
3.2b	(log (sqrt (+ 1 x)))
0.0b	(sqrt (+ 1 x))
0.0b	(sqrt (+ 1 x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`sqrt-prod`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`log-div` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `flip-+` `insert-posit16` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 76

Calls

4 calls:

Slowest

13.0ms	(sqrt (+ 1 x))
7.0ms	(log (sqrt (+ 1 x)))
7.0ms	(log (sqrt (+ 1 x)))
6.0ms	(sqrt (+ 1 x))

series226.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

80.0ms	(log (sqrt (+ 1 x)))
80.0ms	(log (sqrt (+ 1 x)))
37.0ms	(sqrt (+ 1 x))
29.0ms	(sqrt (+ 1 x))

simplify1.4s

Counts

50 → 88

Calls

50 calls:

Slowest

293.0ms	(- (+ (* 1/2 x) (* 1/6 (pow x 3))) (* 1/4 (pow x 2)))
224.0ms	(- (+ (* 1/2 x) (* 1/6 (pow x 3))) (* 1/4 (pow x 2)))
123.0ms	(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
110.0ms	(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
87.0ms	(log (sqrt (+ (pow 1 3) (pow x 3))))

prune765.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

3.3b	(log (sqrt (cbrt (+ 1 x))))
3.2b	(log (sqrt (+ 1 x)))
3.2b	(log (sqrt (* (cbrt (+ 1 x)) (cbrt (+ 1 x)))))
0.2b	(cbrt (+ 1 x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

21×	`log-prod`
18×	`log-pow`
17×	`pow1` `*-un-lft-identity`
16×	`cbrt-div`
12×	`log-div` `sqrt-pow1` `sqrt-div` `sqrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`flip3-+` `flip-+`
8×	`cbrt-prod` `pow1/3`
7×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`pow1/2` `rem-log-exp` `distribute-lft-out`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 93

Calls

4 calls:

Slowest

23.0ms	(log (sqrt (* (cbrt (+ 1 x)) (cbrt (+ 1 x)))))
15.0ms	(log (sqrt (cbrt (+ 1 x))))
7.0ms	(log (sqrt (+ 1 x)))
5.0ms	(cbrt (+ 1 x))

series256.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

74.0ms	(log (sqrt (cbrt (+ 1 x))))
73.0ms	(log (sqrt (+ 1 x)))
66.0ms	(log (sqrt (* (cbrt (+ 1 x)) (cbrt (+ 1 x)))))
43.0ms	(cbrt (+ 1 x))

simplify4.9s

Counts

66 → 105

Calls

66 calls:

Slowest

366.0ms	(- (+ (* 1/3 (/ 1 x)) (* 1/3 (log -1))) (+ (* 1/3 (log (/ -1 x))) (* 1/6 (/ 1 (pow x 2)))))
349.0ms	(- (+ (* 1/6 (/ 1 x)) (* 1/6 (log -1))) (+ (* 1/6 (log (/ -1 x))) (* 1/12 (/ 1 (pow x 2)))))
345.0ms	(- (+ (* 1/2 x) (* 1/6 (pow x 3))) (* 1/4 (pow x 2)))
339.0ms	(- (+ (log (pow (/ 1 x) -1/3)) (* 1/3 (/ 1 x))) (* 1/6 (/ 1 (pow x 2))))
327.0ms	(- (+ (log (pow (/ 1 x) -1/6)) (* 1/6 (/ 1 x))) (* 1/12 (/ 1 (pow x 2))))

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes160.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 20.8b

bsearch51.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.8s	2278×	body	1280	valid
1.1s	1653×	body	640	valid
173.0ms	822×	body	320	valid
139.0ms	2822×	body	80	valid
96.0ms	2718×	body	80	nan
52.0ms	425×	body	160	valid