Details

sample29.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
3.0ms	91×	body	80	nan

simplify2.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`distribute-lft-out`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 45

Calls

2 calls:

17.0ms	(+ 1.0 (sqrt (+ x 1.0)))
66.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series285.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(+ 1.0 (sqrt (+ x 1.0)))
216.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify104.0ms

Counts: 51 → 51

prune126.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

16.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

343.0ms	(* (cbrt x) (cbrt x))
246.0ms	(cbrt x)
268.0ms	(cbrt x)
257.0ms	(cbrt x)

simplify65.0ms

Counts: 85 → 85

prune308.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
0.2b	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
8.3b	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

70×	`cbrt-prod` `*-un-lft-identity`
51×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down` `cube-prod`
17×	`associate-/r*`
13×	`distribute-lft-out`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `flip-+`
3×	`pow-unpow` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `pow-exp` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 149

Calls

4 calls:

17.0ms	(+ 1.0 (sqrt (+ x 1.0)))
45.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
83.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
55.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

series462.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ 1.0 (sqrt (+ x 1.0)))
159.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
182.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
61.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

simplify67.0ms

Counts: 161 → 161

prune390.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(* (sqrt x) (/ (sqrt x) (* (+ 1.0 (sqrt (+ x 1.0))) 1)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log`
12×	`associate-r`
11×	`add-sqr-sqrt` `add-cbrt-cube`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt` `sqrt-prod`
6×	`times-frac` `associate-l` `prod-exp`
4×	`pow1` `cbrt-unprod` `add-log-exp`
3×	`div-exp`
2×	`cbrt-undiv` `flip3-+` `associate-*l/` `associate-/r/` `flip-+` `unswap-sqr`
1×	`+-commutative` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `div-inv` `distribute-lft-out`

Counts

2 → 49

Calls

2 calls:

35.0ms	(+ 1.0 (sqrt (+ x 1.0)))
116.0ms	(* (sqrt x) (/ (sqrt x) (* (+ 1.0 (sqrt (+ x 1.0))) 1)))

series250.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ 1.0 (sqrt (+ x 1.0)))
184.0ms	(* (sqrt x) (/ (sqrt x) (* (+ 1.0 (sqrt (+ x 1.0))) 1)))

simplify48.0ms

Counts: 55 → 55

prune171.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes20.0ms

Accuracy

88.7% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 1.4b

bsearch13.0ms

Steps

Iters	Range		Point
3	2.5852715992345188e-23	3.219064609783079e-23	2.653971370452548e-23

simplify64.0ms

end0.0ms

sample747.0ms

Algorithm

intervals

Results

419.0ms	7994×	body	80	valid
78.0ms	2707×	body	80	nan
1.0ms	6×	body	1280	valid