Details

sample38.0ms

Algorithm

intervals

Results

19.0ms	124×	pre	10240	exit
6.0ms	256×	body	80	valid
2.0ms	132×	pre	80	true

simplify2.0ms

Counts: 1 → 1

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.8b	(/ x0 (- 1.0 x1))
7.5b	(- (/ x0 (- 1.0 x1)) x0)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`times-frac`
12×	`add-cube-cbrt`
6×	`difference-of-squares`
5×	`associate-/r*` `distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

11.0ms	(/ x0 (- 1.0 x1))
59.0ms	(- (/ x0 (- 1.0 x1)) x0)

series91.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ x0 (- 1.0 x1))
51.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify87.0ms

Counts: 58 → 58

prune90.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 7.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ x0 (- 1.0 x1))
0.8b	(/ x0 (- 1.0 x1))
0.8b	(/ x0 (- 1.0 x1))
6.2b	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
34×	`add-cube-cbrt`
15×	`associate-/r*`
13×	`difference-of-squares`
12×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 124

Calls

4 calls:

11.0ms	(/ x0 (- 1.0 x1))
11.0ms	(/ x0 (- 1.0 x1))
11.0ms	(/ x0 (- 1.0 x1))
26.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

series197.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ x0 (- 1.0 x1))
40.0ms	(/ x0 (- 1.0 x1))
36.0ms	(/ x0 (- 1.0 x1))
81.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

simplify151.0ms

Counts: 136 → 136

prune250.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (/ x0 (- 1.0 x1)) x0)
0.8b	(/ x0 (- 1.0 x1))
0.8b	(/ x0 (- 1.0 x1))
6.2b	(- (* (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
30×	`times-frac`
24×	`add-cube-cbrt`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

40.0ms	(+ (/ x0 (- 1.0 x1)) x0)
13.0ms	(/ x0 (- 1.0 x1))
12.0ms	(/ x0 (- 1.0 x1))
122.0ms	(- (* (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))

series478.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (/ x0 (- 1.0 x1)) x0)
36.0ms	(/ x0 (- 1.0 x1))
42.0ms	(/ x0 (- 1.0 x1))
359.0ms	(- (* (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))

simplify41.0ms

Counts: 110 → 110

prune275.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ x0 (- 1.0 x1))
0.8b	(/ x0 (- 1.0 x1))
3.9b	(log (exp (- (* (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))))
6.2b	(- (* (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))

rewrite597.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
26×	`add-cube-cbrt`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/l*` `add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/` `log-pow`
3×	`exp-prod` `flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `exp-sum` `clear-num` `div-inv`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp`

Counts

4 → 104

Calls

4 calls:

13.0ms	(/ x0 (- 1.0 x1))
11.0ms	(/ x0 (- 1.0 x1))
445.0ms	(log (exp (- (* (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))))
125.0ms	(- (* (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))

series292.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ x0 (- 1.0 x1))
38.0ms	(/ x0 (- 1.0 x1))
103.0ms	(log (exp (- (* (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))))
109.0ms	(- (* (* (/ (sqrt x0) (sqrt (- 1.0 x1))) (/ (sqrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))

simplify42.0ms

Counts: 116 → 116

prune353.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.3b

regimes70.0ms

Accuracy

76.7% (0.5b remaining)

Error of 4.7b against oracle of 4.2b and baseline of 6.3b

bsearch37.0ms

Steps

Iters	Range		Point
7	0.000209	0.0186	0.00021208908081054686

simplify1.0ms

end0.0ms

sample952.0ms

Algorithm

intervals

Results

410.0ms	3924×	pre	10240	exit
232.0ms	8000×	body	80	valid
102.0ms	4076×	pre	80	true