Details

sample29.0ms

Algorithm

intervals

Results

13.0ms	136×	pre	10240	exit
4.0ms	256×	body	80	valid
2.0ms	120×	pre	80	true

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	10	7
2	12	7
done	12	7

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.5b

localize4.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ x0 (- 1.0 x1))
7.1b	(- (/ x0 (- 1.0 x1)) x0)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
76×	`times-frac`
69×	`add-cube-cbrt`
63×	`prod-diff`
21×	`fma-neg`
18×	`difference-of-squares`
17×	`distribute-lft-out--`
10×	`associate-/r/`
6×	`flip3--` `flip--`
5×	`associate-/r*` `div-inv`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num`

Counts

2 → 140

Calls

2 calls:

5.0ms	(/ x0 (- 1.0 x1))
44.0ms	(- (/ x0 (- 1.0 x1)) x0)

series83.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ x0 (- 1.0 x1))
43.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify1.9s

Counts

146 → 146

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	190	2805
1	417	2150
2	1025	1818
3	3320	1524
done	5000	1523

prune142.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (sqrt x0) (- (sqrt 1.0) (sqrt x1)))
6.1b	(fma (/ (sqrt x0) (+ (sqrt 1.0) (sqrt x1))) (/ (sqrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
72×	`sqrt-prod`
57×	`*-un-lft-identity`
54×	`times-frac`
29×	`add-cube-cbrt`
28×	`difference-of-squares`
14×	`distribute-lft-out--`
9×	`associate-/r*`
6×	`associate-/l*`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

2 → 95

Calls

2 calls:

13.0ms	(/ (sqrt x0) (- (sqrt 1.0) (sqrt x1)))
0.0ms	(fma (/ (sqrt x0) (+ (sqrt 1.0) (sqrt x1))) (/ (sqrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

series489.0ms

Counts

2 → 6

Calls

2 calls:

162.0ms	(/ (sqrt x0) (- (sqrt 1.0) (sqrt x1)))
326.0ms	(fma (/ (sqrt x0) (+ (sqrt 1.0) (sqrt x1))) (/ (sqrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

simplify1.4s

Counts

101 → 101

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	169	1872
1	364	1749
2	884	1605
3	2424	1493
done	5001	1492

prune148.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 4.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (cbrt x0) (- 1.0 x1))
6.0b	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
21×	`add-cube-cbrt`
18×	`cbrt-prod`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/l*`
5×	`associate-/r*`
4×	`add-exp-log`
3×	`add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

2 → 67

Calls

2 calls:

9.0ms	(/ (cbrt x0) (- 1.0 x1))
0.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series170.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(/ (cbrt x0) (- 1.0 x1))
87.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify2.0s

Counts

73 → 73

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	151	1049
1	309	968
2	901	878
3	3876	847
done	5000	846

prune146.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
6.5b	(fma (/ (* (cbrt x0) (cbrt x0)) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
54×	`times-frac`
42×	`sqrt-prod`
30×	`cbrt-prod`
29×	`add-cube-cbrt`
28×	`difference-of-squares`
14×	`distribute-lft-out--`
9×	`associate-/r*`
6×	`associate-/l*`
4×	`add-exp-log`
3×	`add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

2 → 95

Calls

2 calls:

12.0ms	(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
0.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

series457.0ms

Counts

2 → 6

Calls

2 calls:

238.0ms	(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
219.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

simplify606.0ms

Counts

101 → 101

Iterations

Useful iterations: done (603.0ms)

Iter	Nodes	Cost
0	221	2097
1	516	1982
2	1692	1824
done	5001	1736

prune187.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 4.5b

regimes54.0ms

Accuracy

46% (1.2b remaining)

Error of 6.2b against oracle of 5.0b and baseline of 7.3b

bsearch17.0ms

Steps

Iters	Range		Point
4	1.855	2.985	1.8749218749999998

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	45
1	21	45
done	21	45

end0.0ms

sample699.0ms

Algorithm

intervals

Results

364.0ms	4012×	pre	10240	exit
129.0ms	8000×	body	80	valid
61.0ms	3988×	pre	80	true