Details

sample65.0ms

Algorithm

intervals

Results

29.0ms	126×	pre	10240	exit
10.0ms	256×	body	80	valid
4.0ms	130×	pre	80	true

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	10
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ x0 (- 1.0 x1))
7.5b	(- (/ x0 (- 1.0 x1)) x0)

rewrite95.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp`

Counts

2 → 140

Calls

2 calls:

8.0ms	(/ x0 (- 1.0 x1))
81.0ms	(- (/ x0 (- 1.0 x1)) x0)

series119.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ x0 (- 1.0 x1))
76.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify2.6s

Counts

146 → 146

Iterations

Iter	Nodes
done	5000
3	4183
2	1167
1	450
0	190

prune421.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (cbrt x0) (- 1.0 x1))
6.3b	(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×	`expm1-log1p-u` `pow1` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `fma-udef` `div-inv` `flip--`

Counts

2 → 67

Calls

2 calls:

10.0ms	(/ (cbrt x0) (- 1.0 x1))
0.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series232.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(/ (cbrt x0) (- 1.0 x1))
134.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify1.8s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	3803
2	920
1	314
0	151

prune306.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 5.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (sqrt x0) (- (sqrt 1.0) (sqrt x1)))
6.6b	(fma (/ (sqrt x0) (+ (sqrt 1.0) (sqrt x1))) (/ (sqrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

rewrite25.0ms

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-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `fma-udef` `div-inv` `flip--`

Counts

2 → 95

Calls

2 calls:

20.0ms	(/ (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))

series521.0ms

Counts

2 → 6

Calls

2 calls:

164.0ms	(/ (sqrt x0) (- (sqrt 1.0) (sqrt x1)))
357.0ms	(fma (/ (sqrt x0) (+ (sqrt 1.0) (sqrt x1))) (/ (sqrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

simplify1.5s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
3	3032
2	1007
1	375
0	169

prune257.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 5.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
6.9b	(fma (/ (* (cbrt x0) (cbrt x0)) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

rewrite24.0ms

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×	`expm1-log1p-u` `pow1` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `fma-udef` `div-inv` `flip--`

Counts

2 → 95

Calls

2 calls:

20.0ms	(/ (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))

series480.0ms

Counts

2 → 6

Calls

2 calls:

240.0ms	(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
240.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

simplify1.2s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	1653
1	528
0	226

prune297.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 5.0b

regimes100.0ms

Accuracy

0% (2.1b remaining)

Error of 6.9b against oracle of 4.9b and baseline of 6.9b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample1.1s

Algorithm

intervals

Results

461.0ms	8000×	body	80	valid
431.0ms	3948×	pre	10240	exit
79.0ms	4052×	pre	80	true