Details

sample41.0ms

Algorithm

intervals

Results

17.0ms	140×	pre	10240	exit
7.0ms	256×	body	80	valid
2.0ms	116×	pre	80	true

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ x0 (- 1.0 x1))
7.2b	(- (/ x0 (- 1.0 x1)) x0)

rewrite159.0ms

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:

19.0ms	(/ x0 (- 1.0 x1))
121.0ms	(- (/ x0 (- 1.0 x1)) x0)

series114.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ x0 (- 1.0 x1))
63.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify1.1s

Counts

146 → 146

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	190	2805
1	453	2297
2	1477	1848
done	5000	1715

prune246.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (sqrt x0) (- (sqrt 1.0) (sqrt x1)))
6.2b	(fma (/ (sqrt x0) (+ (sqrt 1.0) (sqrt x1))) (/ (sqrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

rewrite41.0ms

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:

32.0ms	(/ (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))

series839.0ms

Counts

2 → 6

Calls

2 calls:

172.0ms	(/ (sqrt x0) (- (sqrt 1.0) (sqrt x1)))
666.0ms	(fma (/ (sqrt x0) (+ (sqrt 1.0) (sqrt x1))) (/ (sqrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

simplify635.0ms

Counts

101 → 101

Iterations

Useful iterations: done (631.0ms)

Iter	Nodes	Cost
0	169	1872
1	374	1737
2	1387	1605
done	5001	1580

prune188.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 4.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (cbrt x0) (- 1.0 x1))
6.1b	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite16.0ms

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:

13.0ms	(/ (cbrt x0) (- 1.0 x1))
0.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series214.0ms

Counts

2 → 6

Calls

2 calls:

110.0ms	(/ (cbrt x0) (- 1.0 x1))
103.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify519.0ms

Counts

73 → 73

Iterations

Useful iterations: done (516.0ms)

Iter	Nodes	Cost
0	151	1049
1	314	968
2	1105	878
done	5001	849

prune160.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 4.6b

localize16.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
6.6b	(fma (/ (* (cbrt x0) (cbrt x0)) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

rewrite32.0ms

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:

26.0ms	(/ (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))

series488.0ms

Counts

2 → 6

Calls

2 calls:

257.0ms	(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
231.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

simplify777.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (274.0ms)

Iter	Nodes	Cost
0	221	2097
1	525	1968
2	2402	1820
done	5000	1820

prune215.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 4.6b

regimes66.0ms

Accuracy

44.6% (1.3b remaining)

Error of 6.1b against oracle of 4.9b and baseline of 7.1b

bsearch21.0ms

Steps

Iters	Range		Point
4	1.855	2.985	1.8749218749999998

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	56
1	31	56
done	31	56

end0.0ms

sample941.0ms

Algorithm

intervals

Results

471.0ms	4006×	pre	10240	exit
161.0ms	8000×	body	80	valid
98.0ms	3994×	pre	80	true