Details

sample40.0ms

Algorithm

intervals

Results

18.0ms	132×	pre	10240	exit
6.0ms	256×	body	80	valid
3.0ms	124×	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: 7.7b

localize4.0ms

Local error

Found 2 expressions with local error:

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

rewrite55.0ms

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))
42.0ms	(- (/ 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)

simplify924.0ms

Counts

146 → 146

Iterations

Useful iterations: done (920.0ms)

Iter	Nodes	Cost
0	190	2805
1	432	2150
2	1494	1737
done	5000	1659

prune155.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.7b

localize10.0ms

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))

rewrite9.0ms

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:

6.0ms	(/ (cbrt x0) (- 1.0 x1))
0.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series183.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(/ (cbrt x0) (- 1.0 x1))
93.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify424.0ms

Counts

73 → 73

Iterations

Useful iterations: done (422.0ms)

Iter	Nodes	Cost
0	151	1049
1	312	968
2	1038	878
done	5001	872

prune160.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.7b

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (cbrt x0) (- 1.0 x1))
0.7b	(exp (log (fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
6.1b	(fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

6.0ms	(/ (cbrt x0) (- 1.0 x1))
2.0ms	(exp (log (fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
0.0ms	(fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series283.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(/ (cbrt x0) (- 1.0 x1))
100.0ms	(exp (log (fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
97.0ms	(fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify433.0ms

Counts

93 → 93

Iterations

Useful iterations: done (429.0ms)

Iter	Nodes	Cost
0	193	1422
1	388	1319
2	1232	1199
done	5001	1189

prune252.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.7b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (cbrt x0) (- 1.0 x1))
1.5b	(pow E (log (fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
6.1b	(fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

6.0ms	(/ (cbrt x0) (- 1.0 x1))
2.0ms	(pow E (log (fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
0.0ms	(fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series1.8m

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (cbrt x0) (- 1.0 x1))
1.7m	(pow E (log (fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))))
96.0ms	(fma (pow x0 2/3) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify535.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (148.0ms)

Iter	Nodes	Cost
0	220	1652
1	477	1541
2	1597	1439
done	5000	1439

prune251.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.7b

regimes66.0ms

Accuracy

42.1% (1.2b remaining)

Error of 6.1b against oracle of 4.9b and baseline of 6.9b

bsearch29.0ms

Steps

Iters	Range		Point
7	0.000209	0.0186	0.00021208908081054686

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	58
1	34	58
2	36	58
done	36	58

end0.0ms

sample695.0ms

Algorithm

intervals

Results

365.0ms	3916×	pre	10240	exit
131.0ms	8000×	body	80	valid
63.0ms	4084×	pre	80	true