Details

sample58.0ms

Algorithm

intervals

Results

29.0ms	128×	pre	10240	exit
8.0ms	256×	body	80	valid
3.0ms	128×	pre	80	true

simplify7.0ms

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: 8.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(/ x0 (- 1.0 x1))
7.6b	(- (/ x0 (- 1.0 x1)) x0)

rewrite138.0ms

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:

16.0ms	(/ x0 (- 1.0 x1))
114.0ms	(- (/ x0 (- 1.0 x1)) x0)

series128.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ x0 (- 1.0 x1))
69.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify904.0ms

Counts

146 → 146

Iterations

Useful iterations: done (900.0ms)

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

prune221.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (cbrt x0) (- 1.0 x1))
6.5b	(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))

series219.0ms

Counts

2 → 6

Calls

2 calls:

114.0ms	(/ (cbrt x0) (- 1.0 x1))
104.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify583.0ms

Counts

73 → 73

Iterations

Useful iterations: done (580.0ms)

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

prune217.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 5.2b

localize21.0ms

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))

rewrite26.0ms

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:

21.0ms	(/ (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))

series514.0ms

Counts

2 → 6

Calls

2 calls:

250.0ms	(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
264.0ms	(fma (/ (* (cbrt x0) (cbrt x0)) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

simplify1.1s

Counts

101 → 101

Iterations

Useful iterations: 2 (381.0ms)

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

prune263.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 5.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3))
0.5b	(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
0.7b	(pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3)
6.9b	(fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
54×	`times-frac`
42×	`cbrt-prod` `sqrt-prod`
37×	`add-cube-cbrt`
28×	`difference-of-squares`
14×	`distribute-lft-out--`
9×	`associate-/r*`
7×	`add-exp-log`
6×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `pow-exp` `clear-num` `flip--` `rem-cbrt-cube` `fma-udef` `div-inv` `rem-cube-cbrt`

Counts

4 → 143

Calls

4 calls:

2.0ms	(cbrt (pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3))
30.0ms	(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
4.0ms	(pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3)
1.0ms	(fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

series1.1s

Counts

4 → 12

Calls

4 calls:

226.0ms	(cbrt (pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3))
333.0ms	(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
336.0ms	(pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3)
224.0ms	(fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

simplify1.5s

Counts

155 → 155

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	299	4115
1	779	3690
2	4173	3355
done	5001	3353

prune434.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 5.2b

regimes60.0ms

Accuracy

0% (2.1b remaining)

Error of 7.0b against oracle of 4.9b and baseline of 7.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	11	16
1	13	14
done	13	14

end0.0ms

sample1.3s

Algorithm

intervals

Results

526.0ms	8000×	body	80	valid
497.0ms	4054×	pre	10240	exit
69.0ms	3946×	pre	80	true