Details

sample54.0ms

Algorithm

intervals

Results

35.0ms

457×

body

valid

simplify6.1s

Counts

1 → 1

Iterations

Useful iterations: 5 (369.0ms)

Iter	Nodes	Cost
0	11	19
1	23	17
2	52	16
3	122	16
4	315	13
5	858	11
6	2015	11
done	5000	11

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3)))
0.2b	(* 3 (* x.im x.re))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`associate-r` `*-commutative` `fma-udef`

Counts

2 → 30

Calls

2 calls:

1.0ms	(fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3)))
26.0ms	(* 3 (* x.im x.re))

series151.0ms

Counts

2 → 6

Calls

2 calls:

115.0ms	(fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3)))
36.0ms	(* 3 (* x.im x.re))

simplify5.5s

Counts

36 → 36

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	55	350
1	124	339
2	393	295
3	1403	295
4	4251	295
done	5000	295

prune121.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x.re (* (* 3 x.im) x.re) (- (pow x.im 3)))
0.2b	(* (* 3 x.im) x.re)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `*-commutative` `fma-udef`

Counts

2 → 30

Calls

2 calls:

1.0ms	(fma x.re (* (* 3 x.im) x.re) (- (pow x.im 3)))
33.0ms	(* (* 3 x.im) x.re)

series154.0ms

Counts

2 → 6

Calls

2 calls:

112.0ms	(fma x.re (* (* 3 x.im) x.re) (- (pow x.im 3)))
42.0ms	(* (* 3 x.im) x.re)

simplify4.3s

Counts

36 → 36

Iterations

Useful iterations: 2 (180.0ms)

Iter	Nodes	Cost
0	59	353
1	131	340
2	473	296
3	1795	296
done	5001	296

prune177.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3)))) (cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3)))))
15.2b	(cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3))))
15.2b	(cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3))))
15.2b	(cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

12.0ms	(* (cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3)))) (cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3)))))
1.0ms	(cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3))))
1.0ms	(cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3))))
1.0ms	(cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3))))

series918.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(* (cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3)))) (cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3)))))
250.0ms	(cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3))))
209.0ms	(cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3))))
246.0ms	(cbrt (fma x.re (* 3 (* x.im x.re)) (- (pow x.im 3))))

simplify3.7s

Counts

93 → 93

Iterations

Useful iterations: 4 (2.2s)

Iter	Nodes	Cost
0	102	2167
1	204	2024
2	504	1844
3	1223	1563
4	3980	1518
done	5000	1518

prune514.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x.re x.im) (* x.im x.re))
0.1b	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.1b	(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
5.5b	(* (- (* x.re x.re) (* x.im x.im)) x.im)

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `associate-*l/`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
6×	`associate-r`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`+-commutative` `fma-def` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`difference-of-squares`

Counts

4 → 77

Calls

4 calls:

18.0ms	(+ (* x.re x.im) (* x.im x.re))
50.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
60.0ms	(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
57.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.im)

series250.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x.re x.im) (* x.im x.re))
25.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
98.0ms	(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
95.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.im)

simplify2.7s

Counts

89 → 89

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	143	1603
1	427	1398
2	1851	1125
done	5000	1030

prune344.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes72.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
done	10	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.7s

14277×

body

valid