Details

sample70.0ms

Algorithm

intervals

Results

56.0ms

455×

body

valid

simplify285.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

284.0ms

(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.6b

localize44.0ms

Local error

Found 4 expressions with local error:

4.6b	(* (- (* x.re x.re) (* x.im x.im)) x.im)
0.2b	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.2b	(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.0b	(+ (* x.re x.im) (* x.im x.re))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `associate-*l/`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
7×	`associate-l`
6×	`associate-r`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `frac-add` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`+-commutative` `sum-log` `fma-def` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`difference-of-squares`

Counts

4 → 81

Calls

4 calls:

Slowest

45.0ms	(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
29.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
24.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.im)
15.0ms	(+ (* x.re x.im) (* x.im x.re))

series256.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
99.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.im)
29.0ms	(+ (* x.re x.im) (* x.im x.re))
28.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify8.6s

Counts

46 → 93

Calls

46 calls:

Slowest

1.5s	(* (+ (* (* x.re x.re) (* x.re x.re)) (+ (* (* x.im x.im) (* x.im x.im)) (* (* x.re x.re) (* x.im x.im)))) (- (* x.re x.im) (* x.im x.re)))
617.0ms	(+ (* (* (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))) x.im) (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re))))) (* (+ (* x.re x.re) (* x.im x.im)) (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)))
453.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.im)
429.0ms	(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))
384.0ms	(- (* 3 (* x.im (pow x.re 2))) (pow x.im 3))

prune927.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x.im (+ x.re x.im)) (- x.re x.im))
0.2b	(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.2b	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.0b	(* x.im (+ x.re x.im))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
36×	`prod-diff`
33×	`add-cube-cbrt`
26×	`associate-*r/`
24×	`associate-*l/`
23×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+l+`
20×	`flip3-+` `flip-+`
16×	`frac-add`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`frac-times` `associate-r`
9×	`flip3--` `flip--`
7×	`associate-l`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`+-commutative` `sum-log` `fma-def` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 155

Calls

4 calls:

Slowest

40.0ms	(* (* x.im (+ x.re x.im)) (- x.re x.im))
38.0ms	(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
36.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
13.0ms	(* x.im (+ x.re x.im))

series243.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

90.0ms	(* (* x.im (+ x.re x.im)) (- x.re x.im))
90.0ms	(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
32.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
31.0ms	(* x.im (+ x.re x.im))

simplify29.0s

Counts

139 → 167

Calls

139 calls:

Slowest

1.2s	(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
925.0ms	(+ (* (* (* x.im (- (* x.re x.re) (* x.im x.im))) (- (pow x.re 3) (pow x.im 3))) (- (* x.re x.im) (* x.im x.re))) (* (* (- x.re x.im) (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im)))) (* (- (* (* x.re x.im) (* x.re x.im)) (* (* x.im x.re) (* x.im x.re))) x.re)))
837.0ms	(* (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im))) (- (* x.re x.im) (* x.im x.re)))
648.0ms	(* (* (+ (* x.re x.re) (- (* x.im x.im) (* x.re x.im))) (+ (* x.re x.re) (+ (* x.im x.im) (* x.re x.im)))) (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re)))))
639.0ms	(+ (* (* (* x.im (+ x.re x.im)) (- (* x.re x.re) (* x.im x.im))) (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re))))) (* (+ x.re x.im) (* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.re)))

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

59.3b	(fma (- (cbrt x.im)) (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (* (cbrt x.im) (cbrt x.im))))
0.6b	(cbrt x.im)
0.6b	(cbrt x.im)
0.6b	(cbrt x.im)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

Slowest

1.0ms	(cbrt x.im)
1.0ms	(cbrt x.im)
1.0ms	(cbrt x.im)
0.0ms	(fma (- (cbrt x.im)) (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (* (cbrt x.im) (cbrt x.im))))

series1.8s

Counts

4 → 12

Calls

4 calls:

Slowest

807.0ms	(fma (- (cbrt x.im)) (* (cbrt x.im) (cbrt x.im)) (* (cbrt x.im) (* (cbrt x.im) (cbrt x.im))))
345.0ms	(cbrt x.im)
312.0ms	(cbrt x.im)
296.0ms	(cbrt x.im)

simplify566.0ms

Counts

21 → 65

Calls

21 calls:

Slowest

157.0ms	(* (pow (* x.im -1) 1/3) (cbrt -1))
153.0ms	(* (pow (* x.im -1) 1/3) (cbrt -1))
117.0ms	(* (pow (* x.im -1) 1/3) (cbrt -1))
35.0ms	(pow (/ 1 x.im) -1/3)
32.0ms	(pow (/ 1 x.im) -1/3)

prune915.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize107.0ms

Local error

Found 4 expressions with local error:

58.5b	(fma (- (cbrt x.im)) (* (cbrt x.im) (cbrt x.im)) (* (* (* (cbrt (cbrt x.im)) (cbrt (cbrt x.im))) (cbrt (cbrt x.im))) (* (cbrt x.im) (cbrt x.im))))
0.7b	(cbrt (cbrt x.im))
0.7b	(cbrt (cbrt x.im))
0.7b	(cbrt (cbrt x.im))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 62

Calls

4 calls:

Slowest

2.0ms	(cbrt (cbrt x.im))
2.0ms	(cbrt (cbrt x.im))
2.0ms	(cbrt (cbrt x.im))
1.0ms	(fma (- (cbrt x.im)) (* (cbrt x.im) (cbrt x.im)) (* (* (* (cbrt (cbrt x.im)) (cbrt (cbrt x.im))) (cbrt (cbrt x.im))) (* (cbrt x.im) (cbrt x.im))))

series2.1s

Counts

4 → 12

Calls

4 calls:

Slowest

832.0ms	(fma (- (cbrt x.im)) (* (cbrt x.im) (cbrt x.im)) (* (* (* (cbrt (cbrt x.im)) (cbrt (cbrt x.im))) (cbrt (cbrt x.im))) (* (cbrt x.im) (cbrt x.im))))
437.0ms	(cbrt (cbrt x.im))
436.0ms	(cbrt (cbrt x.im))
381.0ms	(cbrt (cbrt x.im))

simplify2.9s

Counts

30 → 74

Calls

30 calls:

Slowest

1.1s	(* (pow (* x.im -1) 1/9) (pow (cbrt -1) 1/3))
790.0ms	(* (pow (* x.im -1) 1/9) (pow (cbrt -1) 1/3))
730.0ms	(* (pow (* x.im -1) 1/9) (pow (cbrt -1) 1/3))
26.0ms	(pow (/ 1 x.im) -1/9)
20.0ms	(pow (/ 1 x.im) -1/9)

prune1.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes141.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch4.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

2.2s

14490×

body

valid