Details

sample210.0ms

Algorithm

intervals

Results

28.0ms	185×	body	80	valid
28.0ms	34×	body	2560	valid
10.0ms	15×	body	1280	valid
7.0ms	7×	body	5120	valid
4.0ms	8×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify456.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

455.0ms

(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.8b	(- (hypot re im) re)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.0b	(hypot re im)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3--` `sqrt-div` `associate-*l/` `flip--`
1×	`hypot-udef` `sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

Slowest

15.0ms	(- (hypot re im) re)
10.0ms	(sqrt (* (- (hypot re im) re) 2.0))
0.0ms	(hypot re im)

series439.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

281.0ms	(sqrt (* (- (hypot re im) re) 2.0))
89.0ms	(- (hypot re im) re)
69.0ms	(hypot re im)

simplify1.0s

Counts

38 → 65

Calls

38 calls:

Slowest

260.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
154.0ms	(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
92.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
54.0ms	(* (- (hypot re im) re) 2.0)
51.0ms	(* (- (hypot re im) re) 2.0)

prune474.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.3b

localize30.0ms

Local error

Found 4 expressions with local error:

17.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0b	(hypot re im)
0.0b	(hypot re im)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

4 → 47

Calls

4 calls:

Slowest

4.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0ms	(hypot re im)
0.0ms	(hypot re im)

series698.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

370.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
191.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
81.0ms	(hypot re im)
56.0ms	(hypot re im)

simplify99.0ms

Counts

15 → 59

Calls

15 calls:

Slowest

42.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
31.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
12.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
3.0ms	(* -1 re)
3.0ms	(* -1 re)

prune714.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 15.2b

localize44.0ms

Local error

Found 4 expressions with local error:

17.2b	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (- re))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re 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 (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (- re))

series661.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

182.0ms	(cbrt (hypot re im))
162.0ms	(cbrt (hypot re im))
161.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (- re))
155.0ms	(cbrt (hypot re im))

simplify794.0ms

Counts

21 → 65

Calls

21 calls:

Slowest

235.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
201.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
175.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
26.0ms	(pow (/ 1 re) -1/3)
26.0ms	(pow (/ -1 re) -1/3)

prune1.0s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 15.2b

localize46.0ms

Local error

Found 4 expressions with local error:

7.6b	(+ (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) (- re))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-log-exp`
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`
3×	`pow1/3`
2×	`sum-log`
1×	`neg-sub0` `+-commutative` `associate-+r-` `fma-def` `flip3-+` `unsub-neg` `neg-log` `flip-+`

Counts

4 → 61

Calls

4 calls:

Slowest

56.0ms	(+ (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) (- re))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series559.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

159.0ms	(cbrt (hypot re im))
156.0ms	(cbrt (hypot re im))
141.0ms	(cbrt (hypot re im))
102.0ms	(+ (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) (- re))

simplify1.4s

Counts

24 → 73

Calls

24 calls:

Slowest

306.0ms	(* (exp (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))))) (/ 1 (exp re)))
280.0ms	(* (exp (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))))) (exp (- re)))
217.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
201.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
190.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))

prune966.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 15.2b

regimes343.0ms

Accuracy

0% (0.3b remaining)

Error of 13.9b against oracle of 13.6b and baseline of 13.9b

bsearch4.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

839.0ms	5955×	body	80	valid
821.0ms	486×	body	1280	valid
719.0ms	737×	body	2560	valid
266.0ms	283×	body	5120	valid
163.0ms	286×	body	640	valid
60.0ms	166×	body	320	valid
19.0ms	87×	body	160	valid