Details

sample132.0ms

Algorithm

intervals

Results

42.0ms	9×	body	5120	valid
26.0ms	204×	body	80	valid
14.0ms	19×	body	2560	valid
6.0ms	12×	body	1280	valid
3.0ms	6×	body	640	valid
2.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify121.0ms

Calls

1 calls:

Slowest

121.0ms

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.4b

localize25.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (hypot re im) re)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `fma-neg` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*l/` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
1×	`sub-neg` `pow1/2` `sqrt-prod`

Calls

2 calls:

Slowest

13.0ms	(- (hypot re im) re)
7.0ms	(sqrt (* (- (hypot re im) re) 2.0))

series725.0ms

Calls

2 calls:

Slowest

471.0ms	(- (hypot re im) re)
254.0ms	(sqrt (* (- (hypot re im) re) 2.0))

simplify447.0ms

Calls

11 calls:

Slowest

250.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
161.0ms	(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
9.0ms	(sqrt (- (hypot re im) re))
8.0ms	(- im re)
5.0ms	(* -2 re)

prune415.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
0.2b	(- (hypot re im) re)
0.0b	(sqrt (- (hypot re im) re))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `sqrt-prod`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`sqrt-div`
3×	`expm1-log1p-u` `flip3--` `pow1/2` `fma-neg` `associate-r` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`pow-prod-down` `associate-*l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

3 calls:

Slowest

9.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
5.0ms	(sqrt (- (hypot re im) re))
4.0ms	(- (hypot re im) re)

series499.0ms

Calls

3 calls:

Slowest

248.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
186.0ms	(sqrt (- (hypot re im) re))
64.0ms	(- (hypot re im) re)

simplify936.0ms

Calls

32 calls:

Slowest

335.0ms	(* (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) (sqrt (- (hypot re im) re))) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
188.0ms	(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt 2.0))
115.0ms	(sqrt (- (* (hypot re im) (hypot re im)) (* re re)))
45.0ms	(* (- (hypot re im) re) 2.0)
34.0ms	(* (- (hypot re im) re) 2.0)

prune637.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 10.3b

localize15.0ms

Local error

Found 2 expressions with local error:

12.8b	(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))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

2.0ms	(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))

series445.0ms

Calls

2 calls:

Slowest

282.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
163.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify17.0ms

Calls

7 calls:

Slowest

12.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
3.0ms	(- im re)
0.0ms	(- (+ re (- (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))))
0.0ms	(- (+ re (- (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))))
0.0ms	(- (+ (* +nan.0 (* (sqrt 2.0) (* re im))) (- (+ (* +nan.0 (* (sqrt 2.0) (pow im 2))) (- (* +nan.0 (* (sqrt 2.0) im)))))))

prune368.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.3b

localize22.0ms

Local error

Found 4 expressions with local error:

12.5b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(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`

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 (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series778.0ms

Calls

4 calls:

Slowest

216.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
194.0ms	(cbrt (hypot re im))
193.0ms	(cbrt (hypot re im))
174.0ms	(cbrt (hypot re im))

simplify515.0ms

Calls

21 calls:

Slowest

141.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
131.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
98.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
21.0ms	(- (* 2 re))
16.0ms	(pow (/ 1 re) -1/3)

prune739.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.2b

regimes245.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch3.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	663×	body	2560	valid
1.1s	6083×	body	80	valid
325.0ms	450×	body	1280	valid
283.0ms	296×	body	5120	valid
145.0ms	279×	body	640	valid
57.0ms	148×	body	320	valid
20.0ms	81×	body	160	valid