Details

sample67.0ms

Algorithm

intervals

Results

18.0ms	35×	body	2560	valid
14.0ms	177×	body	80	valid
13.0ms	19×	body	1280	valid
10.0ms	14×	body	5120	valid
2.0ms	7×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify43.0ms

Calls

1 calls:

Slowest

43.0ms

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

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize27.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ (hypot re im) re)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `sqrt-div` `associate-*l/` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Calls

2 calls:

Slowest

12.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms	(+ (hypot re im) re)

series312.0ms

Calls

2 calls:

Slowest

236.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
76.0ms	(+ (hypot re im) re)

simplify492.0ms

Calls

15 calls:

Slowest

207.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
192.0ms	(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
26.0ms	(* (+ (hypot re im) re) 2.0)
26.0ms	(* (+ (hypot re im) re) 2.0)
12.0ms	(* (exp (hypot re im)) (exp re))

prune395.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.0b

localize33.0ms

Local error

Found 2 expressions with local error:

19.2b	(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))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 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)

series533.0ms

Calls

2 calls:

Slowest

331.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
202.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify95.0ms

Calls

9 calls:

Slowest

52.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
29.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
5.0ms	(+ re im)
5.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
0.0ms	(- (+ (* +nan.0 (sqrt 2.0)) (- (+ (* +nan.0 (/ (sqrt 2.0) re)) (- (* +nan.0 (/ (sqrt 2.0) (pow re 2))))))))

prune352.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.9b

localize18.0ms

Local error

Found 3 expressions with local error:

11.0b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.4b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`pow1`
19×	`sqrt-prod`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1`
9×	`pow1/2`
8×	`swap-sqr`
6×	`associate-r` `associate-l`
5×	`add-cbrt-cube` `add-exp-log` `pow-prod-up` `add-log-exp`
4×	`pow-prod-down` `unswap-sqr`
3×	`expm1-log1p-u` `pow-sqr` `insert-posit16` `log1p-expm1-u`
2×	`flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `fma-def` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

3 calls:

Slowest

23.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
20.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
17.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

series463.0ms

Calls

3 calls:

Slowest

292.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
105.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
66.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify1.6s

Calls

75 calls:

Slowest

370.0ms	(sqrt (* (- (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (* re re)) 2.0))
358.0ms	(sqrt (* (+ (pow (* (sqrt (hypot re im)) (sqrt (hypot re im))) 3) (pow re 3)) 2.0))
163.0ms	(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp re))
160.0ms	(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
73.0ms	(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 15.9b

localize47.0ms

Local error

Found 4 expressions with local error:

10.0b	(+ (* (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im)))) re)
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Calls

4 calls:

Slowest

67.0ms	(+ (* (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im)))) re)
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series552.0ms

Calls

4 calls:

Slowest

159.0ms	(cbrt (hypot re im))
156.0ms	(cbrt (hypot re im))
153.0ms	(cbrt (hypot re im))
83.0ms	(+ (* (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im)))) re)

simplify1.2s

Calls

23 calls:

Slowest

360.0ms	(* (exp (* (* (sqrt (hypot re im)) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (sqrt (cbrt (hypot re im))))) (exp re))
210.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
195.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
194.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
29.0ms	(pow (/ -1 re) -1/3)

prune982.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 15.8b

regimes256.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch3.0ms

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	707×	body	2560	valid
852.0ms	6009×	body	80	valid
261.0ms	305×	body	5120	valid
254.0ms	434×	body	1280	valid
228.0ms	307×	body	640	valid
50.0ms	147×	body	320	valid
21.0ms	91×	body	160	valid