Details

sample70.0ms

Algorithm

intervals

Results

56.0ms

471×

body

valid

simplify440.0ms

Calls

1 calls:

Slowest

440.0ms

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.0b

localize45.0ms

Local error

Found 4 expressions with local error:

4.1b	(* (- (* x.re x.re) (* x.im x.im)) x.re)
0.2b	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.1b	(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
0.0b	(- (* x.re x.re) (* x.im x.im))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

1827×	`associate-l`
1816×	`add-sqr-sqrt`
1209×	`*-un-lft-identity`
1149×	`prod-diff`
629×	`difference-of-squares`
612×	`*-commutative`
393×	`swap-sqr`
381×	`associate-r`
358×	`add-cube-cbrt`
352×	`unswap-sqr`
283×	`distribute-lft-out`
188×	`distribute-lft-out--`
174×	`distribute-rgt-out`
57×	`fma-neg`
12×	`associate-*l/`
8×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `cbrt-unprod`

Calls

4 calls:

Slowest

919.0ms	(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
107.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.re)
65.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
42.0ms	(- (* x.re x.re) (* x.im x.im))

series218.0ms

Calls

4 calls:

Slowest

73.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.re)
66.0ms	(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
41.0ms	(- (* x.re x.re) (* x.im x.im))
38.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)

simplify7.7m

Calls

2517 calls:

Slowest

992.0ms	(* (+ (* (* 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)))
964.0ms	(fma (+ x.re x.im) (* (- x.re x.im) x.re) (- (* (+ (* x.re x.im) (* x.im x.re)) x.im)))
824.0ms	(fma (- (+ (* x.re x.im) (* x.im x.re))) x.im (* (+ (* x.re x.im) (* x.im x.re)) x.im))
803.0ms	(fma (- (* x.re x.re) (* x.im x.im)) x.re (- (* (* (+ (* x.re 1) x.re) x.im) x.im)))
775.0ms	(fma (- (* (+ x.im (* x.im 1)) x.im)) x.re (* (* (+ x.im (* x.im 1)) x.im) x.re))

prune7.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

22.2b	(sqrt (* x.re x.re))
22.2b	(sqrt (* x.re x.re))
0.2b	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.1b	(fma (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re) (- (* (+ (* x.re x.im) (* x.im x.re)) x.im)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`sqrt-prod`
26×	`*-un-lft-identity`
23×	`associate-l`
22×	`pow1`
16×	`add-cube-cbrt`
12×	`sqrt-pow1`
11×	`associate-r` `*-commutative`
10×	`rem-sqrt-square`
8×	`swap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `distribute-rgt-out` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`pow2` `pow-plus` `pow1/2` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `fma-udef`

Calls

4 calls:

Slowest

59.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
6.0ms	(sqrt (* x.re x.re))
6.0ms	(sqrt (* x.re x.re))
0.0ms	(fma (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re) (- (* (+ (* x.re x.im) (* x.im x.re)) x.im)))

series128.0ms

Calls

4 calls:

Slowest

81.0ms	(fma (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re) (- (* (+ (* x.re x.im) (* x.im x.re)) x.im)))
31.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
8.0ms	(sqrt (* x.re x.re))
8.0ms	(sqrt (* x.re x.re))

simplify1.5s

Calls

63 calls:

Slowest

230.0ms	(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
229.0ms	(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
225.0ms	(- (pow x.re 3) (* 3 (* (pow x.im 2) x.re)))
164.0ms	(* (+ (pow (* x.re x.im) 3) (pow (* x.im x.re) 3)) x.im)
150.0ms	(* (- (* (* x.re x.im) (* x.re x.im)) (* (* x.im x.re) (* x.im x.re))) x.im)

prune932.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (* x.re 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)))
0.1b	(* x.re (* x.re x.re))
0.0b	(- (* x.re (* x.re x.re)) (* x.im (+ (+ (* x.re x.im) (* x.re x.im)) (* x.re x.im))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

2576×	`associate-r`
2145×	`*-un-lft-identity`
1935×	`add-sqr-sqrt`
1428×	`prod-diff`
1364×	`distribute-lft-out`
1297×	`associate-l`
743×	`add-cube-cbrt`
602×	`unswap-sqr`
466×	`distribute-rgt-out`
465×	`*-commutative`
302×	`distribute-lft1-in`
214×	`swap-sqr`
182×	`distribute-rgt1-in`
37×	`fma-def`
28×	`fma-neg`
20×	`pow1`
12×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
10×	`+-commutative` `associate-+l+`
8×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`sum-log`
2×	`flip3-+` `cube-unmult` `associate-*r/` `flip-+`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-sqr` `flip--`

Calls

4 calls:

Slowest

729.0ms	(- (* x.re (* x.re x.re)) (* x.im (+ (+ (* x.re x.im) (* x.re x.im)) (* x.re x.im))))
225.0ms	(* x.im (+ (+ (* x.re x.im) (* x.re x.im)) (* x.re x.im)))
102.0ms	(+ (+ (* x.re x.im) (* x.re x.im)) (* x.re x.im))
17.0ms	(* x.re (* x.re x.re))

series465.0ms

Calls

4 calls:

Slowest

377.0ms	(- (* x.re (* x.re x.re)) (* x.im (+ (+ (* x.re x.im) (* x.re x.im)) (* x.re x.im))))
33.0ms	(+ (+ (* x.re x.im) (* x.re x.im)) (* x.re x.im))
32.0ms	(* x.re (* x.re x.re))
22.0ms	(* x.im (+ (+ (* x.re x.im) (* x.re x.im)) (* x.re x.im)))