Details

Time bar (total: 1.1m)

sample106.0ms

Algorithm
intervals
Results
92.0ms475×body80valid

simplify411.0ms

Calls
1 calls:
Slowest
411.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.7b

localize22.0ms

Local error

Found 4 expressions with local error:

6.7b
(* (- (* x.re x.re) (* x.im x.im)) x.re)
0.1b
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.0b
(+ (* x.re x.im) (* x.im x.re))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
169×associate-*l*
161×*-un-lft-identity
74×add-sqr-sqrt
68×distribute-lft-out--
37×distribute-lft-out
30×*-commutative
29×difference-of-squares
16×unswap-sqr
12×swap-sqr associate-*l/
11×associate-*r*
10×distribute-rgt-out
8×pow1 add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
4×flip3-+ flip3-- frac-sub flip-+ insert-posit16 flip--
2×pow-prod-down prod-exp cbrt-unprod
1×+-commutative sum-log sub-neg diff-log
Calls
4 calls:
Slowest
834.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
109.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
76.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
19.0ms
(+ (* x.re x.im) (* x.im x.re))

series220.0ms

Calls
4 calls:
Slowest
74.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)
71.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
50.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
24.0ms
(+ (* x.re x.im) (* x.im x.re))

simplify22.9s

Calls
127 calls:
Slowest
486.0ms
(* (+ (* (* 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)))
454.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
447.0ms
(- (* (* (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))) x.re) (+ (* (* 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.im)))
437.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
436.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

23.9b
(sqrt (* x.re x.re))
23.9b
(sqrt (* x.re x.re))
0.2b
(* (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)

rewrite587.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
37×associate-*l*
35×sqrt-prod
34×*-un-lft-identity
33×associate-*r*
27×pow1
20×add-cube-cbrt
14×*-commutative
12×sqrt-pow1
11×add-cbrt-cube add-exp-log
10×rem-sqrt-square associate-*l/ unswap-sqr
9×swap-sqr
7×distribute-lft-out
6×pow-prod-down difference-of-squares
4×frac-times flip3-+ distribute-rgt-out prod-exp cbrt-unprod flip-+ insert-posit16 add-log-exp
3×flip3-- flip--
2×pow2 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up
1×distribute-lft-out--
Calls
4 calls:
Slowest
477.0ms
(* (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re))
93.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
8.0ms
(sqrt (* x.re x.re))
5.0ms
(sqrt (* x.re x.re))

series136.0ms

Calls
4 calls:
Slowest
66.0ms
(* (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re))
42.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
17.0ms
(sqrt (* x.re x.re))
11.0ms
(sqrt (* x.re x.re))

simplify7.4s

Calls
104 calls:
Slowest
709.0ms
(* (+ (pow (sqrt (* x.re x.re)) 3) (pow x.im 3)) (* (- (* (sqrt (* x.re x.re)) (sqrt (* x.re x.re))) (* x.im x.im)) x.re))
658.0ms
(* (- (* (sqrt (* x.re x.re)) (sqrt (* x.re x.re))) (* x.im x.im)) (* (- (* (sqrt (* x.re x.re)) (sqrt (* x.re x.re))) (* x.im x.im)) x.re))
549.0ms
(* (- (* (sqrt (* x.re x.re)) (sqrt (* x.re x.re))) (* x.im x.im)) (* (- (sqrt (* x.re x.re)) x.im) x.re))
515.0ms
(* (+ (pow (sqrt (* x.re x.re)) 3) (pow x.im 3)) (* (- (pow (sqrt (* x.re x.re)) 3) (pow x.im 3)) x.re))
413.0ms
(sqrt (sqrt x.re))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

23.9b
(sqrt (* x.re x.re))
23.9b
(sqrt (* x.re x.re))
0.2b
(* (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re))
0.1b
(- (* (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re)) (* x.im (* (+ x.re x.re) x.im)))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
87×add-sqr-sqrt
40×associate-*l/
36×*-un-lft-identity
35×sqrt-prod
28×associate-*r*
27×associate-*l* unswap-sqr
25×pow1
22×associate-*r/
18×add-cube-cbrt
17×flip3-+ flip-+
16×frac-sub
15×difference-of-squares
12×frac-times sqrt-pow1
10×rem-sqrt-square flip3-- flip--
9×add-cbrt-cube swap-sqr add-exp-log
7×*-commutative distribute-lft-out--
6×add-log-exp
5×pow-prod-down
4×insert-posit16
3×prod-exp cbrt-unprod distribute-lft-out
2×pow2 pow-plus pow1/2 pow-sqr pow-prod-up
1×sub-neg diff-log
Calls
4 calls:
Slowest
1.9s
(- (* (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re)) (* x.im (* (+ x.re x.re) x.im)))
326.0ms
(* (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re))
10.0ms
(sqrt (* x.re x.re))
10.0ms
(sqrt (* x.re x.re))

series213.0ms

Calls
4 calls:
Slowest
100.0ms
(* (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re))
94.0ms
(- (* (+ (sqrt (* x.re x.re)) x.im) (* (- (sqrt (* x.re x.re)) x.im) x.re)) (* x.im (* (+ x.re x.re) x.im)))
10.0ms
(sqrt (* x.re x.re))
9.0ms
(sqrt (* x.re x.re))

simplify18.1s

Calls
150 calls:
Slowest
705.0ms
(* (+ (pow (sqrt (* x.re x.re)) 3) (pow x.im 3)) (* (- (* (sqrt (* x.re x.re)) (sqrt (* x.re x.re))) (* x.im x.im)) x.re))
636.0ms
(- (* (* (+ (pow (sqrt (* x.re x.re)) 3) (pow x.im 3)) (* (- (pow (sqrt (* x.re x.re)) 3) (pow x.im 3)) x.re)) (+ (* x.re x.re) (- (* x.re x.re) (* x.re x.re)))) (* (* (+ (* (sqrt (* x.re x.re)) (sqrt (* x.re x.re))) (- (* x.im x.im) (* (sqrt (* x.re x.re)) x.im))) (+ (* (sqrt (* x.re x.re)) (sqrt (* x.re x.re))) (+ (* x.im x.im) (* (sqrt (* x.re x.re)) x.im)))) (* x.im (* (+ (pow x.re 3) (pow x.re 3)) x.im))))
565.0ms
(* (+ (pow (sqrt (* x.re x.re)) 3) (pow x.im 3)) (* (- (pow (sqrt (* x.re x.re)) 3) (pow x.im 3)) x.re))
563.0ms
(- (* (* (- (* (sqrt (* x.re x.re)) (sqrt (* x.re x.re))) (* x.im x.im)) (* (- (pow (sqrt (* x.re x.re)) 3) (pow x.im 3)) x.re)) (+ (* x.re x.re) (- (* x.re x.re) (* x.re x.re)))) (* (* (- (sqrt (* x.re x.re)) x.im) (+ (* (sqrt (* x.re x.re)) (sqrt (* x.re x.re))) (+ (* x.im x.im) (* (sqrt (* x.re x.re)) x.im)))) (* x.im (* (+ (pow x.re 3) (pow x.re 3)) x.im))))
557.0ms
(* (- (* (sqrt (* x.re x.re)) (sqrt (* x.re x.re))) (* x.im x.im)) (* (- (* (sqrt (* x.re x.re)) (sqrt (* x.re x.re))) (* x.im x.im)) x.re))

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

23.9b
(sqrt (* x.re x.re))
23.9b
(sqrt (* x.re x.re))
12.6b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.6b
(cbrt (+ (* x.re x.im) (* x.im x.re)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
30×add-sqr-sqrt sqrt-prod
26×cbrt-prod
20×pow1
16×*-commutative add-cube-cbrt
14×associate-*l*
12×sqrt-pow1 distribute-lft-out
10×rem-sqrt-square associate-*r*
8×distribute-rgt-out swap-sqr
4×cbrt-div add-cbrt-cube add-exp-log insert-posit16 add-log-exp unswap-sqr
2×pow2 flip3-+ pow-plus pow1/2 pow1/3 pow-prod-down pow-sqr pow-prod-up flip-+
Calls
4 calls:
Slowest
25.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
16.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
5.0ms
(sqrt (* x.re x.re))
5.0ms
(sqrt (* x.re x.re))

series274.0ms

Calls
4 calls:
Slowest
124.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
122.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
17.0ms
(sqrt (* x.re x.re))
11.0ms
(sqrt (* x.re x.re))

simplify3.0s

Calls
82 calls:
Slowest
383.0ms
(* (exp (* 1/3 (+ (log x.im) (log x.re)))) (cbrt 2))
365.0ms
(* (exp (* 1/3 (+ (log x.im) (log x.re)))) (cbrt 2))
348.0ms
(* (exp (* -1/3 (+ (log (/ 1 x.im)) (log (/ 1 x.re))))) (cbrt 2))
348.0ms
(* (exp (* -1/3 (+ (log (/ -1 x.re)) (log (/ -1 x.im))))) (cbrt 2))
308.0ms
(* (exp (* -1/3 (+ (log (/ -1 x.re)) (log (/ -1 x.im))))) (cbrt 2))

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes157.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch4.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.2s14602×body80valid