Details

Time bar (total: 17.0s)

sample56.0ms

Algorithm
intervals
Results
38.0ms451×body80valid

simplify5.6s

Counts
1 → 1
Iterations

Useful iterations: 6 (2.5s)

IterNodesCost
011362
124322
255322
3146322
4382282
51086243
62763203
done5003203

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x.re x.im) (* x.im x.re))
0.1b
(* (+ (* 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))
8.6b
(* (- (* x.re x.re) (* x.im x.im)) x.re)

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt associate-*l/
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
7×associate-*l*
6×associate-*r*
4×expm1-log1p-u flip3-+ flip3-- frac-sub flip-+ log1p-expm1-u flip--
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log sub-neg fma-def fma-neg diff-log prod-diff difference-of-squares
Counts
4 → 79
Calls
4 calls:
8.0ms
(+ (* x.re x.im) (* x.im x.re))
23.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
32.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
24.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)

series240.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* x.re x.im) (* x.im x.re))
42.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
98.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
71.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)

simplify3.0s

Counts
91 → 91
Iterations

Useful iterations: done (3.0s)

IterNodesCost
014932683
143124145
2183123111
done500221019

prune509.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
42×associate-*l/
19×flip3-+ flip-+
16×frac-sub
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
10×flip3-- flip--
9×add-sqr-sqrt *-un-lft-identity
8×add-log-exp
7×associate-*l* add-cube-cbrt
6×associate-*r/
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×*-commutative
1×+-commutative sum-log sub-neg fma-def fma-neg diff-log prod-diff distribute-lft-out unswap-sqr
Counts
4 → 97
Calls
4 calls:
12.0ms
(+ (* x.re x.im) (* x.im x.re))
23.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
76.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
65.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))

series235.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* x.re x.im) (* x.im x.re))
53.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
76.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
77.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))

simplify2.8s

Counts
109 → 109
Iterations

Useful iterations: done (2.8s)

IterNodesCost
021156612
176939441
2413936969
done500036945

prune662.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
9×associate-*r*
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
2×flip3-+ distribute-rgt-out count-2 pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ distribute-lft-out unswap-sqr
1×distribute-rgt-in +-commutative sum-log fma-def distribute-lft-in flip3-- fma-udef flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 78
Calls
4 calls:
36.0ms
(* (- x.re x.im) x.re)
17.0ms
(+ (* x.im x.re) (* x.im x.re))
20.0ms
(* x.im (+ (* x.im x.re) (* x.im x.re)))
0.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (- (* x.im (+ (* x.im x.re) (* x.im x.re)))))

series244.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (- x.re x.im) x.re)
39.0ms
(+ (* x.im x.re) (* x.im x.re))
37.0ms
(* x.im (+ (* x.im x.re) (* x.im x.re)))
117.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (- (* x.im (+ (* x.im x.re) (* x.im x.re)))))

simplify1.7s

Counts
90 → 90
Iterations

Useful iterations: done (1.7s)

IterNodesCost
011318443
129315383
2110414772
done500014692

prune521.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (* x.im x.re) (* x.im x.re))) (cbrt (+ (* x.im x.re) (* x.im x.re))))
11.9b
(cbrt (+ (* x.im x.re) (* x.im x.re)))
11.9b
(cbrt (+ (* x.im x.re) (* x.im x.re)))
11.9b
(cbrt (+ (* x.im x.re) (* x.im x.re)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
46×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr associate-*r* associate-*l* flip-+
7×distribute-rgt-out count-2 distribute-lft-out
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 113
Calls
4 calls:
68.0ms
(* (cbrt (+ (* x.im x.re) (* x.im x.re))) (cbrt (+ (* x.im x.re) (* x.im x.re))))
7.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))
7.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))
7.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))

series656.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(* (cbrt (+ (* x.im x.re) (* x.im x.re))) (cbrt (+ (* x.im x.re) (* x.im x.re))))
144.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))
150.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))
143.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))

simplify127.0ms

Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
013740397