Details

Time bar (total: 40.8s)

sample68.0ms

Algorithm
intervals
Results
39.0ms443×body80valid

simplify7.9s

Counts
1 → 1
Iterations
IterNodes
done5003
62763
51086
4382
3146
255
124
011

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.9b

localize163.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 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))
0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
8.4b
(* (- (* x.re x.re) (* x.im x.im)) x.re)

rewrite296.0ms

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-+ insert-posit16 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 → 83
Calls
4 calls:
27.0ms
(+ (* x.re x.im) (* x.im x.re))
107.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
68.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
89.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)

series305.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(+ (* x.re x.im) (* x.im x.re))
90.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
84.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
86.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)

simplify5.2s

Counts
95 → 95
Iterations
IterNodes
done5000
21918
1437
0153

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize159.0ms

Local error

Found 4 expressions with local error:

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

rewrite495.0ms

Algorithm
rewrite-expression-head
Rules
44×associate-*l/
18×flip3-+ flip-+
16×frac-sub
15×add-sqr-sqrt
13×pow1 *-un-lft-identity add-cbrt-cube add-exp-log
12×frac-times associate-*l*
11×flip3-- flip--
9×add-cube-cbrt
7×associate-*r*
6×associate-*r/ add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×*-commutative
2×unswap-sqr
1×sub-neg fma-neg diff-log prod-diff distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 111
Calls
4 calls:
50.0ms
(* (- x.re x.im) x.re)
190.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
82.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
162.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))

series311.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (- x.re x.im) x.re)
84.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
67.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
102.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))

simplify8.0s

Counts
123 → 123
Iterations
IterNodes
done5000
24225
1801
0228

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize120.0ms

Local error

Found 3 expressions with local error:

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

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
15×associate-*l*
12×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log
8×add-cube-cbrt
4×distribute-rgt-in distribute-lft-in associate-*r* pow-prod-down prod-exp associate-*r/ cbrt-unprod
3×distribute-lft-neg-in expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u add-log-exp
2×associate-*l/ *-commutative
1×distribute-lft-neg-out neg-mul-1 flip3-+ flip3-- flip-+ fma-udef flip-- distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 71
Calls
3 calls:
75.0ms
(* (- x.re x.im) x.re)
3.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (* (- x.im) (* x.im (+ x.re x.re))))
125.0ms
(* (- x.im) (* x.im (+ x.re x.re)))

series255.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(* (- x.re x.im) x.re)
165.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.re) (* (- x.im) (* x.im (+ x.re x.re))))
34.0ms
(* (- x.im) (* x.im (+ x.re x.re)))

simplify3.0s

Counts
80 → 80
Iterations
IterNodes
done5000
21124
1309
0123

prune996.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize262.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
12.4b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.4b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
12.4b
(cbrt (+ (* x.re x.im) (* x.im x.re)))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 flip-+
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube insert-posit16 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 → 99
Calls
4 calls:
134.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
22.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
24.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
22.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

series1.1s

Counts
4 → 12
Calls
4 calls:
362.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
237.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
230.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
252.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify4.8s

Counts
111 → 111
Iterations
IterNodes
done5000
32077
2778
1313
0125

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes447.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify20.0ms

Iterations
IterNodes
done28
428
326
220
116
010

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.0s14408×body80valid