Details

Time bar (total: 17.3s)

sample54.0ms

Algorithm
intervals
Results
43.0ms480×body80valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done2012
62012
51086
4382
3146
255
124
011

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.0b

localize44.0ms

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))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
6.0b
(* (- (* x.re x.re) (* x.im x.im)) x.re)

rewrite113.0ms

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:
7.0ms
(+ (* x.re x.im) (* x.im x.re))
46.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
36.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
23.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)

series209.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* x.re x.im) (* x.im x.re))
76.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
36.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
60.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)

simplify1.5s

Counts
95 → 95
Iterations
IterNodes
done2006
32006
21872
1436
0153

prune998.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
88×distribute-rgt-in distribute-lft-in
73×prod-diff
57×add-sqr-sqrt *-un-lft-identity
55×add-cube-cbrt
44×associate--l+
24×associate-*l/ associate-*r/
19×flip3-+ flip-+
16×frac-sub
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
10×flip3-- flip--
9×sub-neg
8×add-log-exp
7×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
2×*-commutative
1×+-commutative sum-log fma-def fma-neg diff-log distribute-lft-out unswap-sqr
Counts
4 → 189
Calls
4 calls:
7.0ms
(+ (* x.re x.im) (* x.im x.re))
57.0ms
(- (* (+ x.re x.im) (* x.re (- x.re x.im))) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
23.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
50.0ms
(* (+ x.re x.im) (* x.re (- x.re x.im)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* x.re x.im) (* x.im x.re))
95.0ms
(- (* (+ x.re x.im) (* x.re (- x.re x.im))) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
42.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
71.0ms
(* (+ x.re x.im) (* x.re (- x.re x.im)))

simplify1.2s

Counts
201 → 201
Iterations
IterNodes
done2000
22000
11209
0334

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
12×distribute-rgt-in distribute-lft-in
11×associate-*r*
8×pow1 add-cbrt-cube add-exp-log
6×associate-*l* add-log-exp
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u
2×sub-neg flip3-+ distribute-rgt-out count-2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out unswap-sqr
1×+-commutative sum-log fma-def flip3-- fma-udef flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 104
Calls
4 calls:
21.0ms
(* x.re (- x.re x.im))
8.0ms
(+ (* x.im x.re) (* x.im x.re))
18.0ms
(* x.im (+ (* x.im x.re) (* x.im x.re)))
0.0ms
(fma (+ x.re x.im) (* x.re (- x.re x.im)) (- (* x.im (+ (* x.im x.re) (* x.im x.re)))))

series267.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* x.re (- x.re x.im))
36.0ms
(+ (* x.im x.re) (* x.im x.re))
29.0ms
(* x.im (+ (* x.im x.re) (* x.im x.re)))
133.0ms
(fma (+ x.re x.im) (* x.re (- x.re x.im)) (- (* x.im (+ (* x.im x.re) (* x.im x.re)))))

simplify1.2s

Counts
116 → 116
Iterations
IterNodes
done2015
32015
21295
1413
0165

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

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))))
13.3b
(cbrt (+ (* x.im x.re) (* x.im x.re)))
13.3b
(cbrt (+ (* x.im x.re) (* x.im x.re)))
13.3b
(cbrt (+ (* x.im x.re) (* x.im x.re)))

rewrite71.0ms

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 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 → 117
Calls
4 calls:
37.0ms
(* (cbrt (+ (* x.im x.re) (* x.im x.re))) (cbrt (+ (* x.im x.re) (* x.im x.re))))
6.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))
18.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))
8.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))

series614.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(* (cbrt (+ (* x.im x.re) (* x.im x.re))) (cbrt (+ (* x.im x.re) (* x.im x.re))))
146.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))
135.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))
128.0ms
(cbrt (+ (* x.im x.re) (* x.im x.re)))

simplify991.0ms

Counts
129 → 129
Iterations
IterNodes
done2000
32000
2792
1314
0139

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes136.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done27
327
222
118
010

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.8s14400×body80valid