Details

Time bar (total: 13.1s)

sample96.0ms

Algorithm
intervals
Results
80.0ms437×body80valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done2049
72049
61781
5723
4268
3110
250
123
011

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x.re x.re) (* x.im x.im))
0.1b
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
7.7b
(* (- (* x.re x.re) (* x.im x.im)) x.im)

rewrite73.0ms

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-add flip-+ insert-posit16 log1p-expm1-u flip--
2×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
1×+-commutative sum-log sub-neg fma-def fma-neg diff-log prod-diff
Counts
4 → 84
Calls
4 calls:
8.0ms
(- (* x.re x.re) (* x.im x.im))
20.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
19.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
25.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

series208.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* x.re x.re) (* x.im x.im))
87.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
22.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
63.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

simplify1.1s

Counts
96 → 96
Iterations
IterNodes
done2002
32002
21753
1439
0153

prune433.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
37×*-un-lft-identity
36×prod-diff
33×add-cube-cbrt
26×associate-*r/
24×associate-*l/
23×distribute-rgt-in distribute-lft-in
22×associate-+l+
20×flip3-+ flip-+
16×frac-add
13×pow1 add-cbrt-cube add-exp-log
12×frac-times associate-*r*
9×flip3-- flip--
7×associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u sub-neg insert-posit16 log1p-expm1-u
3×*-commutative
2×unswap-sqr
1×+-commutative sum-log fma-def distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 155
Calls
4 calls:
27.0ms
(* x.im (+ x.re x.im))
52.0ms
(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
21.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
32.0ms
(* (* x.im (+ x.re x.im)) (- x.re x.im))

series221.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* x.im (+ x.re x.im))
77.0ms
(+ (* (* x.im (+ x.re x.im)) (- x.re x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
22.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
78.0ms
(* (* x.im (+ x.re x.im)) (- x.re x.im))

simplify1.3s

Counts
167 → 167
Iterations
IterNodes
done2005
22005
11018
0281

prune900.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
7×associate-*r*
6×associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-+ flip-+
2×pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in +-commutative sum-log fma-def distribute-lft-in fma-udef distribute-lft-out
Counts
4 → 75
Calls
4 calls:
7.0ms
(+ (* x.re x.im) (* x.im x.re))
14.0ms
(* x.im (+ x.re x.im))
0.0ms
(fma (* x.im (+ x.re x.im)) (- x.re x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
27.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

series207.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* x.re x.im) (* x.im x.re))
49.0ms
(* x.im (+ x.re x.im))
108.0ms
(fma (* x.im (+ x.re x.im)) (- x.re x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
22.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify996.0ms

Counts
87 → 87
Iterations
IterNodes
done2001
32001
21372
1321
0116

prune409.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

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))))
13.4b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
13.4b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
13.4b
(cbrt (+ (* x.re x.im) (* x.im x.re)))

rewrite49.0ms

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:
36.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
4.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

series608.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
143.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
158.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
120.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify961.0ms

Counts
111 → 111
Iterations
IterNodes
done2003
32003
2767
1313
0125

prune658.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes137.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done14
114
010

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.6s14287×body80valid