Details

Time bar (total: 17.1s)

sample37.0ms

Algorithm
intervals
Results
20.0ms455×body80valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 5 (602.0ms)

IterNodesCost
011362
123297
261297
3149297
4433257
51519203
done5001203

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.9b

localize22.0ms

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.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
6.5b
(* (- (* x.re x.re) (* x.im x.im)) x.im)

rewrite117.0ms

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*
5×flip3-+ flip-+
4×expm1-log1p-u frac-add log1p-expm1-u
3×flip3-- flip--
2×+-commutative sum-log fma-def pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×difference-of-squares
Counts
4 → 77
Calls
4 calls:
11.0ms
(+ (* x.re x.im) (* x.im x.re))
34.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
40.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
28.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

series235.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* x.re x.im) (* x.im x.re))
91.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
23.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
83.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

simplify2.7s

Counts
89 → 89
Iterations

Useful iterations: done (2.7s)

IterNodesCost
014331443
143922780
2266421796
done500121726

prune467.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
42×associate-*l/
20×flip3-+ flip-+
16×frac-add
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt *-un-lft-identity flip3-- flip--
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 sum-log fma-def *-commutative
1×distribute-lft-out unswap-sqr
Counts
4 → 95
Calls
4 calls:
10.0ms
(+ (* x.re x.im) (* x.im x.re))
35.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
28.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
54.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

series276.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* x.re x.im) (* x.im x.re))
110.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
38.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
89.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

simplify1.2s

Counts
107 → 107
Iterations

Useful iterations: done (1.2s)

IterNodesCost
020555372
175337866
done500135584

prune714.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r* add-log-exp
4×expm1-log1p-u associate-*l/ log1p-expm1-u
2×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
1×+-commutative sum-log fma-def flip3-- fma-udef flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 70
Calls
4 calls:
27.0ms
(* (- x.re x.im) x.im)
6.0ms
(+ (* x.re x.im) (* x.im x.re))
17.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

series280.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (- x.re x.im) x.im)
36.0ms
(+ (* x.re x.im) (* x.im x.re))
38.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
167.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))

simplify1.8s

Counts
82 → 82
Iterations

Useful iterations: done (1.8s)

IterNodesCost
011420079
128314958
2170714373
done500214235

prune545.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)) (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)))
26.3b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
26.3b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
26.3b
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*l/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-+ pow1/3 flip-+
8×*-un-lft-identity add-cube-cbrt
7×cbrt-prod
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube swap-sqr associate-*r* associate-*l* log1p-expm1-u add-log-exp
2×pow-prod-down associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 80
Calls
4 calls:
54.0ms
(* (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)) (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)))
7.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
7.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
7.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))

series702.0ms

Counts
4 → 12
Calls
4 calls:
233.0ms
(* (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)) (cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re)))
148.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
161.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))
158.0ms
(cbrt (* (+ (* x.re x.im) (* x.im x.re)) x.re))

simplify1.5s

Counts
92 → 92
Iterations

Useful iterations: done (1.5s)

IterNodesCost
012838150
132830195
2118828694
done500126962

prune671.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
010337
114297
216297
318297
done18297

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.9s14556×body80valid