Details

Time bar (total: 15.8s)

sample87.0ms

Algorithm
intervals
Results
70.0ms475×body80valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done2002
72002
61970
5833
4340
3156
258
121
011

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.7b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* x.re x.re) (* 3 (* x.im x.im)))
0.2b
(* 3 (* x.im x.im))
5.8b
(* (- (* x.re x.re) (* 3 (* x.im x.im))) x.re)

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt
6×*-un-lft-identity associate-*l* add-cube-cbrt
5×add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
3×insert-posit16
2×flip3-- associate-*l/ *-commutative flip-- unswap-sqr
1×sub-neg diff-log
Counts
3 → 54
Calls
3 calls:
16.0ms
(- (* x.re x.re) (* 3 (* x.im x.im)))
27.0ms
(* 3 (* x.im x.im))
46.0ms
(* (- (* x.re x.re) (* 3 (* x.im x.im))) x.re)

series203.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(- (* x.re x.re) (* 3 (* x.im x.im)))
32.0ms
(* 3 (* x.im x.im))
104.0ms
(* (- (* x.re x.re) (* 3 (* x.im x.im))) x.re)

simplify1.2s

Counts
63 → 63
Iterations
IterNodes
done2008
32008
2798
1240
089

prune311.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize47.0ms

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))
5.7b
(* (- (* x.re x.re) (* x.im x.im)) x.re)

rewrite159.0ms

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×flip3-+ flip3-- frac-sub flip-+ insert-posit16 flip--
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log sub-neg diff-log difference-of-squares
Counts
4 → 72
Calls
4 calls:
16.0ms
(+ (* x.re x.im) (* x.im x.re))
37.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
55.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
49.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)

series244.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ (* x.re x.im) (* x.im x.re))
52.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
72.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
81.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)

simplify1.6s

Counts
84 → 84
Iterations
IterNodes
done2000
32000
21650
1404
0140

prune465.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite169.0ms

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×insert-posit16
3×*-commutative
2×unswap-sqr
1×sub-neg diff-log distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 101
Calls
4 calls:
15.0ms
(* (- x.re x.im) x.re)
27.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
51.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
75.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))

series241.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (- x.re x.im) x.re)
52.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
68.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
71.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))

simplify1.2s

Counts
113 → 113
Iterations
IterNodes
done2009
22009
1753
0215

prune644.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* (- x.re x.im) x.re)) (cbrt (* (- x.re x.im) x.re)))
9.8b
(cbrt (* (- x.re x.im) x.re))
9.8b
(cbrt (* (- x.re x.im) x.re))
9.8b
(cbrt (* (- x.re x.im) x.re))

rewrite84.0ms

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×frac-times add-cbrt-cube swap-sqr associate-*r* associate-*l* insert-posit16 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 → 76
Calls
4 calls:
39.0ms
(* (cbrt (* (- x.re x.im) x.re)) (cbrt (* (- x.re x.im) x.re)))
12.0ms
(cbrt (* (- x.re x.im) x.re))
18.0ms
(cbrt (* (- x.re x.im) x.re))
13.0ms
(cbrt (* (- x.re x.im) x.re))

series1.6s

Counts
4 → 12
Calls
4 calls:
409.0ms
(* (cbrt (* (- x.re x.im) x.re)) (cbrt (* (- x.re x.im) x.re)))
364.0ms
(cbrt (* (- x.re x.im) x.re))
409.0ms
(cbrt (* (- x.re x.im) x.re))
414.0ms
(cbrt (* (- x.re x.im) x.re))

simplify1.4s

Counts
88 → 88
Iterations
IterNodes
done2001
42001
31503
2559
1234
0104

prune598.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes184.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done16
116
011

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.3s14385×body80valid