Details

Time bar (total: 9.1s)

sample47.0ms

Algorithm
intervals
Results
22.0ms272×body80valid

simplify74.0ms

Counts
1 → 1
Iterations
IterNodes
done72
572
466
348
236
119
011

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* x.im y.re) (* x.re y.im))
23.2b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
2 → 44
Calls
2 calls:
6.0ms
(- (* x.im y.re) (* x.re y.im))
24.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series209.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(- (* x.im y.re) (* x.re y.im))
141.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify577.0ms

Counts
50 → 50
Iterations
IterNodes
done5000
21073
1258
089

prune319.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (/ y.re (+ (* y.re y.re) (* y.im y.im))) x.im) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
4.4b
(* (/ y.re (+ (* y.re y.re) (* y.im y.im))) x.im)
13.8b
(/ y.re (+ (* y.re y.re) (* y.im y.im)))
16.9b
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
22×*-un-lft-identity times-frac add-cube-cbrt
16×add-cbrt-cube add-exp-log
15×associate-*l*
6×pow1 associate-/r* associate-/r/ add-log-exp
4×cbrt-undiv div-exp associate-/l*
3×flip3-+ associate-*r* associate-*l/ prod-exp cbrt-unprod flip-+ div-inv
2×clear-num frac-2neg unswap-sqr
1×sub-neg flip3-- diff-log pow-prod-down *-commutative frac-sub flip-- sub-div
Counts
4 → 100
Calls
4 calls:
35.0ms
(- (* (/ y.re (+ (* y.re y.re) (* y.im y.im))) x.im) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
46.0ms
(* (/ y.re (+ (* y.re y.re) (* y.im y.im))) x.im)
22.0ms
(/ y.re (+ (* y.re y.re) (* y.im y.im)))
16.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

series492.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(- (* (/ y.re (+ (* y.re y.re) (* y.im y.im))) x.im) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
132.0ms
(* (/ y.re (+ (* y.re y.re) (* y.im y.im))) x.im)
67.0ms
(/ y.re (+ (* y.re y.re) (* y.im y.im)))
71.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

simplify966.0ms

Counts
112 → 112
Iterations
IterNodes
done5003
22321
1457
0163

prune784.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.9b

localize63.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (/ y.re (+ (* y.re y.re) (* y.im y.im))) x.im)
13.8b
(/ y.re (+ (* y.re y.re) (* y.im y.im)))
27.1b
(sqrt (+ (* y.im y.im) (* y.re y.re)))
27.1b
(sqrt (+ (* y.im y.im) (* y.re y.re)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
19×times-frac
15×associate-*l*
11×add-cbrt-cube add-exp-log
8×pow1
6×sqrt-prod
4×flip3-+ sqrt-div associate-/r/ flip-+ add-log-exp
3×associate-/r* associate-*r* associate-/l*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative
Counts
4 → 93
Calls
4 calls:
32.0ms
(* (/ y.re (+ (* y.re y.re) (* y.im y.im))) x.im)
16.0ms
(/ y.re (+ (* y.re y.re) (* y.im y.im)))
10.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))
11.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (/ y.re (+ (* y.re y.re) (* y.im y.im))) x.im)
59.0ms
(/ y.re (+ (* y.re y.re) (* y.im y.im)))
49.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))
59.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))

simplify709.0ms

Counts
105 → 105
Iterations
IterNodes
done5001
21711
1333
0131

prune630.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ x.re (sqrt (+ (* y.im y.im) (* y.re y.re)))) (/ y.im (sqrt (+ (* y.im y.im) (* y.re y.re)))))
14.8b
(/ (* x.im y.re) (+ (* y.im y.im) (* y.re y.re)))
27.1b
(sqrt (+ (* y.im y.im) (* y.re y.re)))
27.1b
(sqrt (+ (* y.im y.im) (* y.re y.re)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
51×times-frac
34×*-un-lft-identity add-cube-cbrt
30×sqrt-prod
24×associate-*r* associate-*l*
21×add-cbrt-cube add-exp-log
9×unswap-sqr
8×pow1 sqrt-div
6×cbrt-undiv div-exp associate-/r/
5×flip3-+ prod-exp cbrt-unprod flip-+
4×add-log-exp
3×associate-/r* div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l*
Counts
4 → 130
Calls
4 calls:
77.0ms
(* (/ x.re (sqrt (+ (* y.im y.im) (* y.re y.re)))) (/ y.im (sqrt (+ (* y.im y.im) (* y.re y.re)))))
15.0ms
(/ (* x.im y.re) (+ (* y.im y.im) (* y.re y.re)))
9.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))
8.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (/ x.re (sqrt (+ (* y.im y.im) (* y.re y.re)))) (/ y.im (sqrt (+ (* y.im y.im) (* y.re y.re)))))
71.0ms
(/ (* x.im y.re) (+ (* y.im y.im) (* y.re y.re)))
54.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))
58.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))

simplify1.1s

Counts
142 → 142
Iterations
IterNodes
done5001
23273
1610
0198

prune817.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.9b

regimes434.0ms

Accuracy

0% (1.3b remaining)

Error of 23.9b against oracle of 22.5b and baseline of 23.9b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done26
226
124
018

end0.0ms

sample977.0ms

Algorithm
intervals
Results
684.0ms8438×body80valid