Details

sample26.0ms

Algorithm

intervals

Results

13.0ms

274×

body

valid

simplify56.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	72
5	72
4	66
3	48
2	36
1	19
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize34.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
24.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite41.0ms

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))
34.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series209.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(- (* x.im y.re) (* x.re y.im))
142.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

50 → 50

Iterations

Iter	Nodes
done	5000
2	1073
1	258
0	89

prune291.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
15.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 86

Calls

4 calls:

6.0ms	(- (* x.im y.re) (* x.re y.im))
24.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* x.im y.re) (* x.re y.im))
123.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1227
1	313
0	121

prune610.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.6b

localize20.0ms

Local error

Found 3 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
1.3b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
23.8b	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/l/`
1×	`sub-neg` `flip3-+` `diff-log` `flip-+` `pow-flip` `inv-pow`

Counts

3 → 127

Calls

3 calls:

6.0ms	(- (* x.im y.re) (* x.re y.im))
24.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
24.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

series293.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(- (* x.im y.re) (* x.re y.im))
155.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
85.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

simplify1.9s

Counts

136 → 136

Iterations

Iter	Nodes
done	5002
2	2751
1	536
0	195

prune714.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (- (* x.im y.re) (* x.re y.im)))
0.5b	(- (* x.im y.re) (* x.re y.im))
1.3b	(/ 1 (* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im)))))
24.1b	(* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube` `div-exp`
16×	`prod-exp`
15×	`associate-r`
10×	`pow1` `rec-exp` `1-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`frac-times` `associate-/r` `flip3-+` `associate-l/` `cbrt-unprod` `flip-+`
3×	`flip3--` `associate-l` `div-inv` `pow-flip` `flip--` `unswap-sqr`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*r/` `un-div-inv` `inv-pow`
1×	`sub-neg` `diff-log` `*-commutative`

Counts

4 → 131

Calls

4 calls:

11.0ms	(/ 1 (- (* x.im y.re) (* x.re y.im)))
6.0ms	(- (* x.im y.re) (* x.re y.im))
34.0ms	(/ 1 (* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im)))))
41.0ms	(* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (- (* x.im y.re) (* x.re y.im)))
62.0ms	(- (* x.im y.re) (* x.re y.im))
185.0ms	(/ 1 (* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im)))))
71.0ms	(* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (- (* x.im y.re) (* x.re y.im))))

simplify3.6s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
2	3963
1	518
0	172

prune620.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 21.6b

regimes338.0ms

Accuracy

-8.3% (3.5b remaining)

Error of 26.2b against oracle of 22.7b and baseline of 25.9b

bsearch58.0ms

Steps

Iters	Range		Point
9	2.0782291391057034e+47	1.0561172955237832e+55	1.0408011483354069e+55

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

8465×

body

valid