Details

sample140.0ms

Algorithm

intervals

Results

60.0ms	254×	body	80	nan
51.0ms	256×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	22
1	22
0	18

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
0.5b	(* (log base) (log base))
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
20×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
12×	`log-prod`
10×	`associate-l` `log-pow`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow2` `rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `flip3-+` `times-frac` `pow-plus` `pow-sqr` `pow-prod-up` `flip-+` `div-inv` `associate-/l`

Counts

4 → 104

Calls

4 calls:

17.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
28.0ms	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
16.0ms	(* (log base) (log base))
11.0ms	(sqrt (+ (* re re) (* im im)))

series1.0s

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
127.0ms	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
704.0ms	(* (log base) (log base))
67.0ms	(sqrt (+ (* re re) (* im im)))

simplify8.8s

Counts

116 → 116

Iterations

Iter	Nodes
3	12873
2	1710
1	417
0	162

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
0.3b	(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
94×	`log-pow`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
79×	`pow1`
34×	`associate-/r*`
22×	`sqrt-pow1` `pow1/2`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv` `add-log-exp`
4×	`cbrt-undiv` `insert-posit16`
3×	`sqrt-prod`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3-+` `sqrt-div` `1-exp` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 212

Calls

4 calls:

13.0ms	(+ (* re re) (* im im))
14.0ms	(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
11.0ms	(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
11.0ms	(sqrt (+ (* re re) (* im im)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* re re) (* im im))
173.0ms	(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
157.0ms	(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
54.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.0s

Counts

224 → 224

Iterations

Iter	Nodes
3	4642
2	1624
1	611
0	254

prune2.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (log (sqrt (+ (* re re) (* im im)))))
0.3b	(/ 1 (log base))
0.3b	(/ (/ 1 (log base)) (/ 1 (log (sqrt (+ (* re re) (* im im))))))
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

964×	`times-frac`
380×	`add-sqr-sqrt`
379×	`*-un-lft-identity` `add-cube-cbrt`
238×	`log-pow`
190×	`pow1`
56×	`sqrt-pow1` `pow1/2`
52×	`add-exp-log`
43×	`div-inv`
36×	`div-exp`
32×	`associate-/r*`
22×	`associate-/l*`
20×	`add-cbrt-cube`
10×	`cbrt-undiv` `rec-exp` `1-exp`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `sqrt-prod`
2×	`sqrt-div` `pow-flip` `inv-pow`
1×	`rem-sqrt-square` `flip3-+` `associate-/r/` `flip-+` `associate-/l/`

Counts

4 → 519

Calls

4 calls:

7.0ms	(/ 1 (log (sqrt (+ (* re re) (* im im)))))
5.0ms	(/ 1 (log base))
15.0ms	(/ (/ 1 (log base)) (/ 1 (log (sqrt (+ (* re re) (* im im))))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ 1 (log (sqrt (+ (* re re) (* im im)))))
229.0ms	(/ 1 (log base))
148.0ms	(/ (/ 1 (log base)) (/ 1 (log (sqrt (+ (* re re) (* im im))))))
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify7.3s

Counts

531 → 531

Iterations

Iter	Nodes
2	3018
1	1696
0	570

prune6.3s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (/ (log base) (log (sqrt (+ (* re re) (* im im))))) (/ (log base) (log (sqrt (+ (* re re) (* im im)))))) (/ (log base) (log (sqrt (+ (* re re) (* im im)))))))
31.9b	(sqrt (+ (* re re) (* im im)))
31.9b	(sqrt (+ (* re re) (* im im)))
31.9b	(sqrt (+ (* re re) (* im im)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
5×	`frac-times` `associate-*l/`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 66

Calls

4 calls:

56.0ms	(cbrt (* (* (/ (log base) (log (sqrt (+ (* re re) (* im im))))) (/ (log base) (log (sqrt (+ (* re re) (* im im)))))) (/ (log base) (log (sqrt (+ (* re re) (* im im)))))))
7.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt (* (* (/ (log base) (log (sqrt (+ (* re re) (* im im))))) (/ (log base) (log (sqrt (+ (* re re) (* im im)))))) (/ (log base) (log (sqrt (+ (* re re) (* im im)))))))
53.0ms	(sqrt (+ (* re re) (* im im)))
55.0ms	(sqrt (+ (* re re) (* im im)))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify898.0ms

Counts

78 → 78

Iterations

Iter	Nodes
4	3015
3	845
2	329
1	178
0	92

prune1.1s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 7.2b

regimes596.0ms

Accuracy

59% (9.8b remaining)

Error of 16.9b against oracle of 7.1b and baseline of 31.0b

bsearch453.0ms

Steps

Iters	Range		Point
11	8.974002264587472e+123	1.5263377708456642e+150	6.270425502185955e+140
8	-1.1790907230225289e-304	-7.789640258942631e-308	-9.044826970858667e-305
2	-3.1678905667204715e-212	-2.6616175635737e-212	-2.7249016889670465e-212
10	-1.8102216906122654e+101	-1.7705199891395814e+89	-1.144600521445903e+98

simplify7.0ms

Iterations

Iter	Nodes
2	37
1	37
0	34

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.9s	8000×	body	80	valid
2.2s	7915×	body	80	nan