Details

sample119.0ms

Algorithm

intervals

Results

48.0ms	256×	body	80	valid
36.0ms	232×	body	80	nan

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
done	23	28

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

51.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
18.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
34.0ms	(* (log base) (log base))
16.0ms	(sqrt (+ (* re re) (* im im)))

series635.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
135.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
257.0ms	(* (log base) (log base))
59.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

122 → 122

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	200	2451
1	508	2278
2	2910	2043
done	5001	2023

prune885.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.5b

localize74.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
6×	`add-exp-log` `cbrt-prod` `log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

28.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(cbrt base)
2.0ms	(cbrt base)
16.0ms	(sqrt (+ (* re re) (* im im)))

series868.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
336.0ms	(cbrt base)
334.0ms	(cbrt base)
76.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.2s

Counts

77 → 77

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	116	875
1	246	828
2	770	730
3	3896	709
done	5001	705

prune505.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
30.7b	(sqrt (+ (* re re) (* im im)))
30.7b	(sqrt (+ (* re re) (* im im)))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`sqrt-div`
5×	`add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `pow-pow` `pow-exp` `log-pow` `unpow2` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

11.0ms	(pow (log base) 2)
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(pow (log base) 2)
41.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify963.0ms

Counts

76 → 76

Iterations

Useful iterations: done (959.0ms)

Iter	Nodes	Cost
0	74	788
1	199	683
2	573	618
3	1802	597
done	5000	595

prune605.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 7.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* 0.0 0.0) (pow (log base) 2)))))
0.5b	(exp (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* 0.0 0.0) (pow (log base) 2))))
0.5b	(pow (log base) 2)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

30×	`exp-prod`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
17×	`log-pow`
8×	`pow1`
5×	`add-exp-log` `add-log-exp`
4×	`unpow-prod-down` `associate-/r/` `add-cbrt-cube`
3×	`pow-unpow` `log-prod` `flip3-+` `sqrt-prod` `flip-+`
2×	`sqrt-div` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-exp` `rem-exp-log` `unpow2` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

97.0ms	(log (exp (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* 0.0 0.0) (pow (log base) 2)))))
100.0ms	(exp (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* 0.0 0.0) (pow (log base) 2))))
5.0ms	(pow (log base) 2)
12.0ms	(sqrt (+ (* re re) (* im im)))

series588.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(log (exp (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* 0.0 0.0) (pow (log base) 2)))))
179.0ms	(exp (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* 0.0 0.0) (pow (log base) 2))))
222.0ms	(pow (log base) 2)
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

96 → 96

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	168	2154
1	352	2012
2	929	1836
3	2910	1811
done	5001	1805

prune525.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 7.4b

regimes703.0ms

Accuracy

56.4% (10.6b remaining)

Error of 17.7b against oracle of 7.1b and baseline of 31.4b

bsearch511.0ms

Steps

Iters	Range		Point
10	9.626092965892694e+33	1.2401257984366607e+50	3.761101708531406e+48
7	4.126853017756838e-266	3.604729052181412e-264	2.0295662047120213e-265
8	-2.5501859063416286e-236	-1.2968363444848014e-240	-3.4043372425091253e-239
9	-3.515300631622012e+89	-1.3659123153672986e+84	-2.4512950480049453e+86

simplify24.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	63	173
1	85	171
2	98	171
3	103	171
done	103	171

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.6s	8096×	body	80	nan
1.1s	8000×	body	80	valid