Details

sample98.0ms

Algorithm

intervals

Results

35.0ms	256×	body	80	valid
33.0ms	305×	body	80	nan

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite114.0ms

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:

17.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
45.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
11.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
140.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
179.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.0s

Counts

122 → 122

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	200	2451
1	442	2259
2	1344	2035
3	4400	1998
done	5000	1992

prune609.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
0.5b	(/ (+ (+ 0 (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
23×	`pow1`
18×	`log-prod`
10×	`add-exp-log` `associate-r` `log-pow` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `sqrt-prod`
8×	`associate-l`
6×	`swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `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 → 116

Calls

4 calls:

19.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
96.0ms	(/ (+ (+ 0 (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series741.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
218.0ms	(/ (+ (+ 0 (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
275.0ms	(* (log base) (log base))
60.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.7s

Counts

128 → 128

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	214	2682
1	460	2374
2	1479	2144
3	4868	2113
done	5000	2109

prune562.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
58×	`times-frac`
41×	`*-un-lft-identity`
35×	`add-cube-cbrt`
32×	`sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`pow1`
8×	`unpow-prod-down` `div-exp` `prod-exp`
6×	`pow-unpow` `sqrt-div`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp` `log-pow` `div-inv` `unpow2` `sqr-pow`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 140

Calls

4 calls:

148.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
6.0ms	(pow (log base) 2)
4.0ms	(pow (log base) 2)
8.0ms	(sqrt (+ (* re re) (* im im)))

series670.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
234.0ms	(pow (log base) 2)
212.0ms	(pow (log base) 2)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

152 → 152

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	235	5236
1	624	4886
2	2107	4095
done	5000	4080

prune901.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.5b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

5.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
12.0ms	(sqrt (+ (* re re) (* im im)))

series963.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(pow (log base) 2)
472.0ms	(pow (log base) 2)
210.0ms	(pow (log base) 2)
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.4s

Counts

84 → 84

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	74	660
1	165	561
2	360	494
3	981	479
4	4546	467
done	5001	467

prune416.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.4b

regimes610.0ms

Accuracy

44.7% (17.5b remaining)

Error of 17.8b against oracle of 0.4b and baseline of 32.0b

bsearch256.0ms

Steps

Iters	Range		Point
9	5.040002698287175e+135	3.0836743811279107e+144	7.983252801042694e+137
7	-9.188861011096532e+114	-3.6221738814320156e+112	-2.263962099580683e+113

simplify10.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	41	94
1	52	88
2	55	88
done	55	88

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	8062×	body	80	nan
1.5s	8000×	body	80	valid