Details

sample125.0ms

Algorithm

intervals

Results

58.0ms	305×	body	80	nan
31.0ms	256×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize34.0ms

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)))

rewrite106.0ms

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:

22.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
46.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
24.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
147.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
194.0ms	(* (log base) (log base))
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.2s

Counts

122 → 122

Iterations

Useful iterations: done (3.2s)

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

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (+ (* re re) (* im im))) (log base))
0.5b	(/ (+ (* 1/2 (* (log (+ (* 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))
31.8b	(log (+ (* re re) (* im im)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

13.0ms	(* (log (+ (* re re) (* im im))) (log base))
93.0ms	(/ (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
17.0ms	(* (log base) (log base))
9.0ms	(log (+ (* re re) (* im im)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (log (+ (* re re) (* im im))) (log base))
99.0ms	(/ (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
199.0ms	(* (log base) (log base))
73.0ms	(log (+ (* re re) (* im im)))

simplify1.1s

Counts

119 → 119

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	203	2460
1	462	2284
2	1432	2043
done	5000	2024

prune488.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
31.8b	(log (+ (* re re) (* im im)))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
58×	`times-frac`
41×	`*-un-lft-identity`
35×	`add-cube-cbrt`
29×	`add-exp-log` `sqrt-prod`
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`
4×	`cbrt-undiv` `sqrt-div` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`log-prod` `flip3-+` `log-pow` `flip-+`
2×	`pow-to-exp` `log-div` `rec-exp` `pow-pow` `1-exp` `pow-exp` `div-inv` `unpow2` `sqr-pow`
1×	`frac-times` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 139

Calls

4 calls:

212.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
6.0ms	(pow (log base) 2)
6.0ms	(pow (log base) 2)
16.0ms	(log (+ (* re re) (* im im)))

series664.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
208.0ms	(pow (log base) 2)
233.0ms	(pow (log base) 2)
57.0ms	(log (+ (* re re) (* im im)))

simplify1.5s

Counts

151 → 151

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	242	5366
1	643	5037
2	2143	4216
done	5001	4199

prune836.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.9b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
0.4b	(* (log (+ (* re re) (* im im))) (log base))
0.5b	(pow (log base) 2)
31.8b	(log (+ (* re re) (* im im)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`add-cube-cbrt` `associate-r`
17×	`add-exp-log`
13×	`pow1`
11×	`times-frac` `add-cbrt-cube`
9×	`log-prod`
7×	`associate-l`
5×	`prod-exp`
4×	`unpow-prod-down` `flip3-+` `log-pow` `flip-+` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `cbrt-unprod`
2×	`frac-times` `log-div` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `pow-pow` `1-exp` `associate-*r/` `rem-log-exp` `pow-exp` `un-div-inv` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 101

Calls

4 calls:

135.0ms	(* (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
21.0ms	(* (log (+ (* re re) (* im im))) (log base))
5.0ms	(pow (log base) 2)
12.0ms	(log (+ (* re re) (* im im)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
84.0ms	(* (log (+ (* re re) (* im im))) (log base))
203.0ms	(pow (log base) 2)
52.0ms	(log (+ (* re re) (* im im)))

simplify1.2s

Counts

113 → 113

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	229	2579
1	576	2405
2	1811	2103
done	5000	2083

prune545.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.9b

regimes672.0ms

Accuracy

58.8% (10.1b remaining)

Error of 17.5b against oracle of 7.3b and baseline of 32.0b

bsearch262.0ms

Steps

Iters	Range		Point
9	9.20494146023971e+137	2.5400712297185524e+145	9.385054520910622e+137
9	-2.1962666116397044e+118	-2.7069606924754535e+112	-2.178124817795753e+114

simplify10.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	44	90
1	56	88
2	59	88
done	59	88

end0.0ms

sample4.4s

Algorithm

intervals

Results

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