Details

sample56.0ms

Algorithm

intervals

Results

20.0ms	283×	body	80	nan
17.0ms	256×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

localize23.0ms

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))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

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:

13.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
147.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify621.0ms

Counts

122 → 122

Iterations

Useful iterations: done (617.0ms)

Iter	Nodes	Cost
0	200	2451
1	441	2259
2	1349	2035
done	5001	2023

prune480.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite87.0ms

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:

73.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
1.0ms	(pow (log base) 2)
1.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
152.0ms	(pow (log base) 2)
153.0ms	(pow (log base) 2)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts

152 → 152

Iterations

Useful iterations: 2 (427.0ms)

Iter	Nodes	Cost
0	235	5236
1	651	4890
2	2041	4097
done	5000	4097

prune584.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`unpow-prod-down` `associate-r` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

21.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
153.0ms	(pow (log base) 2)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

105 → 105

Iterations

Useful iterations: 3 (656.0ms)

Iter	Nodes	Cost
0	194	2235
1	442	2127
2	1241	1939
3	4481	1910
done	5000	1910

prune455.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(cbrt base)
0.5b	(cbrt base)
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

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:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
184.0ms	(cbrt base)
180.0ms	(cbrt base)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

77 → 77

Iterations

Useful iterations: 4 (718.0ms)

Iter	Nodes	Cost
0	116	875
1	229	828
2	554	732
3	1244	711
4	2978	705
done	5001	705

prune334.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 8.5b

regimes474.0ms

Accuracy

56.4% (10.7b remaining)

Error of 18.1b against oracle of 7.4b and baseline of 32.0b

bsearch332.0ms

Steps

Iters	Range		Point
8	1.8065354105123547e+74	1.0649312883679304e+77	6.589229227697289e+74
7	4.294297119952098e-227	1.0017215422722994e-224	4.423518023204255e-227
9	1.971457584507684e-253	4.800777115565097e-246	4.690812809047299e-246
9	-3.970425942060287e+41	-2.6381962027638094e+36	-3.6785538778066045e+41

simplify10.0ms

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	51	155
1	70	125
done	70	125

end0.0ms

sample1.5s

Algorithm

intervals

Results

562.0ms	8095×	body	80	nan
554.0ms	8000×	body	80	valid