Details

sample104.0ms

Algorithm

intervals

Results

46.0ms	256×	body	80	valid
39.0ms	250×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (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))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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:

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

series384.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
100.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
152.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5001	1205

prune484.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
163×	`add-sqr-sqrt`
162×	`*-un-lft-identity`
158×	`add-cube-cbrt`
141×	`sqrt-prod`
31×	`pow1`
24×	`associate-/l*`
18×	`sqrt-div`
16×	`associate-/r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`log-prod` `swap-sqr` `log-pow`
9×	`flip3-+` `flip-+`
8×	`associate-r` `associate-l` `div-inv`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 278

Calls

4 calls:

30.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms	(* (log base) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
152.0ms	(* (log base) (log base))
155.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify118.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	839	8780
1	3156	8145
2	5001	8032

prune858.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(cbrt (pow (log base) 6))
1.2b	(pow (log base) 6)
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
8×	`cbrt-prod` `unpow-prod-down` `log-pow`
7×	`add-exp-log`
6×	`log-prod` `swap-sqr` `add-cbrt-cube`
4×	`associate-r` `associate-l` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-div` `sqr-pow`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (log base) (log base))
1.0ms	(cbrt (pow (log base) 6))
1.0ms	(pow (log base) 6)
4.0ms	(sqrt (+ (* re re) (* im im)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (log base) (log base))
154.0ms	(cbrt (pow (log base) 6))
195.0ms	(pow (log base) 6)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	256	418
1	943	374
2	5001	332

prune444.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
1.2b	(pow (log base) 6)
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

0.0ms	(cbrt base)
0.0ms	(cbrt base)
1.0ms	(pow (log base) 6)
4.0ms	(sqrt (+ (* re re) (* im im)))

series735.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(cbrt base)
181.0ms	(cbrt base)
196.0ms	(pow (log base) 6)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	194	256
1	505	241
2	1483	233
3	5002	225

prune418.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 8.1b

regimes608.0ms

Accuracy

58.7% (10.1b remaining)

Error of 17.2b against oracle of 7.2b and baseline of 31.5b

bsearch317.0ms

Steps

Iters	Range		Point
6	1.646495042169786e+116	1.0643100901350527e+117	3.330760733395057e+116
7	7.074960480324445e-232	6.748727538830997e-230	3.9287804843970234e-231
7	1.769076508249811e-272	3.131010255446689e-270	2.5876152026746802e-272
3	-3.180651499677689e+91	-2.5227571926526275e+91	-2.6461123752198268e+91

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	84
1	80	84

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
1.3s	8022×	body	80	nan