Details

sample56.0ms

Algorithm

intervals

Results

20.0ms	289×	body	80	nan
17.0ms	256×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune8.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize19.0ms

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)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
29.5b	(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:

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))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
147.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

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

prune449.0ms

Filtered

122 candidates to 84 candidates (68.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

14.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
4.0ms	(* (log base) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
152.0ms	(* (log base) (log base))
152.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	386	1610
1	1345	1484
2	5002	1464

prune505.0ms

Filtered

142 candidates to 86 candidates (60.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log base) (* 2 (log (cbrt base))))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

10.0ms	(* (log base) (* 2 (log (cbrt base))))
0.0ms	(cbrt base)
1.0ms	(cbrt base)
7.0ms	(sqrt (+ (* re re) (* im im)))

series826.0ms

Counts

4 → 12

Calls

4 calls:

423.0ms	(* (log base) (* 2 (log (cbrt base))))
186.0ms	(cbrt base)
180.0ms	(cbrt base)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify113.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	344	623
1	950	572
2	3788	533
3	5001	528

prune435.0ms

Filtered

92 candidates to 61 candidates (66.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
58×	`times-frac`
53×	`*-un-lft-identity`
43×	`add-cube-cbrt`
33×	`pow1`
32×	`associate-r` `associate-l` `sqrt-prod`
30×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`prod-exp`
8×	`div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`pow2` `rec-exp` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`

Counts

4 → 174

Calls

4 calls:

53.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 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)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
156.0ms	(* (log base) (log base))
153.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	676	3305
1	3766	2940
2	5001	2757

prune571.0ms

Filtered

186 candidates to 103 candidates (55.4%)

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 7.2b

regimes582.0ms

Accuracy

56.5% (11.1b remaining)

Error of 18.2b against oracle of 7.0b and baseline of 32.6b

bsearch153.0ms

Steps

Iters	Range		Point
7	1.0063416055669548e+37	1.7493846438227008e+39	1.7100792302483204e+39
8	-6.123670362103977e+80	-1.3413262103445193e+77	-2.1945943864727612e+79

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	50
1	64	50

end0.0ms

sample1.5s

Algorithm

intervals

Results

570.0ms	8087×	body	80	nan
552.0ms	8000×	body	80	valid