Details

sample58.0ms

Algorithm

intervals

Results

19.0ms	268×	body	80	nan
17.0ms	256×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	44	16
2	56	16
3	74	16
4	80	16
5	80	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.3b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

28.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
8.0ms	(* (atan2 im re) (log base))
9.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
26.0ms	(* (atan2 im re) (log base))
142.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	444	1213
1	1816	1100
2	5001	1070

prune419.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (/ 1 base))
0.3b	(/ (atan2 im re) (log (/ 1 base)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

27×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`log-pow`
13×	`log-prod`
12×	`pow1`
9×	`add-exp-log`
6×	`associate-/r*`
5×	`pow-flip` `inv-pow`
4×	`rem-log-exp` `add-cbrt-cube`
3×	`div-exp` `associate-/l*`
2×	`div-inv` `add-log-exp`
1×	`cbrt-undiv` `log-div` `rec-exp` `frac-2neg` `1-exp` `log-rec` `clear-num`

Counts

2 → 68

Calls

2 calls:

3.0ms	(log (/ 1 base))
7.0ms	(/ (atan2 im re) (log (/ 1 base)))

series151.0ms

Counts

2 → 6

Calls

2 calls:

119.0ms	(log (/ 1 base))
32.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify103.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	197	433
1	536	402
2	1518	386
3	3905	369
4	5001	369

prune161.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (cbrt base))
0.3b	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
0.5b	(cbrt base)
0.5b	(cbrt base)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
31×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`cbrt-prod`
11×	`associate-/r*`
10×	`add-exp-log`
9×	`pow1`
8×	`distribute-rgt-out` `log-pow`
7×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*`
5×	`inv-pow`
4×	`add-log-exp`
3×	`pow1/3` `div-exp`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/r/` `div-inv`
1×	`rec-exp` `flip3-+` `1-exp` `flip-+`

Counts

4 → 103

Calls

4 calls:

9.0ms	(/ 1 (cbrt base))
21.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series738.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ 1 (cbrt base))
212.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
171.0ms	(cbrt base)
172.0ms	(cbrt base)

simplify38.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	321	897
1	1111	815
2	5001	733

prune371.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (cbrt base))
0.3b	(/ (atan2 im re) (+ (* (- 2) (log (pow base 1/3))) (log (/ 1 (cbrt base)))))
0.5b	(cbrt base)
5.0b	(pow base 1/3)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
15×	`cbrt-prod`
11×	`add-exp-log`
9×	`associate-/r*`
7×	`add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `div-exp`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `pow1/3` `clear-num` `associate-/r/` `div-inv`
1×	`pow-to-exp` `rec-exp` `pow-pow` `flip3-+` `unpow1/3` `1-exp` `pow-exp` `flip-+` `inv-pow` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

6.0ms	(/ 1 (cbrt base))
23.0ms	(/ (atan2 im re) (+ (* (- 2) (log (pow base 1/3))) (log (/ 1 (cbrt base)))))
1.0ms	(cbrt base)
3.0ms	(pow base 1/3)

series714.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ 1 (cbrt base))
191.0ms	(/ (atan2 im re) (+ (* (- 2) (log (pow base 1/3))) (log (/ 1 (cbrt base)))))
175.0ms	(cbrt base)
169.0ms	(pow base 1/3)

simplify49.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	357	802
1	1443	700
2	5002	677

prune348.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes164.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	11
1	32	11
2	33	11
3	33	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

545.0ms	8000×	body	80	valid
544.0ms	7964×	body	80	nan