Details

sample89.0ms

Algorithm

intervals

Results

37.0ms	303×	body	80	nan
33.0ms	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: 30.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (atan2 im re) (log base))
0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

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:

4.0ms	(* (atan2 im re) (log base))
12.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (atan2 im re) (log base))
40.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
153.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

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

prune426.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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:

2.0ms	(log (/ 1 base))
3.0ms	(/ (atan2 im re) (log (/ 1 base)))

series153.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(log (/ 1 base))
35.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify98.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	197	434
1	514	402
2	1452	386
3	3804	373
4	5002	373

prune171.0ms

Pruning

13 alts after pruning (13 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)))))
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite18.0ms

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:

3.0ms	(/ 1 (cbrt base))
10.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
0.0ms	(cbrt base)
1.0ms	(cbrt base)

series778.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ 1 (cbrt base))
227.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
178.0ms	(cbrt base)
182.0ms	(cbrt base)

simplify38.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (29.0ms)

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

prune373.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (cbrt base))
0.2b	(/ (/ (atan2 im re) (log (cbrt base))) (+ (- 2) (- 1)))
0.3b	(/ (atan2 im re) (log (cbrt base)))
0.6b	(cbrt base)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

336×	`times-frac`
327×	`*-un-lft-identity`
127×	`add-sqr-sqrt` `add-cube-cbrt`
120×	`distribute-lft-out`
80×	`distribute-rgt-neg-in`
70×	`log-pow`
40×	`distribute-lft-neg-in` `neg-mul-1`
39×	`pow1`
36×	`pow1/3`
22×	`associate-/l*`
14×	`associate-/r*`
12×	`add-exp-log` `div-inv`
11×	`add-cbrt-cube`
6×	`cbrt-prod` `log-prod`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`flip3-+` `rem-log-exp` `flip-+` `associate-/l/`

Counts

4 → 278

Calls

4 calls:

1.0ms	(log (cbrt base))
25.0ms	(/ (/ (atan2 im re) (log (cbrt base))) (+ (- 2) (- 1)))
2.0ms	(/ (atan2 im re) (log (cbrt base)))
1.0ms	(cbrt base)

series621.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(log (cbrt base))
99.0ms	(/ (/ (atan2 im re) (log (cbrt base))) (+ (- 2) (- 1)))
87.0ms	(/ (atan2 im re) (log (cbrt base)))
186.0ms	(cbrt base)

simplify99.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	635	3275
1	2872	2986
2	5001	2979

prune537.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes148.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	26	8
2	28	8
3	28	8

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	8000×	body	80	valid
961.0ms	7759×	body	80	nan