Details

sample57.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
18.0ms	276×	body	80	nan

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: 29.5b

localize21.0ms

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))
27.3b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

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))
9.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (atan2 im re) (log base))
35.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
154.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

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

prune424.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(log (/ 1 base))
0.3b	(/ (atan2 im re) (log (/ 1 base)))

rewrite8.0ms

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))
4.0ms	(/ (atan2 im re) (log (/ 1 base)))

series160.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(log (/ 1 base))
35.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify99.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (30.0ms)

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

prune166.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (cbrt base))
0.3b	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`times-frac`
34×	`log-prod`
33×	`cbrt-prod`
22×	`associate-+r+`
12×	`associate-+l+`
8×	`add-exp-log`
6×	`pow1` `distribute-rgt-in` `distribute-lft-in` `associate-/r*`
5×	`add-cbrt-cube` `add-log-exp`
3×	`pow-flip` `pow1/3` `log-rec` `associate-/l*`
2×	`distribute-rgt-out` `div-exp` `log-pow` `div-inv` `inv-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-lft-neg-out` `associate-+r-` `log-div` `rec-exp` `distribute-neg-out` `frac-2neg` `flip3-+` `1-exp` `unsub-neg` `clear-num` `sum-log` `flip-+`

Counts

4 → 117

Calls

4 calls:

4.0ms	(/ 1 (cbrt base))
10.0ms	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series1.1s

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ 1 (cbrt base))
572.0ms	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
185.0ms	(cbrt base)
194.0ms	(cbrt base)

simplify47.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	388	824
1	1329	683
2	5001	551

prune433.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (pow base (- 1/3)))))
0.3b	(+ (* (- 2) (log (cbrt base))) (log (pow base (- 1/3))))
0.6b	(cbrt base)
5.0b	(pow base (- 1/3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`log-prod`
12×	`associate-+l+`
10×	`pow-unpow`
9×	`cbrt-prod` `times-frac`
7×	`add-exp-log` `associate-+r+`
6×	`distribute-rgt-in` `unpow-prod-down` `distribute-lft-in` `add-cbrt-cube`
5×	`pow1` `pow-neg` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `log-rec` `associate-/r` `associate-/l`
2×	`neg-sub0` `associate-+r-` `log-div` `flip3-+` `associate-/r/` `flip-+` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-lft-neg-out` `pow-to-exp` `neg-mul-1` `distribute-neg-out` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `unsub-neg` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 101

Calls

4 calls:

6.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (pow base (- 1/3)))))
9.0ms	(+ (* (- 2) (log (cbrt base))) (log (pow base (- 1/3))))
1.0ms	(cbrt base)
3.0ms	(pow base (- 1/3))

series1.1s

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (pow base (- 1/3)))))
561.0ms	(+ (* (- 2) (log (cbrt base))) (log (pow base (- 1/3))))
187.0ms	(cbrt base)
184.0ms	(pow base (- 1/3))

simplify51.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	419	1025
1	1503	894
2	5001	774

prune423.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes207.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	17
1	26	17
2	26	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

556.0ms	8000×	body	80	valid
519.0ms	7967×	body	80	nan