Details

sample55.0ms

Algorithm

intervals

Results

20.0ms	283×	body	80	nan
17.0ms	256×	body	80	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	16
1	52	16
2	68	16
3	88	16
4	102	16
5	106	16
6	106	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

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))
30.8b	(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×	`expm1-log1p-u` `log1p-expm1-u` `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--` `hypot-def` `div-inv`

Counts

4 → 117

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)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (atan2 im re) (log base))
34.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
143.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	466	1254
1	1924	1122
2	5002	1081

prune422.0ms

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)))

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×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `log-div` `rec-exp` `frac-2neg` `1-exp` `log-rec` `clear-num`

Counts

2 → 72

Calls

2 calls:

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

series147.0ms

Counts

2 → 6

Calls

2 calls:

114.0ms	(log (/ 1 base))
33.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify107.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	201	449
1	540	418
2	1522	402
3	3981	385
4	5002	385

prune178.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

65×	`cbrt-prod`
63×	`times-frac`
58×	`*-un-lft-identity`
53×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`log-prod`
32×	`associate-+l+`
16×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
10×	`distribute-rgt-out`
9×	`pow1`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `div-inv`
5×	`distribute-lft1-in` `log-pow` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-div` `associate-/l*`
2×	`flip3-+` `pow1/3` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `log-div` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log`

Counts

4 → 157

Calls

4 calls:

15.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
8.0ms	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
2.0ms	(cbrt (/ 1 base))
2.0ms	(cbrt (/ 1 base))

series694.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
93.0ms	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
165.0ms	(cbrt (/ 1 base))
170.0ms	(cbrt (/ 1 base))

simplify48.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	448	1447
1	1312	1296
2	5002	1150

prune566.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* 2 (log (pow (/ 1 base) 1/3))) (log (cbrt (/ 1 base))))
0.3b	(/ (atan2 im re) (+ (* 2 (log (pow (/ 1 base) 1/3))) (log (cbrt (/ 1 base)))))
0.5b	(cbrt (/ 1 base))
4.8b	(pow (/ 1 base) 1/3)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
51×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
50×	`log-prod`
39×	`unpow-prod-down`
34×	`associate-+l+`
26×	`cbrt-prod`
17×	`distribute-rgt-in` `distribute-lft-in`
16×	`associate-+r+`
11×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `div-inv`
5×	`add-log-exp`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u`
3×	`pow-unpow` `pow-pow` `div-exp` `associate-/r` `associate-/l` `sqr-pow`
2×	`cbrt-div` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+r-` `log-div` `rec-exp` `pow-flip` `fma-def` `frac-2neg` `unpow1/3` `pow1/3` `1-exp` `clear-num` `sum-log` `inv-pow`

Counts

4 → 155

Calls

4 calls:

18.0ms	(+ (* 2 (log (pow (/ 1 base) 1/3))) (log (cbrt (/ 1 base))))
7.0ms	(/ (atan2 im re) (+ (* 2 (log (pow (/ 1 base) 1/3))) (log (cbrt (/ 1 base)))))
2.0ms	(cbrt (/ 1 base))
4.0ms	(pow (/ 1 base) 1/3)

series830.0ms

Counts

4 → 12

Calls

4 calls:

355.0ms	(+ (* 2 (log (pow (/ 1 base) 1/3))) (log (cbrt (/ 1 base))))
131.0ms	(/ (atan2 im re) (+ (* 2 (log (pow (/ 1 base) 1/3))) (log (cbrt (/ 1 base)))))
172.0ms	(cbrt (/ 1 base))
172.0ms	(pow (/ 1 base) 1/3)

simplify64.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	610	1386
1	1970	1090
2	5001	972

prune550.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes165.0ms

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	23	11
1	25	11
2	25	11

end0.0ms

sample1.5s

Algorithm

intervals

Results

560.0ms	8095×	body	80	nan
545.0ms	8000×	body	80	valid