Details

sample62.0ms

Algorithm

intervals

Results

22.0ms	292×	body	80	nan
18.0ms	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: 29.6b

localize19.0ms

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)))
0.4b	(* (atan2 im re) (log base))
0.4b	(* (log base) (log base))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite63.0ms

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:

30.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
9.0ms	(* (atan2 im re) (log base))
13.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series240.0ms

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))
146.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	466	1254
1	1924	1122
2	5001	1081

prune418.0ms

Pruning

9 alts after pruning (9 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)))

rewrite16.0ms

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:

3.0ms	(log (/ 1 base))
10.0ms	(/ (atan2 im re) (log (/ 1 base)))

series150.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(log (/ 1 base))
32.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify100.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	201	450
1	518	418
2	1456	402
3	3870	389
4	5001	389

prune179.0ms

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

34×	`log-prod`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
22×	`associate-+r+`
21×	`cbrt-prod`
12×	`associate-+l+`
10×	`distribute-rgt-out` `log-pow`
9×	`pow1`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
5×	`pow-flip` `associate-/r*` `inv-pow` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-rec` `associate-/l*`
2×	`flip3-+` `pow1/3` `associate-/r/` `flip-+` `div-inv`
1×	`cbrt-undiv` `+-commutative` `distribute-lft-neg-out` `associate-+r-` `log-div` `distribute-neg-out` `fma-def` `frac-2neg` `div-exp` `unsub-neg` `clear-num` `sum-log`

Counts

4 → 119

Calls

4 calls:

24.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
18.0ms	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series1.1s

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
520.0ms	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
170.0ms	(cbrt base)
170.0ms	(cbrt base)

simplify47.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	490	1205
1	1500	1048
2	5002	921

prune501.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

21.0ms	(/ (atan2 im re) (+ (* (- 2) (log (pow (/ 1 base) -1/3))) (log (/ 1 (cbrt base)))))
31.0ms	(+ (* (- 2) (log (pow (/ 1 base) -1/3))) (log (/ 1 (cbrt base))))
1.0ms	(cbrt base)
7.0ms	(pow (/ 1 base) -1/3)

series1.1s

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (atan2 im re) (+ (* (- 2) (log (pow (/ 1 base) -1/3))) (log (/ 1 (cbrt base)))))
523.0ms	(+ (* (- 2) (log (pow (/ 1 base) -1/3))) (log (/ 1 (cbrt base))))
170.0ms	(cbrt base)
173.0ms	(pow (/ 1 base) -1/3)

simplify73.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	769	1553
1	2628	1369
2	5001	1271

prune624.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes192.0ms

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	27	12
1	33	12
2	34	12
3	34	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

553.0ms	8023×	body	80	nan
539.0ms	8000×	body	80	valid