Details

sample56.0ms

Algorithm

intervals

Results

20.0ms	289×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize18.0ms

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))
0.6b	(* (log base) (log base))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

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:

16.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (atan2 im re) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
25.0ms	(* (atan2 im re) (log base))
144.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (47.0ms)

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

prune419.0ms

Filtered

129 candidates to 89 candidates (69.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (/ 1 base))
0.4b	(/ (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)))

series151.0ms

Counts

2 → 6

Calls

2 calls:

113.0ms	(log (/ 1 base))
38.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify105.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (33.0ms)

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

prune186.0ms

Filtered

78 candidates to 46 candidates (59.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
0.4b	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
0.6b	(cbrt (/ 1 base))
0.6b	(cbrt (/ 1 base))

rewrite30.0ms

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:

12.0ms	(+ (* 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))

series715.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
96.0ms	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
175.0ms	(cbrt (/ 1 base))
181.0ms	(cbrt (/ 1 base))

simplify51.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (37.0ms)

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

prune575.0ms

Filtered

169 candidates to 134 candidates (79.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (pow base -1/3))
0.3b	(/ (/ (atan2 im re) (log (pow base -1/3))) (+ 2 1))
0.3b	(/ (atan2 im re) (log (pow base -1/3)))
5.0b	(pow base -1/3)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

136×	`times-frac`
108×	`*-un-lft-identity`
74×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`log-pow`
19×	`associate-/l*`
17×	`distribute-lft-out`
14×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`associate-/r*`
7×	`log-prod` `div-inv`
6×	`unpow-prod-down`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `rem-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `associate-/r/` `sqr-pow`
1×	`pow-pow` `flip3-+` `flip-+` `associate-/l/`

Counts

4 → 175

Calls

4 calls:

2.0ms	(log (pow base -1/3))
10.0ms	(/ (/ (atan2 im re) (log (pow base -1/3))) (+ 2 1))
2.0ms	(/ (atan2 im re) (log (pow base -1/3)))
1.0ms	(pow base -1/3)

series539.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(log (pow base -1/3))
78.0ms	(/ (/ (atan2 im re) (log (pow base -1/3))) (+ 2 1))
62.0ms	(/ (atan2 im re) (log (pow base -1/3)))
168.0ms	(pow base -1/3)

simplify76.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	569	1500
1	2909	1422
2	5002	1413

prune488.0ms

Filtered

187 candidates to 141 candidates (75.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes118.0ms

Accuracy

0% (0.3b 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: 0 (0.0ms)

Iter	Nodes	Cost
0	19	6
1	21	6
2	23	6
3	23	6

end0.0ms

sample1.5s

Algorithm

intervals

Results

584.0ms	8000×	body	80	valid
577.0ms	8087×	body	80	nan