Details

sample75.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
27.0ms	252×	body	80	nan

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 34.6b

localize23.0ms

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))
0.5b	(* (log base) (log base))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

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:

13.0ms	(/ (- (* (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)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
31.0ms	(* (atan2 im re) (log base))
145.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (51.0ms)

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

prune448.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

3.0ms

(/ (atan2 im re) (log base))

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(/ (atan2 im re) (log base))

simplify53.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 4 (49.0ms)

Iter	Nodes	Cost
0	105	215
1	272	201
2	673	200
3	1915	198
4	5002	196

prune105.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`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` `associate-/l`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `hypot-udef` `flip3--` `frac-2neg` `flip3-+` `pow-plus` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `flip-+` `div-inv`

Counts

4 → 109

Calls

4 calls:

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

series266.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot re im)
34.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
33.0ms	(* (atan2 im re) (log base))
149.0ms	(* (log base) (log base))

simplify52.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	396	1034
1	1698	917
2	5001	875

prune382.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
0.4b	(* (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
0.4b	(* (atan2 im re) (log base))
0.5b	(pow (log base) 2)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

151×	`times-frac`
109×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
88×	`add-cube-cbrt`
48×	`add-exp-log` `associate-r`
24×	`div-exp`
20×	`add-cbrt-cube`
13×	`associate-/r*`
12×	`pow1` `1-exp`
11×	`prod-exp`
9×	`div-inv`
8×	`unswap-sqr`
6×	`cbrt-undiv` `rec-exp` `log-prod` `associate-l`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `associate-/l*`
2×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `associate-/r/` `log-pow` `-commutative` `flip--`
1×	`pow-to-exp` `pow-flip` `pow-pow` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `un-div-inv` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 213

Calls

4 calls:

5.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
30.0ms	(* (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
4.0ms	(* (atan2 im re) (log base))
2.0ms	(pow (log base) 2)

series453.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
65.0ms	(* (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
26.0ms	(* (atan2 im re) (log base))
151.0ms	(pow (log base) 2)

simplify95.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	791	2460
1	3520	2068
2	5001	1862

prune577.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes197.0ms

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	18	13
1	18	13

end0.0ms

sample2.1s

Algorithm

intervals

Results

930.0ms	8000×	body	80	valid
841.0ms	8012×	body	80	nan