Details

sample58.0ms

Algorithm

intervals

Results

21.0ms	276×	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: 29.5b

localize20.0ms

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)))

rewrite26.0ms

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))
10.0ms	(/ (- (* (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)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (atan2 im re) (log base))
33.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
146.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (46.0ms)

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

prune428.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(* (atan2 im re) (log base))
0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (* 1 (hypot re im))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))

rewrite22.0ms

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:

1.0ms	(hypot re im)
4.0ms	(* (atan2 im re) (log base))
9.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (* 1 (hypot re im))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))

series259.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot re im)
33.0ms	(* (atan2 im re) (log base))
34.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (* 1 (hypot re im))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
148.0ms	(* (log base) (log base))

simplify53.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	400	1082
1	1739	960
2	5001	912

prune397.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (* 2 (log (cbrt base))))
0.4b	(* (log base) (log (cbrt base)))
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
24×	`cbrt-prod`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-l`
6×	`associate-r`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `log-pow` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`*-commutative`
1×	`unswap-sqr`

Counts

4 → 106

Calls

4 calls:

7.0ms	(* (log base) (* 2 (log (cbrt base))))
5.0ms	(* (log base) (log (cbrt base)))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series1.2s

Counts

4 → 12

Calls

4 calls:

415.0ms	(* (log base) (* 2 (log (cbrt base))))
393.0ms	(* (log base) (log (cbrt base)))
178.0ms	(cbrt base)
175.0ms	(cbrt base)

simplify43.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	314	817
1	1256	728
2	5002	688

prune476.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma 0.0 0.0 (pow (log base) 2)) (log (hypot re im)))
0.4b	(/ (log base) (/ (fma 0.0 0.0 (pow (log base) 2)) (atan2 im re)))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

109×	`times-frac`
66×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
26×	`pow1`
20×	`log-pow`
17×	`associate-/r*`
13×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`unpow-prod-down`
7×	`div-inv` `associate-/l*`
6×	`pow-unpow`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `frac-2neg` `pow-exp` `clear-num` `unpow2` `sqr-pow`
1×	`associate-/r/`

Counts

4 → 161

Calls

4 calls:

3.0ms	(/ (fma 0.0 0.0 (pow (log base) 2)) (log (hypot re im)))
7.0ms	(/ (log base) (/ (fma 0.0 0.0 (pow (log base) 2)) (atan2 im re)))
3.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)

series659.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ (fma 0.0 0.0 (pow (log base) 2)) (log (hypot re im)))
142.0ms	(/ (log base) (/ (fma 0.0 0.0 (pow (log base) 2)) (atan2 im re)))
151.0ms	(pow (log base) 2)
150.0ms	(pow (log base) 2)

simplify68.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	533	1763
1	2241	1587
2	5001	1586

prune590.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes230.0ms

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	23	14
1	25	14
2	25	14

end0.0ms

sample1.5s

Algorithm

intervals

Results

594.0ms	8000×	body	80	valid
558.0ms	7967×	body	80	nan