Details

sample52.0ms

Algorithm

intervals

Results

17.0ms	255×	body	80	nan
17.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	33	16
2	33	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `hypot-def` `div-inv`

Counts

4 → 119

Calls

4 calls:

16.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
88.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
144.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	467	1408
1	1820	1268
2	5001	1217

prune459.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`pow1`
12×	`log-prod`
9×	`add-exp-log` `times-frac` `add-cbrt-cube`
8×	`associate-r` `associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`flip3-+` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

3 → 99

Calls

3 calls:

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

series344.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
96.0ms	(* (log (hypot re im)) (log base))
143.0ms	(* (log base) (log base))

simplify56.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	377	1035
1	1559	925
2	5002	895

prune343.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (hypot (log base) 0.0) 1))
0.3b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
0.3b	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
0.4b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
157×	`times-frac`
104×	`add-sqr-sqrt`
93×	`div-exp`
90×	`*-un-lft-identity`
85×	`add-cube-cbrt`
62×	`prod-exp`
50×	`add-cbrt-cube`
44×	`associate-l`
41×	`1-exp`
20×	`cbrt-undiv`
15×	`rec-exp`
14×	`associate-/r*`
13×	`cbrt-unprod`
11×	`div-inv`
7×	`pow1` `associate-r` `unswap-sqr`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 236

Calls

4 calls:

5.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
3.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
29.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

series945.0ms

Counts

4 → 12

Calls

4 calls:

344.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
150.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
344.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
107.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

simplify91.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	940	3390
1	4243	2753
2	5001	2552

prune643.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
23×	`add-exp-log` `add-cbrt-cube`
18×	`log-prod` `pow-prod-down`
16×	`add-sqr-sqrt`
15×	`distribute-rgt-in` `distribute-lft-in`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`prod-exp` `cbrt-unprod`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `times-frac` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `flip3--` `pow-plus` `div-exp` `associate-l/` `associate-/r/` `log-pow` `-commutative` `flip--` `associate-/l/` `difference-of-squares`
1×	`pow2` `frac-2neg` `div-sub` `swap-sqr` `clear-num` `associate-/r*` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

5.0ms	(* (log (hypot re im)) (log base))
43.0ms	(/ (- (* (* (log (hypot re im)) (log base)) (* (log (hypot re im)) (log base))) (* (* (atan2 im re) 0.0) (* (atan2 im re) 0.0))) (* (- (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0))))
13.0ms	(* (* (log (hypot re im)) (log base)) (* (log (hypot re im)) (log base)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series633.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (log (hypot re im)) (log base))
134.0ms	(/ (- (* (* (log (hypot re im)) (log base)) (* (log (hypot re im)) (log base))) (* (* (atan2 im re) 0.0) (* (atan2 im re) 0.0))) (* (- (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0))))
130.0ms	(* (* (log (hypot re im)) (log base)) (* (log (hypot re im)) (log base)))
266.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	553	1893
1	2782	1584
2	5001	1576

prune383.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes221.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	15
1	24	15
2	24	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

551.0ms	8000×	body	80	valid
542.0ms	7830×	body	80	nan