Details

sample48.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
15.0ms	216×	body	80	nan

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: 32.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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:

13.0ms	(/ (+ (* (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)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
158.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (50.0ms)

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

prune476.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.3b	(* (log (exp (log (hypot re im)))) (log base))
0.5b	(* (log base) (log base))
5.8b	(exp (log (hypot re im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
23×	`pow1`
15×	`log-prod`
14×	`log-pow`
12×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`exp-prod` `associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum` `associate-/r` `associate-/l`
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` `rem-exp-log`

Counts

4 → 120

Calls

4 calls:

15.0ms	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
8.0ms	(* (log (exp (log (hypot re im)))) (log base))
5.0ms	(* (log base) (log base))
2.0ms	(exp (log (hypot re im)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
108.0ms	(* (log (exp (log (hypot re im)))) (log base))
153.0ms	(* (log base) (log base))
47.0ms	(exp (log (hypot re im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	422	1267
1	1601	1092
2	5001	1044

prune483.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

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))
30.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
3.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

349.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
355.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
496.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
140.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))

simplify101.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	936	3396
1	4367	2773
2	5001	2572

prune664.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(/ (- (* (log (/ 1 base)) (log (hypot re im))) (* (atan2 im re) 0.0)) (- (+ (pow (log base) 2) (* 0.0 0.0))))
0.3b	(* (log (/ 1 base)) (log (hypot re im)))
0.5b	(pow (log base) 2)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
30×	`times-frac`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`pow1`
10×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`expm1-log1p-u` `neg-mul-1` `unpow-prod-down` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `associate-/l*`
2×	`associate-/r/` `associate-/l/` `distribute-neg-frac`
1×	`cbrt-undiv` `distribute-lft-neg-out` `pow-to-exp` `hypot-udef` `flip3--` `pow-flip` `pow-pow` `frac-2neg` `flip3-+` `div-sub` `div-exp` `log-rec` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `div-inv` `unpow2` `inv-pow` `unswap-sqr` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

0.0ms	(hypot re im)
33.0ms	(/ (- (* (log (/ 1 base)) (log (hypot re im))) (* (atan2 im re) 0.0)) (- (+ (pow (log base) 2) (* 0.0 0.0))))
6.0ms	(* (log (/ 1 base)) (log (hypot re im)))
2.0ms	(pow (log base) 2)

series547.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot re im)
219.0ms	(/ (- (* (log (/ 1 base)) (log (hypot re im))) (* (atan2 im re) 0.0)) (- (+ (pow (log base) 2) (* 0.0 0.0))))
123.0ms	(* (log (/ 1 base)) (log (hypot re im)))
154.0ms	(pow (log base) 2)

simplify66.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	520	1839
1	2104	1720
2	5002	1689

prune514.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes222.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

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

543.0ms	8129×	body	80	nan
530.0ms	8000×	body	80	valid