Details

sample59.0ms

Algorithm

intervals

Results

19.0ms	268×	body	80	nan
17.0ms	256×	body	80	valid

simplify6.0ms

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: 33.3b

localize25.0ms

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))
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite75.0ms

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:

40.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
86.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
149.0ms	(* (log base) (log base))
33.0ms	(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

prune458.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (exp (log (hypot re im)))) (log base))
0.5b	(* (log base) (log base))
5.8b	(exp (log (hypot re im)))

rewrite74.0ms

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:

40.0ms	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
17.0ms	(* (log (exp (log (hypot re im)))) (log base))
9.0ms	(* (log base) (log base))
3.0ms	(exp (log (hypot re im)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
95.0ms	(* (log (exp (log (hypot re im)))) (log base))
144.0ms	(* (log base) (log base))
42.0ms	(exp (log (hypot re im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (44.0ms)

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

prune456.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.3b	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.5b	(* (log base) (log base))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
44×	`add-sqr-sqrt` `*-un-lft-identity`
42×	`add-cube-cbrt`
25×	`add-exp-log`
24×	`sqrt-prod`
20×	`add-cbrt-cube`
17×	`pow1`
10×	`div-exp` `associate-/l*`
9×	`div-inv`
7×	`cbrt-undiv` `associate-/r*`
6×	`log-prod` `swap-sqr` `log-pow`
5×	`prod-exp`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `cbrt-unprod`
2×	`frac-2neg` `sqrt-div` `1-exp` `clear-num` `associate-/r/`
1×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+` `fma-udef` `associate-/l/` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

23.0ms	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
8.0ms	(/ (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))
12.0ms	(* (log base) (log base))

series991.0ms

Counts

4 → 12

Calls

4 calls:

393.0ms	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
320.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
133.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
144.0ms	(* (log base) (log base))

simplify71.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	552	2655
1	2004	2343
2	5002	2317

prune728.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`add-cbrt-cube`
30×	`add-sqr-sqrt`
26×	`times-frac` `prod-exp`
25×	`div-exp`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
13×	`associate-r`
10×	`cbrt-undiv` `1-exp`
9×	`cbrt-unprod`
7×	`pow1` `associate-l`
6×	`associate-/l*`
5×	`rec-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `un-div-inv` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 127

Calls

4 calls:

5.0ms	(/ 1 (hypot (log base) 0.0))
8.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
34.0ms	(* (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (/ 1 (hypot (log base) 0.0)))
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

331.0ms	(/ 1 (hypot (log base) 0.0))
336.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
328.0ms	(* (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (/ 1 (hypot (log base) 0.0)))
125.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	492	1767
1	2097	1440
2	5001	1414

prune395.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes235.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	14
1	23	14
2	23	14

end0.0ms

sample1.6s

Algorithm

intervals

Results

555.0ms	7964×	body	80	nan
550.0ms	8000×	body	80	valid