Details

sample53.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
17.0ms	266×	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

prune6.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.9b

Counts

2 → 1

localize19.0ms

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)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 273

Calls

4 calls:

44.0ms	(/ (+ (* (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))
5.0ms	(* (log base) (log base))
18.0ms	(sqrt (+ (* re re) (* im im)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
153.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	479	3824
1	1842	3481
2	5002	3419

prune518.0ms

Filtered

285 candidates to 104 candidates (36.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	276	9	285
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	277	9	286

Merged error: 0.1b

Counts

286 → 9

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (+ (* (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))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

399×	`*-un-lft-identity`
184×	`distribute-lft-out`
176×	`associate-l`
117×	`times-frac`
108×	`pow1`
96×	`log-pow`
86×	`swap-sqr`
41×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
13×	`associate-/r*`
12×	`log-prod`
9×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in`
3×	`expm1-log1p-u` `log1p-expm1-u` `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 → 223

Calls

3 calls:

43.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log (hypot re im)) (log base))
5.0ms	(* (log base) (log base))

series356.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
100.0ms	(* (log (hypot re im)) (log base))
149.0ms	(* (log base) (log base))

simplify72.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	387	2985
1	1580	2671
2	5002	2630

prune366.0ms

Filtered

232 candidates to 73 candidates (31.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	223	9	232
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	231	10	241

Merged error: 0b

Counts

241 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

1545×	`*-un-lft-identity`
1390×	`times-frac`
689×	`add-sqr-sqrt`
572×	`sqrt-prod`
519×	`add-cube-cbrt`
480×	`associate-l`
440×	`distribute-lft-out`
358×	`swap-sqr`
281×	`pow1`
270×	`log-pow`
172×	`associate-r`
113×	`unswap-sqr`
57×	`*-commutative`
49×	`associate-/l*`
42×	`associate-/r*`
25×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`div-inv` `associate-/l/`
10×	`div-exp`
7×	`cbrt-undiv`
6×	`log-prod`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `cbrt-unprod`
2×	`sqrt-div` `1-exp` `associate-/r/`
1×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip-+` `fma-udef`

Counts

4 → 907

Calls

4 calls:

51.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
7.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
5.0ms	(* (log base) (log base))

series606.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
156.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
106.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
152.0ms	(* (log base) (log base))

simplify245.0ms

Algorithm

egg-herbie

Counts

919 → 919

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	1440	21933
1	3908	19342
2	5002	18974

prune1.0s

Filtered

919 candidates to 190 candidates (20.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	917	2	919
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	920	9	929

Merged error: 0b

Counts

929 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) 4)))
0.4b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
58×	`add-sqr-sqrt` `*-un-lft-identity`
56×	`add-cube-cbrt`
19×	`pow1`
16×	`associate-/l*`
12×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`associate-/l/`
7×	`log-pow`
6×	`log-prod` `swap-sqr` `associate-/r*`
5×	`div-inv`
4×	`expm1-log1p-u` `unpow-prod-down` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `pow-unpow` `distribute-lft-in` `div-exp`
2×	`frac-2neg` `clear-num`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `pow-prod-down` `pow-exp` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `unswap-sqr` `sqr-pow`

Counts

4 → 148

Calls

4 calls:

7.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) 4)))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
5.0ms	(* (log base) (log base))
3.0ms	(pow (log base) 4)

series606.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) 4)))
107.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
151.0ms	(* (log base) (log base))
169.0ms	(pow (log base) 4)

simplify78.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	581	2151
1	2499	2021
2	5002	2017

prune750.0ms

Filtered

160 candidates to 118 candidates (73.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	160	9	169

Merged error: 0b

Counts

169 → 9

regimes225.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	17
1	26	17
2	26	17

end0.0ms

sample1.5s

Algorithm

intervals

Results

558.0ms	8000×	body	80	valid
541.0ms	8146×	body	80	nan