Details

sample72.0ms

Algorithm

intervals

Results

24.0ms	250×	body	80	nan
22.0ms	256×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune5.0ms

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: 33.2b

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))
0.6b	(* (log base) (log base))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

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×	`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` `div-inv`

Counts

4 → 110

Calls

4 calls:

12.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
76.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5002	1203

prune592.0ms

Filtered

122 candidates to 84 candidates (68.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	13	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Merged error: 7.2b

Counts

123 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(pow (log base) 2)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`unpow-prod-down` `associate-r` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

10.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
75.0ms	(pow (log base) 2)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	443	1231
1	1594	1134
2	5001	1115

prune568.0ms

Filtered

105 candidates to 76 candidates (72.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	101	17	118

Merged error: 7.2b

Counts

118 → 17

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (* 0.0 0.0) (pow (log base) 2))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
0.6b	(pow (log base) 2)
0.6b	(pow (log base) 2)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
151×	`add-sqr-sqrt`
150×	`add-cube-cbrt` `*-un-lft-identity`
141×	`sqrt-prod`
24×	`associate-/r*`
18×	`sqrt-div`
15×	`associate-/r/`
11×	`add-exp-log`
9×	`pow1` `flip3-+` `add-cbrt-cube` `flip-+`
8×	`unpow-prod-down` `div-inv`
6×	`pow-unpow` `associate-/l*`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow-to-exp` `pow-pow` `pow-exp` `log-pow` `associate-/l/` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 244

Calls

4 calls:

19.0ms	(/ (sqrt (+ (* 0.0 0.0) (pow (log base) 2))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
2.0ms	(pow (log base) 2)
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (sqrt (+ (* 0.0 0.0) (pow (log base) 2))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
76.0ms	(pow (log base) 2)
75.0ms	(pow (log base) 2)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify140.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	812	8104
1	3798	7614
2	5001	7542

prune1.0s

Filtered

256 candidates to 131 candidates (51.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	255	18	273

Merged error: 7.2b

Counts

273 → 18

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* 0.0 0.0) (pow (log base) 2)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(pow (log base) 2)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`unpow-prod-down` `associate-r` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

11.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* 0.0 0.0) (pow (log base) 2)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* 0.0 0.0) (pow (log base) 2)))
91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
75.0ms	(pow (log base) 2)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	439	1242
1	1585	1132
2	5002	1113

prune480.0ms

Filtered

105 candidates to 76 candidates (72.4%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	16	16
Picked	0	1	1
Done	0	1	1
Total	105	18	123

Merged error: 7.2b

Counts

123 → 18

regimes685.0ms

Accuracy

57% (10.7b remaining)

Error of 18.0b against oracle of 7.4b and baseline of 32.2b

bsearch310.0ms

Steps

Iters	Range		Point
8	5.936133990141283e+82	9.555849306330013e+86	2.2360511850626944e+85
6	5.0919682425458094e-191	7.285182887723109e-190	4.084191447942957e-190
8	-1.9703772701366753e-306	2.12138673346124e-307	-1.2300165181090967e-307
8	-24776207428773.418	-5704240281.847295	-24361133460477.875

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	61
1	65	61

end0.0ms

sample2.1s

Algorithm

intervals

Results

889.0ms	8000×	body	80	valid
646.0ms	7842×	body	80	nan

Details

sample72.0ms

simplify3.0ms

prune5.0ms

localize19.0ms

rewrite29.0ms

series297.0ms

simplify57.0ms

prune592.0ms

localize25.0ms

rewrite23.0ms

series341.0ms

simplify51.0ms

prune568.0ms

localize24.0ms

rewrite44.0ms

series326.0ms

simplify140.0ms

prune1.0s

localize25.0ms

rewrite25.0ms

series298.0ms

simplify56.0ms

prune480.0ms

regimes685.0ms

bsearch310.0ms

simplify2.0ms

end0.0ms

sample2.1s

Profiling