Details

sample64.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
19.0ms	241×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune4.0ms

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: 30.4b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

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:

9.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
95.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
143.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

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

prune431.0ms

Filtered

122 candidates to 84 candidates (68.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	106	16	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	16	123

Merged error: 7.2b

Counts

123 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
163×	`add-sqr-sqrt`
162×	`*-un-lft-identity`
158×	`add-cube-cbrt`
141×	`sqrt-prod`
31×	`pow1`
24×	`associate-/l*`
18×	`sqrt-div`
16×	`associate-/r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`log-prod` `swap-sqr` `log-pow`
9×	`flip3-+` `flip-+`
8×	`associate-r` `associate-l` `div-inv`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 278

Calls

4 calls:

34.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
9.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
148.0ms	(* (log base) (log base))
145.0ms	(* (log base) (log base))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify117.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	839	8780
1	3156	8145
2	5001	8032

prune761.0ms

Filtered

290 candidates to 137 candidates (47.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	285	5	290
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	289	17	306

Merged error: 7.2b

Counts

306 → 17

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

44×	`pow1`
30×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod` `swap-sqr` `log-pow`
12×	`associate-r` `associate-l`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `sqrt-prod` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 123

Calls

4 calls:

5.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (log base) (log base))
146.0ms	(* (log base) (log base))
147.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	183	556
1	603	486
2	2608	453
3	5001	429

prune462.0ms

Filtered

135 candidates to 69 candidates (51.1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	133	19	152

Merged error: 7.1b

Counts

152 → 19

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`sqrt-div`
5×	`add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `pow-pow` `pow-exp` `log-pow` `unpow2` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(pow (log base) 2)
34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	169	373
1	482	348
2	1597	348
3	5002	344

prune290.0ms

Filtered

76 candidates to 56 candidates (73.7%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	17	17
Picked	0	1	1
Done	0	1	1
Total	76	19	95

Merged error: 7.1b

Counts

95 → 19

Details

sample64.0ms

simplify4.0ms

prune4.0ms

localize19.0ms

rewrite30.0ms

series360.0ms

simplify58.0ms

prune431.0ms

localize21.0ms

rewrite84.0ms

series441.0ms

simplify117.0ms

prune761.0ms

localize24.0ms

rewrite22.0ms

series480.0ms

simplify89.0ms

prune462.0ms

localize24.0ms

rewrite15.0ms

series254.0ms

simplify62.0ms

prune290.0ms

regimes449.0ms

bsearch4.0ms

Profiling