Details

analyze1.1s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 46.952782%

Guaranteed chance to sample good point: 88.149127%

sample39.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
2.0ms	18×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune4.0ms

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: 35.3b

Counts

2 → 1

localize19.0ms

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))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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)) (* (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)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
25.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	457	1397
1	1716	1276
2	5001	1225

prune209.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	111	11	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	12	123

Merged error: 7.3b

Counts

123 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify147.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (138.0ms)

Iter	Nodes	Cost
0	273	768
1	973	677
2	4633	614
3	5001	580

prune199.0ms

Filtered

71 candidates to 127 candidates (-78.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	125	14	139

Merged error: 7.3b

Counts

139 → 14

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)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
25×	`pow1`
23×	`add-cube-cbrt` `associate-r`
17×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
12×	`log-prod`
11×	`times-frac`
10×	`log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`flip3-+` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod` `*-commutative`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `associate-*l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `rec-exp` `pow-plus` `1-exp` `associate-*r/` `pow-sqr` `un-div-inv` `pow-prod-up` `div-inv`

Counts

4 → 121

Calls

4 calls:

12.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (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)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
16.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	581	1547
1	2548	1393
2	5001	1339

prune190.0ms

Filtered

83 candidates to 133 candidates (-60.2%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	131	16	147

Merged error: 7.3b

Counts

147 → 16

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.7b	(cbrt base)
0.7b	(cbrt base)
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
6×	`add-exp-log` `cbrt-prod` `log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
22.0ms	(cbrt base)
23.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	244	528
1	664	483
2	1904	432
3	5001	430

prune90.0ms

Filtered

55 candidates to 77 candidates (-40.0%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	3	10	13
Picked	0	1	1
Done	0	2	2
Total	78	15	93

Merged error: 7.2b

Counts

93 → 15

Details

analyze1.1s

sample39.0ms

simplify3.0ms

prune4.0ms

localize19.0ms

rewrite26.0ms

series71.0ms

simplify58.0ms

prune209.0ms

localize22.0ms

rewrite23.0ms

series57.0ms

simplify147.0ms

prune199.0ms

localize19.0ms

rewrite29.0ms

series68.0ms

simplify74.0ms

prune190.0ms

localize27.0ms

rewrite13.0ms

series76.0ms

simplify54.0ms

prune90.0ms

regimes724.0ms

bsearch1.0ms

Profiling