Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 46.952782%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

26.0ms	256×	body	80	valid
1.0ms	13×	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: 32.3b

Counts

2 → 1

localize18.0ms

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))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

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

series67.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
17.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

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

prune218.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	14	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 8.1b

Counts

123 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
30.1b	(sqrt (+ (* re re) (* im im)))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
58×	`add-sqr-sqrt`
42×	`pow1`
34×	`sqrt-pow1`
28×	`sqrt-div`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`swap-sqr`
18×	`pow1/2`
13×	`associate-r` `associate-l`
10×	`pow-prod-up` `unswap-sqr`
8×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
6×	`log-prod` `pow-prod-down` `pow-sqr` `log-pow`
4×	`frac-times` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`pow2` `rem-sqrt-square` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`sqrt-unprod` `rem-square-sqrt`

Counts

4 → 149

Calls

4 calls:

4.0ms	(* (log base) (log base))
14.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (log base) (log base))
6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	301	1061
1	1141	972
2	5002	934

prune180.0ms

Filtered

77 candidates to 161 candidates (-109.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	161	14	175

Merged error: 8.1b

Counts

175 → 14

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))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

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:

6.0ms	(* (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))
16.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify150.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (141.0ms)

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

prune215.0ms

Filtered

71 candidates to 127 candidates (-78.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	124	17	141

Merged error: 8.1b

Counts

141 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

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

series85.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
22.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (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	464	1397
1	1754	1281
2	5002	1229

prune131.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	4	11	15
Picked	1	0	1
Done	0	1	1
Total	121	18	139

Merged error: 8.0b

Counts

139 → 18

regimes525.0ms

Accuracy

58.2% (10.3b remaining)

Error of 17.5b against oracle of 7.2b and baseline of 31.8b

bsearch125.0ms

Steps

Iters	Range		Point
8	1.152822974566198e+150	4.214238667559254e+153	1.2475125811220505e+150
9	-1.1984104416062531e+67	-7.160644028716364e+58	-5.021003692737104e+62

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	37
1	46	37

end0.0ms

sample2.1s

Algorithm

intervals

sampling

Space saved by range analysis: 46.952782%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

785.0ms	8000×	body	80	valid
48.0ms	531×	body	80	nan

Details

sample1.1s

simplify3.0ms

prune4.0ms

localize18.0ms

rewrite25.0ms

series67.0ms

simplify57.0ms

prune218.0ms

localize23.0ms

rewrite32.0ms

series32.0ms

simplify54.0ms

prune180.0ms

localize22.0ms

rewrite21.0ms

series57.0ms

simplify150.0ms

prune215.0ms

localize20.0ms

rewrite25.0ms

series85.0ms

simplify58.0ms

prune131.0ms

regimes525.0ms

bsearch125.0ms

simplify1.0ms

end0.0ms

sample2.1s

Profiling