Details

sample482.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.520795%

Guaranteed chance to sample good point: 28.598151%

Results

25.0ms	256×	body	80	valid
15.0ms	140×	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: 29.2b

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))
0.5b	(* (log base) (log base))
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
21.0ms	(* (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	457	1397
1	1716	1276
2	5001	1225

prune227.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	107	15	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 7.1b

Counts

123 → 15

localize22.0ms

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))
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite48.0ms

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:

18.0ms	(/ (/ (+ (* (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))))
5.0ms	(* (log base) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (/ (+ (* (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))))
14.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify122.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	850	8815
1	3118	8203
2	5001	8093

prune450.0ms

Filtered

136 candidates to 290 candidates (-113.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	288	2	290
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	288	17	305

Merged error: 7.0b

Counts

305 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (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))
27.0b	(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))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
20.0ms	(* (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 (46.0ms)

Iter	Nodes	Cost
0	464	1397
1	1754	1281
2	5002	1229

prune195.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	4	11	15
Picked	1	0	1
Done	0	1	1
Total	122	17	139

Merged error: 7.0b

Counts

139 → 17

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (neg (pow 0.0 3)) 0.0) (* (pow (log base) 3) (log base)))) (- (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
0.7b	(pow (log base) 3)
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
23×	`pow1`
19×	`associate-l`
18×	`log-prod`
17×	`distribute-rgt-in` `distribute-lft-in`
12×	`add-exp-log` `associate--l+` `add-cbrt-cube`
10×	`times-frac`
8×	`associate-r` `log-pow`
6×	`swap-sqr`
4×	`unpow-prod-down` `cube-prod` `add-log-exp`
3×	`pow-unpow` `prod-exp` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `sub-neg` `flip3--` `flip3-+` `sqrt-div` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `flip--` `flip-+`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow-plus` `pow1/2` `unpow3` `div-exp` `associate-*l/` `pow-exp` `pow-sqr` `pow-prod-up` `div-inv` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`

Counts

4 → 131

Calls

4 calls:

17.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (neg (pow 0.0 3)) 0.0) (* (pow (log base) 3) (log base)))) (- (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (neg (pow 0.0 3)) 0.0) (* (pow (log base) 3) (log base)))) (- (* (log base) (log base)) (* 0.0 0.0)))
16.0ms	(* (log base) (log base))
17.0ms	(pow (log base) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify132.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	698	2334
1	3878	2031
2	5001	2010

prune234.0ms

Filtered

89 candidates to 143 candidates (-60.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	1	14	15
Picked	1	0	1
Done	0	1	1
Total	140	20	160

Merged error: 7.0b

Counts

160 → 20

regimes767.0ms

Accuracy

59.3% (9.9b remaining)

Error of 17.6b against oracle of 7.7b and baseline of 32.1b

bsearch84.0ms

Steps

Iters	Range		Point
6	6.4848302412504975e+146	4.362182965464172e+147	6.912776057609603e+146
8	-1.146677772056477e+149	-4.705897028711979e+144	-9.048963224313869e+144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	44
1	50	44

end0.0ms

sample2.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.520795%

Guaranteed chance to sample good point: 28.598151%

Results

753.0ms	8000×	body	80	valid
374.0ms	4156×	body	80	nan

Details

sample482.0ms

simplify3.0ms

prune4.0ms

localize19.0ms

rewrite28.0ms

series64.0ms

simplify58.0ms

prune227.0ms

localize22.0ms

rewrite48.0ms

series58.0ms

simplify122.0ms

prune450.0ms

localize21.0ms

rewrite25.0ms

series85.0ms

simplify58.0ms

prune195.0ms

localize28.0ms

rewrite31.0ms

series64.0ms

simplify132.0ms

prune234.0ms

regimes767.0ms

bsearch84.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling