Details

analyze439.0ms

Algorithm: search

sample40.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
3.0ms	34×	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

prune6.0ms

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: 32.1b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (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))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

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:

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

series68.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
27.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

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

prune240.0ms

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: 8.0b

Counts

123 → 15

localize25.0ms

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))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

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)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (/ (+ (* (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))))
19.0ms	(* (log base) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify120.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	850	8816
1	3118	8203
2	5001	8093

prune468.0ms

Filtered

136 candidates to 290 candidates (-113.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	289	1	290
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	290	15	305

Merged error: 8.0b

Counts

305 → 15

localize20.0ms

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)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

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:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
24.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (61.0ms)

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

prune210.0ms

Filtered

83 candidates to 133 candidates (-60.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	129	4	133
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	132	16	148

Merged error: 7.9b

Counts

148 → 16

localize26.0ms

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) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`pow1/3` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

12.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series102.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
22.0ms	(cbrt base)
22.0ms	(cbrt base)
8.0ms	(sqrt (+ (* re re) (* im im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	384	1340
1	1264	1221
2	5001	1183

prune127.0ms

Filtered

66 candidates to 80 candidates (-21.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	79	17	96

Merged error: 7.9b

Counts

96 → 17

regimes587.0ms

Accuracy

54.4% (11.0b remaining)

Error of 18.5b against oracle of 7.5b and baseline of 31.6b

bsearch807.0ms

Steps

Iters	Range		Point
7	3.324644789917205e+120	8.097093288381994e+121	9.308212919727322e+120
7	1.2099830407569744e-167	4.7143064297499345e-166	1.2275721563055769e-167
6	1.6652756259030225e-207	7.79258069291757e-207	7.686405131369307e-207
8	-0.0005277783850781407	-1.7170668541937725e-07	-0.0005166771296062651

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	99
1	95	99
2	95	99

end0.0ms

analyze438.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

788.0ms	8000×	body	80	valid
90.0ms	965×	body	80	nan

Details

analyze439.0ms

sample40.0ms

simplify3.0ms

prune6.0ms

localize19.0ms

rewrite27.0ms

series68.0ms

simplify59.0ms

prune240.0ms

localize25.0ms

rewrite45.0ms

series64.0ms

simplify120.0ms

prune468.0ms

localize20.0ms

rewrite32.0ms

series66.0ms

simplify77.0ms

prune210.0ms

localize26.0ms

rewrite19.0ms

series102.0ms

simplify43.0ms

prune127.0ms

regimes587.0ms

bsearch807.0ms

simplify3.0ms

end0.0ms

analyze438.0ms

sample1.1s

Profiling