Details

sample50.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
15.0ms	234×	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 (100.0%)

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: 34.6b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (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))
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

413×	`*-un-lft-identity`
189×	`distribute-lft-out`
182×	`associate-l`
117×	`times-frac`
111×	`pow1`
98×	`log-pow`
88×	`swap-sqr`
44×	`add-sqr-sqrt`
39×	`add-cube-cbrt`
13×	`associate-/r*`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`associate-r` `sqrt-prod`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`flip3-+` `flip-+`
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 → 239

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
42.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
15.0ms	(sqrt (+ (* re re) (* im im)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
108.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
148.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	447	3802
1	1736	3598
2	5001	3555

prune381.0ms

Filtered

251 candidates to 84 candidates (66.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	237	14	251
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	238	14	252

Merged error: 6.5b

Counts

252 → 14

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))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

460×	`*-un-lft-identity`
207×	`distribute-lft-out`
201×	`associate-l`
144×	`times-frac`
138×	`sqrt-prod`
125×	`pow1`
106×	`log-pow`
94×	`swap-sqr`
59×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
16×	`associate-/r*`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 277

Calls

4 calls:

41.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms	(* (log base) (log base))
7.0ms	(* (log base) (log base))
15.0ms	(sqrt (+ (* re re) (* im im)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
151.0ms	(* (log base) (log base))
154.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	383	4631
1	1303	4482
2	5001	4458

prune445.0ms

Filtered

289 candidates to 86 candidates (70.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	284	5	289
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	286	17	303

Merged error: 6.0b

Counts

303 → 17

localize27.0ms

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))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

460×	`*-un-lft-identity`
207×	`distribute-lft-out`
201×	`associate-l`
144×	`times-frac`
138×	`sqrt-prod`
125×	`pow1`
106×	`log-pow`
94×	`swap-sqr`
59×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
16×	`associate-/r*`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 277

Calls

4 calls:

44.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
15.0ms	(sqrt (+ (* re re) (* im im)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
164.0ms	(* (log base) (log base))
154.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	383	4631
1	1303	4482
2	5001	4458

prune464.0ms

Filtered

289 candidates to 86 candidates (70.2%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	283	6	289
Fresh	3	13	16
Picked	0	1	1
Done	0	0	0
Total	286	20	306

Merged error: 6.0b

Counts

306 → 20

localize29.0ms

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) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.5b	(cbrt base)
0.5b	(cbrt base)
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

753×	`*-un-lft-identity`
529×	`distribute-lft-out`
512×	`associate-l`
207×	`times-frac`
173×	`pow1`
168×	`log-pow`
42×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
23×	`associate-/r*`
9×	`associate-/l*`
8×	`sqrt-prod`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
4×	`add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `sqrt-div` `swap-sqr` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 297

Calls

4 calls:

75.0ms	(/ (+ (* (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)
16.0ms	(sqrt (+ (* re re) (* im im)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (+ (* (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)))
185.0ms	(cbrt base)
184.0ms	(cbrt base)
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	359	7202
1	1261	6758
2	5001	6719

prune331.0ms

Filtered

309 candidates to 67 candidates (78.3%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	303	6	309
Fresh	4	14	18
Picked	1	0	1
Done	0	1	1
Total	308	21	329

Merged error: 6.0b

Counts

329 → 21

regimes738.0ms

Accuracy

55.9% (10.9b remaining)

Error of 17.9b against oracle of 6.9b and baseline of 31.7b

bsearch506.0ms

Steps

Iters	Range		Point
8	1.8928424626778097e+105	3.5603919313378187e+108	2.191848355099136e+106
10	6.123762721398031e-164	8.253311997854725e-152	8.173008569527876e-164
8	9.432266112294676e-213	5.800535530920395e-210	1.1577999421500484e-210
9	1.3859774453333566e-282	3.4576835320353003e-275	8.348787158178368e-276
9	-1.0862791531793222e-233	-5.4386842601520746e-241	-7.360482992436006e-240
7	-2.6592165972836943e+99	-1.6773217067290726e+97	-1.400795767930609e+99

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	100	165
1	100	165

end0.0ms

sample1.4s

Algorithm

intervals

Results

543.0ms	8000×	body	80	valid
523.0ms	7882×	body	80	nan