Details

sample20.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 31.1b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt (+ (* re re) (* im im))))
0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
25×	`log-pow`
24×	`pow1` `times-frac`
20×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
16×	`sqrt-prod`
15×	`distribute-lft-out`
12×	`associate-l`
11×	`log-prod`
7×	`add-exp-log` `sqrt-pow1` `pow1/2`
6×	`sqrt-div` `swap-sqr` `add-cbrt-cube` `associate-/l*` `add-log-exp`
4×	`log-div` `flip3-+` `associate-/r*` `flip-+`
2×	`div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 108

Calls

4 calls:

20.0ms	(log (sqrt (+ (* re re) (* im im))))
16.0ms	(+ (* re re) (* im im))
21.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
17.0ms	(sqrt (+ (* re re) (* im im)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(log (sqrt (+ (* re re) (* im im))))
28.0ms	(+ (* re re) (* im im))
144.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify100.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	264	988
1	912	917
2	2977	917
3	5003	917

prune254.0ms

Filtered

120 candidates to 71 candidates (59.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	105	15	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	15	121

Merged error: 7.0b

Counts

121 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.4b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

224×	`associate-/r*`
208×	`frac-times`
207×	`sqrt-prod`
201×	`add-sqr-sqrt`
185×	`*-un-lft-identity`
154×	`add-cube-cbrt`
143×	`associate-/l*`
135×	`log-pow`
127×	`times-frac`
113×	`pow1`
46×	`associate-r`
33×	`associate-l` `clear-num`
32×	`frac-2neg`
30×	`sqrt-pow1` `pow1/2`
28×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`associate-*r/`
15×	`unswap-sqr`
13×	`associate-*l/`
10×	`distribute-lft-out`
9×	`div-exp`
8×	`prod-exp`
6×	`add-log-exp`
5×	`cbrt-undiv`
4×	`sqrt-div` `swap-sqr` `cbrt-unprod`
3×	`flip3-+` `un-div-inv` `flip-+` `div-inv`
2×	`log-div` `rec-exp` `1-exp` `div-sub`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `*-commutative`

Counts

4 → 452

Calls

4 calls:

17.0ms	(+ (* re re) (* im im))
43.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
22.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
17.0ms	(sqrt (+ (* re re) (* im im)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* re re) (* im im))
149.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
222.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify85.0ms

Algorithm

egg-herbie

Counts

464 → 464

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1260	5791
1	5002	5310

prune682.0ms

Filtered

464 candidates to 163 candidates (35.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	451	13	464
Fresh	11	3	14
Picked	1	0	1
Done	0	0	0
Total	463	16	479

Merged error: 6.9b

Counts

479 → 16

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.8b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

121×	`*-un-lft-identity`
74×	`sqrt-prod`
72×	`add-sqr-sqrt`
67×	`times-frac`
59×	`add-cube-cbrt`
50×	`pow-unpow`
45×	`associate-l`
41×	`log-pow`
34×	`associate-r`
33×	`unpow-prod-down`
30×	`log-prod`
25×	`distribute-lft-out`
22×	`pow1`
15×	`distribute-rgt-in` `distribute-lft-in`
14×	`add-exp-log`
13×	`associate-*l/`
10×	`swap-sqr`
9×	`add-cbrt-cube`
7×	`associate-/r*`
6×	`pow-pow` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`sqrt-pow1` `pow1/2` `div-inv` `associate-/l*` `sqr-pow`
2×	`flip3-+` `sqrt-div` `div-exp` `sqrt-pow2` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `rec-exp` `frac-2neg` `1-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `*-commutative`

Counts

4 → 208

Calls

4 calls:

19.0ms	(+ (* re re) (* im im))
45.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
23.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
17.0ms	(sqrt (+ (* re re) (* im im)))

series817.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* re re) (* im im))
378.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
367.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	705	2541
1	2857	2115
2	5002	1957

prune414.0ms

Filtered

220 candidates to 119 candidates (54.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	215	5	220
Fresh	9	6	15
Picked	0	1	1
Done	0	0	0
Total	224	12	236

Merged error: 6.8b

Counts

236 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (* (/ 1 (sqrt (log 10.0))) (cbrt (/ 1 (sqrt (log 10.0))))) (log (pow (sqrt (+ (* re re) (* im im))) (* (cbrt (/ 1 (sqrt (log 10.0)))) (cbrt (/ 1 (sqrt (log 10.0))))))))
5.8b	(pow (sqrt (+ (* re re) (* im im))) (* (cbrt (/ 1 (sqrt (log 10.0)))) (cbrt (/ 1 (sqrt (log 10.0))))))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

680×	`add-sqr-sqrt`
451×	`cbrt-prod`
442×	`times-frac`
434×	`*-un-lft-identity`
392×	`sqrt-prod`
278×	`pow-unpow`
267×	`add-cube-cbrt`
232×	`associate-r`
215×	`log-pow`
208×	`associate-*l/`
196×	`associate-/r*`
190×	`associate-l`
182×	`cbrt-div`
169×	`frac-times`
164×	`unswap-sqr`
94×	`swap-sqr`
85×	`pow1`
84×	`associate-/l*`
33×	`unpow-prod-down`
30×	`log-prod`
28×	`frac-2neg` `clear-num`
25×	`distribute-lft-out`
20×	`add-exp-log`
18×	`add-cbrt-cube`
15×	`distribute-rgt-in` `distribute-lft-in`
14×	`div-inv`
13×	`associate-*r/`
9×	`prod-exp` `cbrt-unprod`
6×	`pow-pow` `add-log-exp`
4×	`*-commutative`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down` `sqr-pow`
2×	`cbrt-undiv` `flip3-+` `sqrt-div` `div-exp` `sqrt-pow2` `flip-+`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `rec-exp` `1-exp` `pow-exp` `sum-log`

Counts

4 → 713

Calls

4 calls:

16.0ms	(+ (* re re) (* im im))
261.0ms	(* (* (/ 1 (sqrt (log 10.0))) (cbrt (/ 1 (sqrt (log 10.0))))) (log (pow (sqrt (+ (* re re) (* im im))) (* (cbrt (/ 1 (sqrt (log 10.0)))) (cbrt (/ 1 (sqrt (log 10.0))))))))
47.0ms	(pow (sqrt (+ (* re re) (* im im))) (* (cbrt (/ 1 (sqrt (log 10.0)))) (cbrt (/ 1 (sqrt (log 10.0))))))
16.0ms	(sqrt (+ (* re re) (* im im)))

series1.1s

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
558.0ms	(* (* (/ 1 (sqrt (log 10.0))) (cbrt (/ 1 (sqrt (log 10.0))))) (log (pow (sqrt (+ (* re re) (* im im))) (* (cbrt (/ 1 (sqrt (log 10.0)))) (cbrt (/ 1 (sqrt (log 10.0))))))))
518.0ms	(pow (sqrt (+ (* re re) (* im im))) (* (cbrt (/ 1 (sqrt (log 10.0)))) (cbrt (/ 1 (sqrt (log 10.0))))))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify156.0ms

Algorithm

egg-herbie

Counts

725 → 725

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2096	15183
1	5001	14553

prune1.6s

Filtered

725 candidates to 348 candidates (48.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	719	6	725
Fresh	4	6	10
Picked	1	0	1
Done	1	0	1
Total	725	12	737

Merged error: 6.8b

Counts

737 → 12

regimes594.0ms

Accuracy

55.5% (10.8b remaining)

Error of 18.2b against oracle of 7.4b and baseline of 31.6b

bsearch221.0ms

Steps

Iters	Range		Point
10	1.4300156806233347e+71	2.8787744468916765e+83	2.2414384362599133e+83
7	2.8231387681942284e-225	7.358046812615038e-224	4.543347056569168e-225
8	-1.8208622260955044e-231	-6.0728879748155805e-236	-2.3437866053113895e-235
7	-2.368357192809402e+37	-1.5412000392698586e+35	-2.3080563981284436e+37

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	128
1	62	128

end0.0ms

sample497.0ms

Algorithm

intervals

Results

358.0ms

8000×

body

valid