Details

sample30.0ms

Algorithm

intervals

Results

21.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
33.5b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

3.0ms	(+ (* re re) (* im im))
11.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series226.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* re re) (* im im))
163.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	256	741
1	895	697
2	2846	694
3	5001	694

prune245.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
33.5b	(sqrt (+ (* re re) (* im im)))
33.5b	(sqrt (+ (* re re) (* im im)))
33.5b	(sqrt (+ (* re re) (* im im)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

126×	`pow1`
94×	`log-pow`
72×	`times-frac`
60×	`sqrt-div`
54×	`cbrt-div`
45×	`pow1/3` `pow-prod-up`
34×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
30×	`flip3-+` `pow-plus` `flip-+`
28×	`frac-times`
26×	`log-div` `div-sub`
25×	`pow-prod-down`
18×	`associate-/l*`
15×	`pow-sqr`
14×	`associate-*l/`
10×	`pow2`
9×	`sqrt-prod`
8×	`associate-*r/`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow3`
4×	`associate-/r*` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 177

Calls

4 calls:

166.0ms	(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
34.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify150.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	480	3559
1	955	3468
2	3016	3076
3	5003	3048

prune442.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
0.5b	(cbrt (sqrt (+ (* re re) (* im im))))
0.6b	(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
33.5b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
84×	`add-sqr-sqrt`
83×	`add-cube-cbrt` `*-un-lft-identity`
68×	`log-pow`
52×	`pow1`
29×	`associate-/r*`
22×	`pow1/3`
11×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`cbrt-prod` `sqrt-prod` `div-inv`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `add-log-exp`
2×	`cbrt-div` `frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`

Counts

4 → 186

Calls

4 calls:

7.0ms	(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
3.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
3.0ms	(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
91.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
171.0ms	(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	557	2597
1	2527	2482
2	5002	2476

prune573.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (log 10.0))) (/ 3 (/ (sqrt (log 10.0)) (log (cbrt (sqrt (+ (* re re) (* im im))))))))
0.5b	(/ (sqrt (log 10.0)) (log (cbrt (sqrt (+ (* re re) (* im im))))))
0.5b	(cbrt (sqrt (+ (* re re) (* im im))))
33.5b	(sqrt (+ (* re re) (* im im)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

319×	`times-frac`
209×	`add-sqr-sqrt`
143×	`*-un-lft-identity`
135×	`add-cube-cbrt`
122×	`associate-r`
115×	`sqrt-prod`
82×	`log-pow`
60×	`pow1`
45×	`add-exp-log`
30×	`pow1/3`
27×	`add-cbrt-cube`
25×	`associate-l`
20×	`unswap-sqr`
19×	`div-exp`
12×	`prod-exp`
10×	`cbrt-undiv`
7×	`associate-/l*`
6×	`cbrt-prod` `cbrt-unprod` `div-inv`
5×	`associate-/r*`
4×	`sqrt-div` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`cbrt-div` `flip3-+` `flip-+`
1×	`frac-times` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r/` `*-commutative`

Counts

4 → 287

Calls

4 calls:

88.0ms	(* (/ 1 (sqrt (log 10.0))) (/ 3 (/ (sqrt (log 10.0)) (log (cbrt (sqrt (+ (* re re) (* im im))))))))
4.0ms	(/ (sqrt (log 10.0)) (log (cbrt (sqrt (+ (* re re) (* im im))))))
2.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (/ 1 (sqrt (log 10.0))) (/ 3 (/ (sqrt (log 10.0)) (log (cbrt (sqrt (+ (* re re) (* im im))))))))
218.0ms	(/ (sqrt (log 10.0)) (log (cbrt (sqrt (+ (* re re) (* im im))))))
92.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1154	4493
1	5001	4016

prune762.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 7.4b

regimes1.1s

Accuracy

54.4% (11.2b remaining)

Error of 19.0b against oracle of 7.8b and baseline of 32.4b

bsearch160.0ms

Steps

Iters	Range		Point
10	6.472804768013941e+57	7.878752005036544e+72	3.1269387827755257e+72
10	9.571965910596565e-239	1.5176730339456097e-221	9.786140971348553e-239
7	1.464443963987268e-279	2.3443748708823334e-278	2.3223338671593632e-278
0	-5.970240647024179e+102	-5.959551046543281e+102	-5.96489584678373e+102

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	45
1	68	45
2	78	45
3	78	45

end0.0ms

sample728.0ms

Algorithm

intervals

Results

587.0ms

8000×

body

valid