Details

sample19.0ms

Algorithm

intervals

Results

11.0ms

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: 33.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 63

Calls

2 calls:

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

series171.0ms

Counts

2 → 6

Calls

2 calls:

135.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify130.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (123.0ms)

Iter	Nodes	Cost
0	221	664
1	556	631
2	1309	628
3	4047	628
4	5001	627

prune195.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
107×	`add-sqr-sqrt`
78×	`sqrt-prod`
66×	`*-un-lft-identity`
61×	`log-pow`
60×	`add-cube-cbrt`
52×	`pow1`
46×	`associate-r`
27×	`add-exp-log`
25×	`associate-l`
17×	`add-cbrt-cube`
16×	`sqrt-pow1` `pow1/2`
15×	`unswap-sqr`
9×	`div-exp`
8×	`prod-exp`
7×	`associate-/r*`
6×	`associate-/l*`
5×	`cbrt-undiv`
4×	`sqrt-div` `cbrt-unprod`
3×	`div-inv` `add-log-exp`
2×	`log-div` `rec-exp` `flip3-+` `1-exp` `div-sub` `flip-+`
1×	`frac-times` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 194

Calls

3 calls:

29.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
10.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series374.0ms

Counts

3 → 9

Calls

3 calls:

136.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
199.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	613	2721
1	2460	2427
2	5001	2325

prune411.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.3b	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.9b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
45×	`add-cube-cbrt`
41×	`sqrt-prod`
30×	`log-prod`
25×	`pow-unpow` `associate-l`
24×	`unpow-prod-down`
16×	`add-exp-log`
15×	`pow1`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-cbrt-cube`
8×	`log-pow`
5×	`unswap-sqr`
4×	`associate-r` `prod-exp` `add-log-exp` `sqr-pow`
3×	`pow-pow` `rem-log-exp`
2×	`pow-to-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `pow-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `flip3-+` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `sqrt-pow2` `flip-+`

Counts

4 → 151

Calls

4 calls:

5.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
15.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
8.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series1.0s

Counts

4 → 12

Calls

4 calls:

303.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
358.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
340.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	558	2291
1	2343	1895
2	5001	1744

prune418.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.0b

localize37.0ms

Local error

Found 4 expressions with local error:

2.5b	(pow (fabs (cbrt (+ (* re re) (* im im)))) (/ (/ 1 (sqrt (log 10.0))) 2))
2.5b	(pow (sqrt (cbrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
31.9b	(cbrt (+ (* re re) (* im im)))
31.9b	(cbrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
104×	`pow-unpow`
92×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
19×	`pow1`
12×	`unpow-prod-down` `log-pow`
9×	`cbrt-prod`
6×	`add-exp-log`
5×	`pow-pow` `div-inv`
4×	`cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`pow-to-exp` `sqrt-pow1` `flip3-+` `pow-exp` `flip-+` `sqr-pow`
1×	`pow1/2` `sqrt-pow2`

Counts

4 → 168

Calls

4 calls:

10.0ms	(pow (fabs (cbrt (+ (* re re) (* im im)))) (/ (/ 1 (sqrt (log 10.0))) 2))
9.0ms	(pow (sqrt (cbrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series815.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(pow (fabs (cbrt (+ (* re re) (* im im)))) (/ (/ 1 (sqrt (log 10.0))) 2))
385.0ms	(pow (sqrt (cbrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
96.0ms	(cbrt (+ (* re re) (* im im)))
96.0ms	(cbrt (+ (* re re) (* im im)))

simplify75.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	805	2101
1	3493	1990
2	5003	1867

prune776.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.0b

regimes783.0ms

Accuracy

56.1% (11.0b remaining)

Error of 18.2b against oracle of 7.2b and baseline of 32.2b

bsearch228.0ms

Steps

Iters	Range		Point
8	301235630897810.75	2.0109691215084654e+18	1.9824297347259786e+18
7	-2.596632299517903e-272	-3.6457286778949607e-274	-8.804121592020497e-274
9	-8.983960399464967e-179	-2.006309498428036e-184	-2.0278572522938575e-184
9	-6.606528294779468e+144	-1.6450582212898727e+137	-2.6163751838198674e+143

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	106
1	66	106

end0.0ms

sample482.0ms

Algorithm

intervals

Results

346.0ms

8000×

body

valid