Details

sample20.0ms

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: 34.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

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:

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

series169.0ms

Counts

2 → 6

Calls

2 calls:

130.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify127.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (117.0ms)

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

prune178.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.7b

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))
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite187.0ms

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:

163.0ms	(/ (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)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
39.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify153.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	480	3562
1	986	3468
2	3056	3076
3	5003	3048

prune429.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3 (/ (log (cbrt (sqrt (+ (* re re) (* im im))))) (log 10.0)))
0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
0.6b	(/ (log (cbrt (sqrt (+ (* re re) (* im im))))) (log 10.0))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

41×	`times-frac`
35×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity` `log-pow`
27×	`pow1`
24×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow1/3`
6×	`cbrt-prod` `sqrt-div` `sqrt-prod`
5×	`associate-/l*`
4×	`cbrt-div` `associate-/r*` `add-log-exp`
3×	`flip3-+` `associate-l` `flip-+`
2×	`cbrt-undiv` `log-div` `div-sub` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 117

Calls

4 calls:

12.0ms	(* 3 (/ (log (cbrt (sqrt (+ (* re re) (* im im))))) (log 10.0)))
3.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
12.0ms	(/ (log (cbrt (sqrt (+ (* re re) (* im im))))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* 3 (/ (log (cbrt (sqrt (+ (* re re) (* im im))))) (log 10.0)))
90.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
157.0ms	(/ (log (cbrt (sqrt (+ (* re re) (* im im))))) (log 10.0))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	372	1322
1	1525	1222
2	5001	1218

prune379.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (log (cbrt (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))))) (log 10.0))
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-div`
60×	`sqrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`log-div` `div-sub`
21×	`add-sqr-sqrt`
20×	`times-frac`
18×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
16×	`log-pow`
14×	`associate-*l/`
9×	`sqrt-prod`
8×	`associate-*r/`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1/3` `associate-/l*`
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 → 112

Calls

4 calls:

94.0ms	(/ (log (cbrt (* (* (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)))
6.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (log (cbrt (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))))) (log 10.0))
35.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	416	2909
1	747	2811
2	1616	2782
3	5002	2546

prune405.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.6b

regimes820.0ms

Accuracy

56.3% (10.8b remaining)

Error of 18.1b against oracle of 7.4b and baseline of 32.0b

bsearch174.0ms

Steps

Iters	Range		Point
9	2.5638491307155068e+47	1.8078460056449616e+54	9.713984258822547e+53
11	-1.697635983764772e-254	-9.078934504337964e-275	-3.399148512472067e-257
6	-9.994260456895444e-161	-1.1592916664118923e-161	-1.180833083521909e-161
9	-1.7413215916897266e+149	-8.628191100553707e+143	-8.76230374871451e+143

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	42
1	58	42
2	58	42

end0.0ms

sample501.0ms

Algorithm

intervals

Results

361.0ms

8000×

body

valid