Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	188×	body	80	valid
5.0ms	26×	body	2560	valid
3.0ms	18×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	10×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div` `sqrt-prod`
3×	`add-exp-log` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `distribute-lft-out`

Counts

3 → 40

Calls

3 calls:

11.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series249.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
46.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	244	351
1	743	325
2	2278	315
3	5001	312

prune143.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
7.4b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
27.6b	(cbrt (+ (* re re) (* im im)))
27.6b	(cbrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

12.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
2.0ms	(cbrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
79.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
89.0ms	(cbrt (+ (* re re) (* im im)))
91.0ms	(cbrt (+ (* re re) (* im im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	323	928
1	1214	868
2	5002	841

prune289.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.0b

localize19.0ms

Local error

Found 4 expressions with local error:

26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(sqrt (+ (* re re) (* im im)))
27.6b	(cbrt (+ (* re re) (* im im)))
27.6b	(cbrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

6.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
92.0ms	(cbrt (+ (* re re) (* im im)))
92.0ms	(cbrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	141	444
1	440	420
2	1469	416
3	5002	414

prune366.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.0b

localize30.0ms

Local error

Found 4 expressions with local error:

26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(sqrt (+ (* re re) (* im im)))
27.6b	(cbrt (+ (* re re) (* im im)))
27.6b	(cbrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))
2.0ms	(cbrt (+ (* re re) (* im im)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
93.0ms	(cbrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	141	444
1	440	420
2	1469	416
3	5002	414

prune413.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.0b

regimes195.0ms

Accuracy

58.6% (8.8b remaining)

Error of 26.8b against oracle of 18.0b and baseline of 39.3b

bsearch102.0ms

Steps

Iters	Range		Point
10	3.070645734072953e+74	1.5848411429422667e+86	2.5975290754985087e+85
9	-1.2356307952735333e-300	-8.537658570634138e-307	-8.679895838128237e-307

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	45
1	45	45

end0.0ms

sample676.0ms

Algorithm

intervals

Results

201.0ms	6010×	body	80	valid
143.0ms	747×	body	2560	valid
77.0ms	476×	body	1280	valid
69.0ms	283×	body	5120	valid
39.0ms	275×	body	640	valid
13.0ms	137×	body	320	valid
4.0ms	72×	body	160	valid