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: 31.9b

localize13.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

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)))

series174.0ms

Counts

2 → 6

Calls

2 calls:

137.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify125.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (118.0ms)

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

prune190.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
30.6b	(log (+ (* re re) (* im im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
82×	`add-sqr-sqrt`
54×	`sqrt-prod`
52×	`add-cube-cbrt` `*-un-lft-identity`
33×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
18×	`add-exp-log`
17×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `div-inv` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+`
1×	`frac-times` `frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 153

Calls

3 calls:

34.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
10.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
3.0ms	(log (+ (* re re) (* im im)))

series377.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
185.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
52.0ms	(log (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	528	2082
1	2065	1915
2	5001	1832

prune361.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize19.0ms

Local error

Found 3 expressions with local error:

0.3b

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

13.9b

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

17.9b

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
44×	`times-frac`
39×	`add-cube-cbrt` `*-un-lft-identity`
25×	`pow-unpow` `associate-l` `sqrt-prod`
21×	`log-prod`
12×	`pow1` `unpow-prod-down`
11×	`add-exp-log`
8×	`log-pow` `add-cbrt-cube`
7×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `sqr-pow`
3×	`rem-log-exp` `add-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `pow-pow` `div-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 117

Calls

3 calls:

22.0ms

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

5.0ms

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

7.0ms

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series1.0s

Counts

3 → 9

Calls

3 calls:

391.0ms

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

292.0ms

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

317.0ms

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	463	1699
1	1990	1501
2	5001	1310

prune322.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
0.4b	(/ (* (/ (sqrt 1/2) (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (sqrt (log 10.0)))
0.5b	(* (/ (sqrt 1/2) (sqrt 1)) (/ (* (/ (sqrt 1/2) (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (sqrt (log 10.0))))
30.6b	(log (+ (* re re) (* im im)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

104×	`sqrt-prod`
102×	`times-frac`
99×	`add-sqr-sqrt`
86×	`associate-l`
69×	`*-un-lft-identity`
67×	`add-cube-cbrt`
51×	`add-exp-log`
50×	`add-cbrt-cube`
19×	`pow1`
17×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
15×	`associate-r`
12×	`unswap-sqr`
11×	`log-pow`
9×	`log-prod`
7×	`associate-/r*`
4×	`div-inv` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`
2×	`log-div` `pow-prod-down` `*-commutative`
1×	`frac-times` `frac-2neg` `flip3-+` `associate-r/` `rem-log-exp` `clear-num` `flip-+` `associate-/l/` `associate-/l`

Counts

4 → 207

Calls

4 calls:

26.0ms	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
18.0ms	(/ (* (/ (sqrt 1/2) (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (sqrt (log 10.0)))
50.0ms	(* (/ (sqrt 1/2) (sqrt 1)) (/ (* (/ (sqrt 1/2) (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (sqrt (log 10.0))))
3.0ms	(log (+ (* re re) (* im im)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
172.0ms	(/ (* (/ (sqrt 1/2) (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (sqrt (log 10.0)))
226.0ms	(* (/ (sqrt 1/2) (sqrt 1)) (/ (* (/ (sqrt 1/2) (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (sqrt (log 10.0))))
51.0ms	(log (+ (* re re) (* im im)))

simplify104.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	794	3393
1	3738	2932
2	5003	2566

prune573.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 8.4b

regimes481.0ms

Accuracy

57.8% (10.5b remaining)

Error of 17.7b against oracle of 7.1b and baseline of 32.1b

bsearch84.0ms

Steps

Iters	Range		Point
10	2.1628060713373462e+108	9.659658509577212e+121	5.0139743767423275e+120
5	-212885859736577.44	-96076744023787.5	-205316960046999.47

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	34
1	49	34

end0.0ms

sample486.0ms

Algorithm

intervals

Results

345.0ms

8000×

body

valid