Details

sample57.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
15.0ms	228×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
39.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
9.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
104.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
145.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	445	1362
1	1751	1236
2	5001	1205

prune435.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
163×	`add-sqr-sqrt`
162×	`*-un-lft-identity`
158×	`add-cube-cbrt`
141×	`sqrt-prod`
31×	`pow1`
24×	`associate-/l*`
18×	`sqrt-div`
16×	`associate-/r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`log-prod` `swap-sqr` `log-pow`
9×	`flip3-+` `flip-+`
8×	`associate-r` `associate-l` `div-inv`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 278

Calls

4 calls:

59.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
9.0ms	(* (log base) (log base))
12.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
149.0ms	(* (log base) (log base))
147.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify125.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	839	8779
1	3156	8145
2	5001	8032

prune789.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
25×	`pow1`
23×	`add-cube-cbrt` `associate-r`
17×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
12×	`log-prod`
11×	`times-frac`
10×	`log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`flip3-+` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod` `*-commutative`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `associate-*l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `rec-exp` `pow-plus` `1-exp` `associate-*r/` `pow-sqr` `un-div-inv` `pow-prod-up` `div-inv`

Counts

4 → 121

Calls

4 calls:

55.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
143.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify85.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	569	1511
1	2601	1356
2	5002	1314

prune581.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`sqrt-div`
5×	`add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `pow-pow` `pow-exp` `log-pow` `unpow2` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

3.0ms	(pow (log base) 2)
7.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(pow (log base) 2)
39.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify69.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	169	373
1	482	348
2	1597	348
3	5002	344

prune319.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 7.3b

regimes368.0ms

Accuracy

56.1% (10.8b remaining)

Error of 18.1b against oracle of 7.3b and baseline of 31.9b

bsearch293.0ms

Steps

Iters	Range		Point
11	0.20548432973886355	1.350953981158519e+19	8.920902837436811e+18
9	6.871693121039297e-214	2.3818606310508455e-205	1.7504457734233236e-212
6	-8.503884137585762e-180	-9.23562821985809e-181	-4.364140895511951e-180
9	-8.37881605524702e+155	-2.07562538812607e+147	-7.144500791031524e+147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	84
1	56	84

end0.0ms

sample1.6s

Algorithm

intervals

Results

560.0ms	8062×	body	80	nan
536.0ms	8000×	body	80	valid