Details

sample53.0ms

Algorithm

intervals

Results

18.0ms	258×	body	80	nan
18.0ms	256×	body	80	valid

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: 32.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (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))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
13.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
99.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
148.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	1361
1	1721	1236
2	5001	1205

prune447.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`unpow-prod-down` `associate-r` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

21.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
147.0ms	(pow (log base) 2)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	443	1231
1	1594	1134
2	5001	1115

prune555.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (+ (* 0.0 0.0) (pow (log base) 2))) (/ (sqrt (+ (* 0.0 0.0) (pow (log base) 2))) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
22×	`times-frac`
20×	`sqrt-prod`
11×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
8×	`unpow-prod-down`
6×	`pow-unpow` `sqrt-div` `associate-l` `unswap-sqr`
4×	`flip3-+` `flip-+` `add-log-exp`
2×	`frac-times` `pow-to-exp` `pow-pow` `associate-*l/` `pow-exp` `prod-exp` `associate-/r/` `log-pow` `cbrt-unprod` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 107

Calls

4 calls:

60.0ms	(* (sqrt (+ (* 0.0 0.0) (pow (log base) 2))) (/ (sqrt (+ (* 0.0 0.0) (pow (log base) 2))) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0))))
1.0ms	(pow (log base) 2)
1.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (sqrt (+ (* 0.0 0.0) (pow (log base) 2))) (/ (sqrt (+ (* 0.0 0.0) (pow (log base) 2))) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0))))
144.0ms	(pow (log base) 2)
144.0ms	(pow (log base) 2)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	511	1734
1	1989	1492
2	5001	1444

prune481.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 6.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
0.7b	(pow (pow (log base) 2) 3)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`unpow-prod-down`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow-unpow` `cube-prod`
8×	`add-exp-log`
6×	`pow-exp`
5×	`add-cbrt-cube` `sqr-pow`
4×	`pow-to-exp` `log-pow` `unpow2` `add-log-exp`
3×	`pow-pow` `sqrt-prod`
2×	`sqrt-div`
1×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `flip-+` `rem-cube-cbrt`

Counts

4 → 90

Calls

4 calls:

1.0ms	(pow (log base) 2)
1.0ms	(pow (log base) 2)
3.0ms	(pow (pow (log base) 2) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (log base) 2)
148.0ms	(pow (log base) 2)
186.0ms	(pow (pow (log base) 2) 3)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	277	408
1	1052	353
2	5001	342

prune456.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 6.6b

regimes585.0ms

Accuracy

58.2% (10.2b remaining)

Error of 17.7b against oracle of 7.5b and baseline of 31.9b

bsearch154.0ms

Steps

Iters	Range		Point
8	1.549048552128315e+135	2.9532459451765213e+138	1.3463574974000498e+136
8	-2.199513247113217e+113	-2.8144411357532195e+110	-1.2229383473576894e+113

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	41
1	53	41

end0.0ms

sample1.4s

Algorithm

intervals

Results

545.0ms	8000×	body	80	valid
545.0ms	7871×	body	80	nan