Details

sample62.0ms

Algorithm

intervals

Results

22.0ms	269×	body	80	nan
17.0ms	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: 33.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite76.0ms

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:

38.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
17.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
95.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
157.0ms	(* (log base) (log base))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5001	1205

prune473.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
16×	`log-pow`
14×	`associate-l`
12×	`swap-sqr` `associate-r`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 115

Calls

4 calls:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(* (log base) (log base))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
151.0ms	(* (log base) (log base))
156.0ms	(* (log base) (log base))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify151.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	262	720
1	966	639
2	4681	599
3	5001	592

prune454.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(cbrt base)
0.5b	(cbrt base)
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
6×	`add-exp-log` `cbrt-prod` `log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
4.0ms	(cbrt base)
8.0ms	(sqrt (+ (* re re) (* im im)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
184.0ms	(cbrt base)
341.0ms	(cbrt base)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	225	495
1	626	452
2	1627	429
3	5001	422

prune407.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(cbrt base)
4.9b	(pow (/ 1 base) -1/3)
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`unpow-prod-down`
12×	`pow1`
11×	`add-exp-log`
9×	`times-frac`
6×	`log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `pow-exp` `log-pow` `add-log-exp`
3×	`cbrt-prod` `distribute-rgt-in` `pow-unpow` `pow-pow` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-exp`
1×	`pow-to-exp` `rem-sqrt-square` `rec-exp` `pow-flip` `flip3-+` `pow1/3` `1-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `inv-pow` `unswap-sqr` `sqr-pow`

Counts

4 → 86

Calls

4 calls:

16.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
7.0ms	(pow (/ 1 base) -1/3)
8.0ms	(sqrt (+ (* re re) (* im im)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
179.0ms	(cbrt base)
173.0ms	(pow (/ 1 base) -1/3)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify113.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	374	609
1	1206	551
2	4161	523
3	5001	506

prune442.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.7b

regimes476.0ms

Accuracy

50.8% (12.2b remaining)

Error of 19.4b against oracle of 7.2b and baseline of 32.0b

bsearch307.0ms

Steps

Iters	Range		Point
9	1.2541788676248254e+51	1.5635109057620477e+57	5.939275393622702e+55
8	1.409614265361797e-253	2.275648902463069e-250	6.2627205528332935e-252
7	-7.935120877791785e-109	-1.7839400895387346e-110	-1.8126465248308595e-110
8	-5.5614676401474626e+85	-1.4299070736075093e+82	-4.621917751541982e+85

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	76
1	79	76
2	82	76
3	82	76

end0.0ms

sample1.6s

Algorithm

intervals

Results

564.0ms	7964×	body	80	nan
558.0ms	8000×	body	80	valid