Details

sample60.0ms

Algorithm

intervals

Results

22.0ms	276×	body	80	nan
19.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	33	16
2	33	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (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))
27.3b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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` `hypot-def` `div-inv`

Counts

4 → 119

Calls

4 calls:

10.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
143.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	467	1408
1	1820	1268
2	5001	1217

prune476.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (* 1 (hypot re im))) (log base))
0.5b	(* (log base) (log base))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`pow1`
22×	`add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac` `associate-l` `log-pow`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-/r` `associate-/l`
2×	`flip3-+` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `hypot-udef` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

1.0ms	(hypot re im)
10.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (* 1 (hypot re im))) (log base))
5.0ms	(* (log base) (log base))

series397.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot re im)
105.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
98.0ms	(* (log (* 1 (hypot re im))) (log base))
145.0ms	(* (log base) (log base))

simplify54.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	398	1152
1	1604	1012
2	5002	969

prune444.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0))))
0.3b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (* 1 (hypot re im))) (log base))
0.5b	(* (log base) (log base))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
70×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
66×	`add-cube-cbrt`
24×	`pow1`
21×	`add-exp-log`
18×	`associate-/r*`
15×	`add-cbrt-cube`
12×	`log-prod`
11×	`associate-/r/`
9×	`associate-l` `log-pow`
8×	`div-exp` `associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `swap-sqr` `flip-+` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`rec-exp` `frac-2neg` `1-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`pow2` `pow-flip` `pow-plus` `pow-sqr` `pow-prod-up` `inv-pow`

Counts

4 → 186

Calls

4 calls:

14.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0))))
10.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)))
6.0ms	(* (log (* 1 (hypot re im))) (log base))
5.0ms	(* (log base) (log base))

series530.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0))))
144.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)))
99.0ms	(* (log (* 1 (hypot re im))) (log base))
150.0ms	(* (log base) (log base))

simplify94.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	662	3288
1	3099	2903
2	5001	2776

prune601.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (log (cbrt base)))
0.4b	(* (log base) (* 2 (log (cbrt base))))
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
24×	`cbrt-prod`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-l`
6×	`associate-r`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `log-pow` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`*-commutative`
1×	`unswap-sqr`

Counts

4 → 106

Calls

4 calls:

6.0ms	(* (log base) (log (cbrt base)))
10.0ms	(* (log base) (* 2 (log (cbrt base))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series1.3s

Counts

4 → 12

Calls

4 calls:

515.0ms	(* (log base) (log (cbrt base)))
416.0ms	(* (log base) (* 2 (log (cbrt base))))
175.0ms	(cbrt base)
177.0ms	(cbrt base)

simplify45.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	314	813
1	1256	728
2	5002	688

prune435.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes292.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	21
1	36	21
2	36	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

618.0ms	8000×	body	80	valid
589.0ms	7967×	body	80	nan