Details

sample69.0ms

Algorithm

intervals

Results

27.0ms	282×	body	80	nan
22.0ms	256×	body	80	valid

simplify6.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 34.9b

Counts

2 → 1

localize19.0ms

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))
32.4b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

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)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (* (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))
151.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	467	1408
1	1820	1268
2	5001	1220

prune438.0ms

Filtered

131 candidates to 95 candidates (72.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Merged error: 0.2b

Counts

132 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r` `associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow-prod-down` `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 → 109

Calls

4 calls:

1.0ms	(hypot re im)
9.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log (hypot re im)) (log base))
5.0ms	(* (log base) (log base))

series411.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot re im)
108.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
101.0ms	(* (log (hypot re im)) (log base))
152.0ms	(* (log base) (log base))

simplify56.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	394	1062
1	1578	949
2	5001	919

prune529.0ms

Filtered

121 candidates to 85 candidates (70.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	108	13	121
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	119	15	134

Merged error: 0.0b

Counts

134 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
0.3b	(* (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
0.4b	(* (log (hypot re im)) (log base))
0.5b	(pow (log base) 2)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

151×	`times-frac`
109×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
88×	`add-cube-cbrt`
48×	`add-exp-log` `associate-r`
24×	`div-exp`
20×	`add-cbrt-cube`
13×	`pow1` `associate-/r*`
12×	`1-exp`
11×	`prod-exp`
9×	`div-inv`
8×	`unswap-sqr`
7×	`associate-l`
6×	`cbrt-undiv` `rec-exp` `log-prod`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `log-pow` `associate-/l*`
2×	`frac-times` `flip3-+` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `flip-+`
1×	`pow-to-exp` `pow-flip` `pow-pow` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `un-div-inv` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 214

Calls

4 calls:

6.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
20.0ms	(* (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
5.0ms	(* (log (hypot re im)) (log base))
3.0ms	(pow (log base) 2)

series581.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
134.0ms	(* (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
99.0ms	(* (log (hypot re im)) (log base))
148.0ms	(pow (log base) 2)

simplify95.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	817	2448
1	3803	2055
2	5001	1844

prune569.0ms

Filtered

226 candidates to 130 candidates (57.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	223	3	226
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	226	15	241

Merged error: 0.0b

Counts

241 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log base) (* 2 (log (cbrt base))))
0.4b	(* (log (hypot re im)) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

7.0ms	(* (log base) (* 2 (log (cbrt base))))
5.0ms	(* (log (hypot re im)) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series846.0ms

Counts

4 → 12

Calls

4 calls:

412.0ms	(* (log base) (* 2 (log (cbrt base))))
94.0ms	(* (log (hypot re im)) (log base))
167.0ms	(cbrt base)
173.0ms	(cbrt base)

simplify141.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	350	747
1	1065	660
2	4495	627
3	5001	627

prune329.0ms

Filtered

111 candidates to 72 candidates (64.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	110	16	126

Merged error: 0b

Counts

126 → 16

regimes292.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	13
1	24	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

707.0ms	8000×	body	80	valid
669.0ms	8049×	body	80	nan