Details

sample56.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
17.0ms	258×	body	80	nan

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize20.0ms

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)))

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:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(/ (+ (* (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)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
100.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
153.0ms	(* (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	1217

prune474.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 100

Calls

3 calls:

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

series361.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(* (log (* 1 (hypot re im))) (log base))
108.0ms	(/ (+ (* (log (* 1 (hypot re im))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
152.0ms	(* (log base) (log base))

simplify55.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	381	1125
1	1567	988
2	5002	945

prune537.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
44×	`add-sqr-sqrt` `*-un-lft-identity`
42×	`add-cube-cbrt`
25×	`add-exp-log`
24×	`sqrt-prod`
20×	`add-cbrt-cube`
17×	`pow1`
10×	`div-exp` `associate-/l*`
9×	`div-inv`
7×	`cbrt-undiv` `associate-/r*`
6×	`log-prod` `swap-sqr` `log-pow`
5×	`prod-exp`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `cbrt-unprod`
2×	`frac-2neg` `sqrt-div` `1-exp` `clear-num` `associate-/r/`
1×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+` `fma-udef` `associate-/l/` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

4.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
1.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
10.0ms	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms	(* (log base) (log base))

series1.0s

Counts

4 → 12

Calls

4 calls:

344.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
136.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
416.0ms	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
145.0ms	(* (log base) (log base))

simplify66.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	552	2655
1	2009	2343
2	5001	2317

prune592.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

735×	`times-frac`
355×	`add-sqr-sqrt` `*-un-lft-identity`
353×	`add-cube-cbrt`
135×	`sqrt-prod`
47×	`associate-/l*`
30×	`div-inv`
27×	`add-exp-log`
17×	`pow1` `add-cbrt-cube`
15×	`div-exp`
9×	`associate-/r*` `associate-/r/`
7×	`cbrt-undiv`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`rec-exp` `frac-2neg` `sqrt-div` `1-exp` `clear-num`
1×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `fma-udef` `associate-/l/` `unswap-sqr`

Counts

4 → 416

Calls

4 calls:

3.0ms	(/ (hypot (log base) 0.0) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
1.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
20.0ms	(/ (/ 1 (/ (hypot (log base) 0.0) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms	(* (log base) (log base))

series1.1s

Counts

4 → 12

Calls

4 calls:

377.0ms	(/ (hypot (log base) 0.0) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
137.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
423.0ms	(/ (/ 1 (/ (hypot (log base) 0.0) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
149.0ms	(* (log base) (log base))

simplify144.0ms

Algorithm

egg-herbie

Counts

428 → 428

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1572	11552
1	5002	9653

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes286.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	24
1	33	24

end0.0ms

sample1.4s

Algorithm

intervals

Results

557.0ms	8000×	body	80	valid
520.0ms	7871×	body	80	nan