Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

271×

body

valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
26.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

4.0ms	(- (* x.im y.re) (* x.re y.im))
9.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series130.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (* x.im y.re) (* x.re y.im))
90.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify107.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	270	481
1	1012	432
2	3842	422
3	5001	421

prune158.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.3b	(- (* x.im y.re) (* x.re y.im))
17.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-exp-log`
32×	`prod-exp`
27×	`add-cbrt-cube`
26×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
21×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`pow1` `rec-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `hypot-udef` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 120

Calls

4 calls:

1.0ms	(hypot y.re y.im)
13.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
4.0ms	(- (* x.im y.re) (* x.re y.im))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series398.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot y.re y.im)
191.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
41.0ms	(- (* x.im y.re) (* x.re y.im))
121.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify64.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	546	1122
1	2249	931
2	5002	929

prune330.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
17.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `hypot-udef` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 131

Calls

4 calls:

1.0ms	(hypot y.re y.im)
12.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
4.0ms	(- (* x.im y.re) (* x.re y.im))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series328.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot y.re y.im)
125.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
36.0ms	(- (* x.im y.re) (* x.re y.im))
121.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify52.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	460	1435
1	1669	1331
2	5001	1322

prune439.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
0.3b	(- (* x.im y.re) (* x.re y.im))
0.3b	(* (/ 1 (sqrt (hypot y.re y.im))) (/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im))))
17.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

350×	`times-frac`
261×	`add-sqr-sqrt`
181×	`*-un-lft-identity`
171×	`add-cube-cbrt`
110×	`sqrt-prod`
82×	`associate-r`
50×	`add-exp-log`
32×	`add-cbrt-cube`
25×	`unswap-sqr`
22×	`div-exp` `associate-l`
17×	`div-inv`
16×	`associate-/l*`
13×	`cbrt-undiv`
12×	`prod-exp`
9×	`associate-/r*`
6×	`pow1` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 324

Calls

4 calls:

9.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
4.0ms	(- (* x.im y.re) (* x.re y.im))
47.0ms	(* (/ 1 (sqrt (hypot y.re y.im))) (/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im))))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series575.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
41.0ms	(- (* x.im y.re) (* x.re y.im))
192.0ms	(* (/ 1 (sqrt (hypot y.re y.im))) (/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im))))
124.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify71.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1191	5061
1	5001	4533

prune934.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.5b

regimes255.0ms

Accuracy

16.4% (9.9b remaining)

Error of 14.9b against oracle of 5.0b and baseline of 16.8b

bsearch207.0ms

Steps

Iters	Range		Point
8	2.1643198323001914e+150	2.946747073993286e+153	1.9537314790331482e+152
9	5.205620924581097e-64	4.292417494179173e-57	5.2737837352095884e-64
8	2.4480199621176693e-81	3.8498438171014314e-78	3.8050518390474684e-78
9	-5.749378329514241e+85	-6.325617960473731e+78	-7.280462391920087e+83
9	-4.3302507567477494e+162	-4.9616708661001533e+154	-5.030681393622023e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	40
1	48	40
2	48	40

end0.0ms

sample526.0ms

Algorithm

intervals

Results

303.0ms

8503×

body

valid