Details

sample33.0ms

Algorithm

intervals

Results

21.0ms

276×

body

valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 26.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
26.5b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
14.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
36.0ms	(- (* x.im y.re) (* x.re y.im))
85.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	316	555
1	1343	496
2	5001	481

prune205.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.3b	(- (* x.im y.re) (* x.re y.im))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
15.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite37.0ms

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:

0.0ms	(hypot y.re y.im)
3.0ms	(- (* x.im y.re) (* x.re y.im))
23.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series384.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot y.re y.im)
36.0ms	(- (* x.im y.re) (* x.re y.im))
185.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
115.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify60.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (49.0ms)

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

prune316.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize10.0ms

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))
15.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite23.0ms

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:

0.0ms	(hypot y.re y.im)
9.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series323.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(hypot y.re y.im)
116.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
41.0ms	(- (* x.im y.re) (* x.re y.im))
114.0ms	(/ (- (* 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

prune390.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
0.3b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.3b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))))
15.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
26×	`times-frac`
25×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `associate-l` `add-cbrt-cube`
16×	`sqrt-prod`
14×	`associate-r`
11×	`pow1`
10×	`sqrt-div`
7×	`prod-exp` `cbrt-unprod`
6×	`frac-times` `associate-*r/` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
2×	`flip3--` `*-commutative` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `clear-num`

Counts

4 → 129

Calls

4 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
25.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
58.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series617.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* x.im y.re) (* x.re y.im))
270.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
187.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))))
118.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify81.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	527	1554
1	2666	1314
2	5001	1267

prune408.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.6b

regimes241.0ms

Accuracy

32.2% (8.1b remaining)

Error of 12.6b against oracle of 4.5b and baseline of 16.5b

bsearch81.0ms

Steps

Iters	Range		Point
6	2.702607740933448e+197	1.1619739797922657e+198	3.26314722618804e+197
8	-6.216769361477498e+182	-9.641701532767943e+179	-2.235279546431987e+180

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	40	15
2	43	15
3	43	15

end0.0ms

sample879.0ms

Algorithm

intervals

Results

655.0ms

8445×

body

valid