Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

268×

body

valid

simplify13.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.0b	(- (* x.im y.re) (* x.re y.im))
23.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

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))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series158.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* y.re y.re) (* y.im y.im))
41.0ms	(- (* x.im y.re) (* x.re y.im))
89.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (34.0ms)

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

prune219.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.5b

localize11.0ms

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)))
1.0b	(- (* x.im y.re) (* x.re y.im))
13.4b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite40.0ms

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)
25.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
3.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series385.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot y.re y.im)
183.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
39.0ms	(- (* x.im y.re) (* x.re y.im))
113.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify62.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (51.0ms)

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

prune350.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

localize11.0ms

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))
1.0b	(- (* x.im y.re) (* x.re y.im))
13.4b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite24.0ms

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))

series308.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot y.re y.im)
112.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
38.0ms	(- (* x.im y.re) (* x.re y.im))
112.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify255.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (37.0ms)

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

prune454.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.1b	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
1.0b	(- (* x.im y.re) (* x.re y.im))
13.5b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

2.0ms	(/ 1 (hypot y.re y.im))
9.0ms	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
17.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (hypot y.re y.im))
118.0ms	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
36.0ms	(- (* x.im y.re) (* x.re y.im))
111.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	419	955
1	1966	794
2	5001	763

prune334.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.6b

regimes236.0ms

Accuracy

31.7% (8.5b remaining)

Error of 13.1b against oracle of 4.6b and baseline of 17.1b

bsearch79.0ms

Steps

Iters	Range		Point
8	1.7858638569530692e+102	1.3063160135701974e+105	1.0448271563216688e+105
8	-2.8314860341645623e+153	-1.4473582621843552e+150	-2.0609572803500826e+150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	16
1	33	16
2	33	16

end0.0ms

sample531.0ms

Algorithm

intervals

Results

310.0ms

8489×

body

valid