Details

sample43.0ms

Algorithm

intervals

Results

30.0ms

274×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
21.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite31.0ms

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`
4×	`flip3-+` `flip-+`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `fma-def` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 61

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
5.0ms	(+ (* x.re y.re) (* x.im y.im))
19.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
31.0ms	(+ (* x.re y.re) (* x.im y.im))
87.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify138.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	290	532
1	1199	475
2	4872	462
3	5001	462

prune199.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
14.0b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
92×	`prod-exp`
63×	`div-exp`
50×	`add-cbrt-cube`
41×	`1-exp`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
15×	`rec-exp`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`pow1`
7×	`associate-r` `associate-l`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*`
1×	`frac-times` `associate-r/` `associate-l/` `*-commutative` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

0.0ms	(fma x.re y.re (* x.im y.im))
4.0ms	(/ 1 (* (hypot y.re y.im) 1))
21.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series384.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma x.re y.re (* x.im y.im))
51.0ms	(/ 1 (* (hypot y.re y.im) 1))
179.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
114.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify44.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	486	1191
1	1654	892
2	5002	884

prune272.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
0.0b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
14.0b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
4×	`prod-exp` `associate-/r*` `div-inv`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`fma-udef` `associate-/l/`

Counts

3 → 89

Calls

3 calls:

0.0ms	(fma x.re y.re (* x.im y.im))
6.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
2.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series276.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma x.re y.re (* x.im y.im))
121.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
117.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify77.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	297	767
1	1133	677
2	3251	677
3	5001	670

prune256.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 (* (hypot y.re y.im) 1)))
0.4b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im)))
6.3b	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
7.9b	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`add-exp-log` `associate-l` `add-cbrt-cube`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
12×	`pow1`
10×	`associate-r`
6×	`prod-exp` `cbrt-unprod`
5×	`sqrt-div` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-pow1` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-l/` `associate-/r`
2×	`pow-flip` `*-commutative` `fma-udef`
1×	`distribute-rgt-in` `frac-times` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `pow1/2` `associate-r/` `clear-num` `associate-/l/` `associate-/l` `inv-pow`

Counts

4 → 117

Calls

4 calls:

6.0ms	(sqrt (/ 1 (* (hypot y.re y.im) 1)))
53.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im)))
14.0ms	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
20.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

series697.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt (/ 1 (* (hypot y.re y.im) 1)))
188.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im)))
257.0ms	(/ (* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im))) (hypot y.re y.im))
166.0ms	(* (sqrt (/ 1 (* (hypot y.re y.im) 1))) (fma x.re y.re (* x.im y.im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	470	1373
1	2227	1115
2	5001	1054

prune406.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.6b

regimes174.0ms

Accuracy

17.7% (9.0b remaining)

Error of 14.7b against oracle of 5.7b and baseline of 16.6b

bsearch54.0ms

Steps

Iters	Range		Point
9	9.681338502808346e+165	1.3966723912888989e+171	2.2577310345661958e+167

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	21	10
2	21	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

858.0ms

8483×

body

valid