Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify18.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.8b	(- (* 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)))

rewrite16.0ms

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:

2.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* 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)))

series151.0ms

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))
88.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (33.0ms)

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

prune200.0ms

Filtered

73 candidates to 59 candidates (80.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.8b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-exp-log`
38×	`prod-exp`
32×	`add-cbrt-cube`
29×	`div-exp`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`1-exp`
13×	`associate-r`
10×	`cbrt-undiv`
9×	`pow1` `rec-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
2×	`flip3--` `pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 143

Calls

4 calls:

4.0ms	(/ 1 (* (hypot y.re y.im) 1))
26.0ms	(* (/ 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))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series385.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (* (hypot y.re y.im) 1))
188.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
34.0ms	(- (* x.im y.re) (* x.re y.im))
112.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify63.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	555	1207
1	2306	1003
2	5003	995

prune327.0ms

Filtered

155 candidates to 94 candidates (60.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

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))
0.8b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite27.0ms

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)
12.0ms	(/ (/ (- (* 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))

series314.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(hypot y.re y.im)
119.0ms	(/ (/ (- (* 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))
116.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify49.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (36.0ms)

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

prune423.0ms

Filtered

143 candidates to 112 candidates (78.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize14.0ms

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)) (hypot y.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
0.8b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

1566×	`times-frac`
738×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
564×	`sqrt-prod`
98×	`associate-/l*`
59×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
15×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
6×	`div-sub` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 763

Calls

4 calls:

14.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
31.0ms	(/ (/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (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))

series474.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
119.0ms	(/ (/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
36.0ms	(- (* x.im y.re) (* x.re y.im))
116.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify172.0ms

Algorithm

egg-herbie

Counts

775 → 775

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1959	16693
1	5001	15325

prune1.4s

Filtered

775 candidates to 336 candidates (43.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.6b

regimes251.0ms

Accuracy

31.9% (9.0b remaining)

Error of 12.6b against oracle of 3.6b and baseline of 16.8b

bsearch175.0ms

Steps

Iters	Range		Point
10	2.7020643455585323e+180	2.94630534130054e+190	1.4538292767703705e+189
10	1.8137782181329498e-137	8.569503808472031e-128	6.17656804791985e-128
7	-2.85855713936286e-142	-2.3598379269180502e-144	-1.2987370292207596e-142
7	-9.149408721955617e+132	-1.9322020034710515e+131	-5.392764808821395e+132

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	39
1	54	39
2	54	39

end0.0ms

sample502.0ms

Algorithm

intervals

Results

298.0ms

8469×

body

valid