Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

264×

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 26.0b

Counts

2 → 1

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))
25.5b	(/ (- (* 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:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
4.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
35.0ms	(- (* x.im y.re) (* x.re y.im))
86.0ms	(/ (- (* 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 (33.0ms)

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

prune195.0ms

Filtered

73 candidates to 59 candidates (80.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Merged error: 13.6b

Counts

74 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
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))
16.3b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite33.0ms

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:

5.0ms	(/ 1 (* (hypot y.re y.im) 1))
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))

series385.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (* (hypot y.re y.im) 1))
182.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
38.0ms	(- (* x.im y.re) (* x.re y.im))
115.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify66.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (50.0ms)

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

prune332.0ms

Filtered

155 candidates to 94 candidates (60.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	148	7	155
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	150	10	160

Merged error: 5.1b

Counts

160 → 10

localize9.0ms

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))
16.3b	(/ (- (* 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:

1.0ms	(hypot y.re y.im)
8.0ms	(/ (/ (- (* 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))

series312.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(hypot y.re y.im)
114.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
40.0ms	(- (* x.im y.re) (* x.re y.im))
115.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify56.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (37.0ms)

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

prune350.0ms

Filtered

143 candidates to 111 candidates (77.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	137	6	143
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	143	10	153

Merged error: 5.1b

Counts

153 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (* x.re y.im) (hypot y.re y.im)) (hypot y.re y.im))
0.6b	(/ (/ (* x.im y.re) (hypot y.re y.im)) (hypot y.re y.im))
9.6b	(/ (* x.im y.re) (hypot y.re y.im))
10.9b	(/ (* x.re y.im) (hypot y.re y.im))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/l*`
14×	`cbrt-undiv` `div-exp`
12×	`associate-/r*` `div-inv`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 146

Calls

4 calls:

6.0ms	(/ (/ (* x.re y.im) (hypot y.re y.im)) (hypot y.re y.im))
6.0ms	(/ (/ (* x.im y.re) (hypot y.re y.im)) (hypot y.re y.im))
4.0ms	(/ (* x.im y.re) (hypot y.re y.im))
5.0ms	(/ (* x.re y.im) (hypot y.re y.im))

series274.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (/ (* x.re y.im) (hypot y.re y.im)) (hypot y.re y.im))
70.0ms	(/ (/ (* x.im y.re) (hypot y.re y.im)) (hypot y.re y.im))
65.0ms	(/ (* x.im y.re) (hypot y.re y.im))
69.0ms	(/ (* x.re y.im) (hypot y.re y.im))

simplify55.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	495	1158
1	2166	1010
2	5001	996

prune368.0ms

Filtered

158 candidates to 114 candidates (72.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	152	6	158
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	158	10	168

Merged error: 0.8b

Counts

168 → 10

regimes262.0ms

Accuracy

58.2% (3.7b remaining)

Error of 4.2b against oracle of 0.5b and baseline of 9.3b

bsearch83.0ms

Steps

Iters	Range		Point
8	1.2141124285881934e+88	4.905813436801621e+90	3.9720357455707494e+89
9	-2.4621318815891244e+121	-4.263755120124944e+115	-4.7784752409435425e+115

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	22
1	31	22

end0.0ms

sample578.0ms

Algorithm

intervals

Results

337.0ms

8488×

body

valid