Details

sample38.0ms

Algorithm

intervals

Results

21.0ms

486×

body

valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	24	7
1	44	6
2	58	6
3	60	6
4	60	6

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 18.1b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (/ z t) (/ z t) (/ (* x x) (* y y)))
20.8b	(/ (* x x) (* y y))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
225×	`times-frac`
162×	`add-cube-cbrt` `*-un-lft-identity`
96×	`swap-sqr` `associate-r` `associate-l`
32×	`*-commutative` `unswap-sqr`
15×	`associate-/r` `associate-/l`
14×	`add-exp-log` `add-cbrt-cube`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`frac-2neg` `clear-num` `fma-udef` `div-inv`

Counts

2 → 285

Calls

2 calls:

1.0ms	(fma (/ z t) (/ z t) (/ (* x x) (* y y)))
17.0ms	(/ (* x x) (* y y))

series154.0ms

Counts

2 → 6

Calls

2 calls:

115.0ms	(fma (/ z t) (/ z t) (/ (* x x) (* y y)))
39.0ms	(/ (* x x) (* y y))

simplify78.0ms

Algorithm

egg-herbie

Counts

291 → 291

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	928	1921
1	5001	1743

prune350.0ms

Filtered

291 candidates to 124 candidates (42.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	282	9	291
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	284	9	293

Merged error: 0.1b

Counts

293 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cbrt x) (/ y x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
86×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`cbrt-prod`
16×	`associate-/r*`
12×	`add-cbrt-cube`
9×	`add-exp-log` `associate-/r/` `associate-/l*`
8×	`div-inv`
6×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `div-exp`
2×	`frac-2neg` `clear-num`

Counts

4 → 163

Calls

4 calls:

9.0ms	(/ (cbrt x) (/ y x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(cbrt x)

series764.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (cbrt x) (/ y x))
210.0ms	(cbrt x)
216.0ms	(cbrt x)
209.0ms	(cbrt x)

simplify113.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	490	1172
1	2209	1061
2	5002	1023

prune470.0ms

Filtered

175 candidates to 139 candidates (79.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	175	9	184

Merged error: 0.1b

Counts

184 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(cbrt x)

series845.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(cbrt x)
210.0ms	(cbrt x)
213.0ms	(cbrt x)
205.0ms	(cbrt x)

simplify216.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	42	172
1	83	160
2	195	152
3	695	152
4	4069	152
5	5001	152

prune245.0ms

Filtered

64 candidates to 56 candidates (87.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	64	9	73

Merged error: 0.1b

Counts

73 → 9

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (/ (fabs x) y) y)
0.2b	(fma (/ z t) (/ z t) (* (fabs x) (/ (/ (fabs x) y) y)))
4.9b	(* (fabs x) (/ (/ (fabs x) y) y))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
102×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
93×	`add-cube-cbrt`
43×	`associate-r`
34×	`associate-/l*`
28×	`associate-*r/`
20×	`associate-/l/`
17×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
10×	`div-inv`
6×	`cbrt-undiv` `div-exp` `clear-num`
5×	`pow1`
4×	`frac-2neg` `un-div-inv`
3×	`expm1-log1p-u` `associate-l` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
1×	`pow-prod-down` `*-commutative` `fma-udef`

Counts

3 → 188

Calls

3 calls:

8.0ms	(/ (/ (fabs x) y) y)
1.0ms	(fma (/ z t) (/ z t) (* (fabs x) (/ (/ (fabs x) y) y)))
21.0ms	(* (fabs x) (/ (/ (fabs x) y) y))

series125.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(/ (/ (fabs x) y) y)
70.0ms	(fma (/ z t) (/ z t) (* (fabs x) (/ (/ (fabs x) y) y)))
32.0ms	(* (fabs x) (/ (/ (fabs x) y) y))

simplify133.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	594	1373
1	2711	1241
2	5002	1218

prune414.0ms

Filtered

197 candidates to 148 candidates (75.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	4	3	7
Picked	0	1	1
Done	1	0	1
Total	199	7	206

Merged error: 0.1b

Counts

206 → 7

regimes169.0ms

Accuracy

-0.9% (4.0b remaining)

Error of 4.1b against oracle of 0.1b and baseline of 4.1b

bsearch9.0ms

Steps

Iters	Range		Point
1	-6.900302478404349e-161	-6.65880283091198e-161	-6.7191777427850724e-161

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	15
1	23	15

end0.0ms

sample987.0ms

Algorithm

intervals

Results

593.0ms

15412×

body

valid