Details

analyze78.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	50%	12.6%	6
50%	37.5%	12.6%	7
56.2%	25%	18.8%	8
62.4%	18.7%	18.8%	9
65.6%	12.5%	22%	10
68.7%	9.4%	22%	11
70.2%	6.2%	23.5%	12
71.8%	4.7%	23.5%	13
72.6%	3.1%	24.3%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample787.0ms (16.5%)

Results

735.0ms	8256×	body	128	valid
9.0ms	92×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

265×	`fma-def_binary64`
84×	`fma-neg_binary64`
35×	`distribute-rgt-in_binary64`
25×	`unsub-neg_binary64`
24×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	33	10
3	71	10
4	161	10
5	238	10
6	325	10
7	429	10
8	669	10
9	714	10
10	746	10

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	8.2b	(-.f64 x (.f64 y (.f64 x x)))
▶	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 52 to 31 computations (40.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

series6.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 x (-.f64 1 (*.f64 x y)))

rewrite35.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

682×	`log1p-expm1-u_binary64`
682×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
73×	`add-sqr-sqrt_binary64`
68×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	146	10
2	1841	10

Stop Event

1×	node limit

Counts

1 → 21

Calls

1 calls:

35.0ms

(*.f64 x (-.f64 1 (*.f64 x y)))

simplify36.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1023×	`fma-neg_binary64`
478×	`cancel-sign-sub-inv_binary64`
266×	`associate-l_binary64`
251×	`unswap-sqr_binary64`
205×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	218
1	23	218
2	50	218
3	124	218
4	349	218
5	1199	218
6	2253	218
7	3990	218

Stop Event

1×	node limit

Counts

45 → 26

prune18.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	22	4	26
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	22	6	28

Error

0.0b

Counts

28 → 6

Alt Table

Status	Error	Program
	34.5b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)
▶	1.4b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
	9.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) x) (+.f64 1 (*.f64 x y)))
	14.3b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 3)) x) (+.f64 (+.f64 1 (pow.f64 (.f64 x y) 2)) (.f64 x y)))
	8.2b	(-.f64 x (.f64 y (.f64 x x)))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 426 to 253 computations (40.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
✓	0.6b	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)

series1.2s (24.5%)

Counts

2 → 48

Calls

2 calls:

1.1s	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
27.0ms	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))

rewrite48.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
91×	`add-sqr-sqrt_binary64`
87×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	207	22
2	2334	22

Stop Event

1×	node limit

Counts

2 → 65

Calls

2 calls:

46.0ms	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))
46.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Rules

916×	`times-frac_binary64`
368×	`fma-def_binary64`
299×	`cancel-sign-sub-inv_binary64`
154×	`distribute-neg-frac_binary64`
152×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	2130
1	441	2060
2	1576	1912

Stop Event

1×	node limit

Counts

113 → 124

prune92.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	150	6	156

Error

0.0b

Counts

156 → 6

Alt Table

Status	Error	Program
	14.3b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 3)) x) (+.f64 (+.f64 1 (pow.f64 (.f64 x y) 2)) (.f64 x y)))
▶	1.5b	(pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 1 (.f64 x y)))) 3)
	34.5b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)
✓	1.4b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
	8.2b	(-.f64 x (.f64 y (.f64 x x)))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 3476 to 2303 computations (33.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 1 (.f64 x y))))
✓	0.2b	(cbrt.f64 (-.f64 1 (*.f64 x y)))
✓	0.7b	(cbrt.f64 x)
✓	0.7b	(pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 1 (.f64 x y)))) 3)

series1.2s (24.2%)

Counts

4 → 84

Calls

4 calls:

1.1s	(pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 1 (.f64 x y)))) 3)
33.0ms	(cbrt.f64 x)
26.0ms	(.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 1 (.f64 x y))))
16.0ms	(cbrt.f64 (-.f64 1 (*.f64 x y)))

rewrite61.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`log-prod_binary64`
423×	`prod-diff_binary64`
181×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`
173×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	230	34
2	2688	34

Stop Event

1×	node limit

Counts

4 → 127

Calls

4 calls:

59.0ms	(.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 1 (.f64 x y))))
59.0ms	(cbrt.f64 (-.f64 1 (*.f64 x y)))
59.0ms	(cbrt.f64 x)
59.0ms	(pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 1 (.f64 x y)))) 3)

simplify102.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-def_binary64`
513×	`cancel-sign-sub-inv_binary64`
266×	`distribute-neg-frac_binary64`
204×	`sub-neg_binary64`
176×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	3306
1	690	3196
2	2462	2996

Stop Event

1×	node limit

Counts

211 → 226

prune139.0ms (2.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	225	7	232

Error

0.0b

Counts

232 → 7

Alt Table

Status	Error	Program
	14.3b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 3)) x) (+.f64 (+.f64 1 (pow.f64 (.f64 x y) 2)) (.f64 x y)))
✓	1.5b	(pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 1 (.f64 x y)))) 3)
▶	1.6b	(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)))
	34.5b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)
✓	1.4b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
	8.2b	(-.f64 x (.f64 y (.f64 x x)))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 5672 to 3494 computations (38.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)
✓	0.6b	(cbrt.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
	0.6b	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))
✓	0.6b	(cbrt.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2))

series113.0ms (2.4%)

Counts

3 → 72

Calls

3 calls:

49.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)
37.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2))
27.0ms	(cbrt.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))

rewrite57.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

506×	`log-prod_binary64`
423×	`prod-diff_binary64`
184×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`
169×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	242	46
2	2747	46

Stop Event

1×	node limit

Counts

3 → 84

Calls

3 calls:

55.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)
55.0ms	(cbrt.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
55.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2))

simplify84.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

302×	`fma-neg_binary64`
265×	`sub-neg_binary64`
251×	`associate-/r*_binary64`
186×	`fma-def_binary64`
166×	`neg-sub0_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	4744
1	1008	4478
2	3897	4438

Stop Event

1×	node limit

Counts

156 → 200

prune489.0ms (10.3%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	456	2	458
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	456	9	465

Error

Counts

465 → 9

Alt Table

Status	Error	Program
	14.3b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 3)) x) (+.f64 (+.f64 1 (pow.f64 (.f64 x y) 2)) (.f64 x y)))
✓	1.5b	(pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 1 (.f64 x y)))) 3)
	35.9b	(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)) (.f64 (cbrt.f64 (exp.f64 (.f64 (log.f64 (.f64 x (-.f64 1 (.f64 x y)))) 1/3))) (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))) 2)))
	11.8b	(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 x (fma.f64 y (neg.f64 x) 1))) 4))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))) 2)))
✓	1.6b	(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)))
	34.5b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)
✓	1.4b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
	8.2b	(-.f64 x (.f64 y (.f64 x x)))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 25030 to 16945 computations (32.3% saved)

regimes63.0ms (1.3%)

Accuracy

Total 0.1b remaining (75.6%)

Threshold costs 0.1b (75.6%)

Counts

18 → 1

Compiler

Compiled 921 to 635 computations (31.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	27	10
3	33	10
4	37	10
5	38	10

Stop Event

1×

saturated

end136.0ms (2.9%)

Compiler: Compiled 202 to 139 computations (31.2% saved)

Iter	Nodes	Cost
0	7	10
1	16	10
2	33	10
3	71	10
4	161	10
5	238	10
6	325	10
7	429	10
8	669	10
9	714	10
10	746	10

Iter	Nodes	Cost
0	7	10
1	16	10
2	33	10
3	71	10
4	161	10
5	238	10
6	325	10
7	429	10
8	669	10
9	714	10
10	746	10

Details

analyze78.0ms (1.6%)

sample787.0ms (16.5%)

simplify14.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite35.0ms (0.7%)

simplify36.0ms (0.7%)

prune18.0ms (0.4%)

localize7.0ms (0.1%)

series1.2s (24.5%)

rewrite48.0ms (1%)

simplify46.0ms (1%)

prune92.0ms (1.9%)

localize8.0ms (0.2%)

series1.2s (24.2%)

rewrite61.0ms (1.3%)

simplify102.0ms (2.2%)

prune139.0ms (2.9%)

localize11.0ms (0.2%)

series113.0ms (2.4%)

rewrite57.0ms (1.2%)

simplify84.0ms (1.8%)

prune489.0ms (10.3%)

regimes63.0ms (1.3%)

simplify2.0ms (0%)

end136.0ms (2.9%)

Profiling

Iter	Nodes	Cost
0	7	10
1	16	10
2	33	10
3	71	10
4	161	10
5	238	10
6	325	10
7	429	10
8	669	10
9	714	10
10	746	10