Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample1.4s (31.7%)

Results

648.0ms	2131×	body	1024	valid
323.0ms	4391×	body	128	valid
210.0ms	1031×	body	512	valid
72.0ms	506×	body	256	valid
68.0ms	197×	body	2048	valid

Compiler

Compiled 38 to 35 computations (7.9% saved)

simplify62.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

978×	`times-frac_binary64`
434×	`unswap-sqr_binary64`
378×	`associate-*l/_binary64`
368×	`fma-neg_binary64`
358×	`fma-def_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	19	15
2	25	15
3	34	15
4	59	15
5	113	15
6	235	15
7	600	15
8	1504	15
9	2557	15
10	4582	15
11	4956	15
12	4701	15

prune2.0ms (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

Error

32.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	32.2b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Compiler

Compiled 36 to 33 computations (8.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
✓	0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
✓	3.0b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

series22.0ms (0.5%)

Counts

3 → 20

Calls

3 calls:

12.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
8.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
2.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`*-un-lft-identity_binary64`
75×	`add-sqr-sqrt_binary64`
64×	`add-cube-cbrt_binary64`
63×	`times-frac_binary64`
54×	`prod-diff_binary64`

Counts

3 → 149

Calls

3 calls:

11.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
4.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
3.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

simplify122.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-neg_binary64`
409×	`cancel-sign-sub-inv_binary64`
312×	`distribute-rgt-in_binary64`
288×	`fma-def_binary64`
267×	`distribute-lft-in_binary64`

Counts

169 → 220

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	3241
1	339	3128
2	809	2722
3	2297	2604
4	4742	2603
5	4949	2603

prune179.0ms (4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	217	3	220
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	218	3	221

Error

0.0b

Counts

221 → 3

Alt Table

Status	Error	Program
	32.9b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) (/.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) -1)
▶	28.4b	(fma.f64 (pow.f64 x 3) -1/3 x)
	32.1b	(-.f64 (exp.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))) 1)

Compiler

Compiled 5060 to 4609 computations (8.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/3 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 (pow.f64 x 3) -1/3 x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (pow.f64 x 3) -1/3 x)

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

435×	`neg-mul-1_binary64`
394×	`associate-l_binary64`
372×	`associate-r_binary64`
317×	`distribute-rgt-out_binary64`
261×	`exp-prod_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	232
1	35	197
2	87	197
3	323	197
4	1660	197
5	4537	197
6	5209	197

prune9.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	16	3	19

Error

0.0b

Counts

19 → 3

Alt Table

Status	Error	Program
	32.9b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) (/.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) -1)
✓	28.4b	(fma.f64 (pow.f64 x 3) -1/3 x)
▶	32.1b	(-.f64 (exp.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))) 1)

Compiler

Compiled 227 to 180 computations (20.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (exp.f64 (*.f64 x -2)))
✓	2.9b	(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
✓	3.0b	(-.f64 (exp.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))) 1)

series619.0ms (13.7%)

Counts

3 → 36

Calls

3 calls:

216.0ms	(-.f64 (exp.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))) 1)
207.0ms	(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
196.0ms	(log1p.f64 (exp.f64 (*.f64 x -2)))

rewrite36.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`prod-diff_binary64`
82×	`*-un-lft-identity_binary64`
82×	`add-sqr-sqrt_binary64`
76×	`exp-sum_binary64`
76×	`add-cube-cbrt_binary64`

Counts

3 → 159

Calls

3 calls:

12.0ms	(-.f64 (exp.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))) 1)
4.0ms	(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
0.0ms	(log1p.f64 (exp.f64 (*.f64 x -2)))

simplify181.0ms (4%)

Algorithm

1×	egg-herbie

Rules

1017×	`fma-neg_binary64`
415×	`fma-def_binary64`
376×	`associate-l_binary64`
370×	`times-frac_binary64`
342×	`associate-r_binary64`

Counts

195 → 201

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	2718
1	357	2623
2	888	2612
3	3055	2610
4	4440	2610
5	4868	2610
6	4949	2610
7	4845	2610

prune184.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	201	3	204

Error

0.0b

Counts

204 → 3

Alt Table

Status	Error	Program
▶	32.9b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) (/.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) -1)
✓	28.4b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	32.1b	(-.f64 (exp.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))) 1)

Compiler

Compiled 6636 to 6048 computations (8.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
✓	0.5b	(/.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 (*.f64 -2 x)))))
✓	0.5b	(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 (*.f64 -2 x)))))
✓	32.9b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) (/.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) -1)

series59.0ms (1.3%)

Counts

4 → 40

Calls

4 calls:

30.0ms	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) (/.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) -1)
12.0ms	(/.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 (*.f64 -2 x)))))
12.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 (*.f64 -2 x)))))
5.0ms	(sqrt.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
42×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
36×	`sqrt-prod_binary64`

Counts

4 → 131

Calls

4 calls:

6.0ms	(/.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 (*.f64 -2 x)))))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 (*.f64 -2 x)))))
3.0ms	(sqrt.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
0.0ms	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) (/.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) -1)

simplify112.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-neg_binary64`
318×	`fma-def_binary64`
216×	`associate-/l*_binary64`
182×	`times-frac_binary64`
180×	`cancel-sign-sub-inv_binary64`

Counts

171 → 213

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	204	3662
1	444	3211
2	1188	3188
3	3968	2881
4	4915	2881

prune200.0ms (4.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	248	3	251

Error

0.0b

Counts

251 → 3

Alt Table

Status	Error	Program
✓	32.9b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) (/.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))) -1)
✓	28.4b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	32.1b	(-.f64 (exp.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))) 1)

Compiler

Compiled 7003 to 6217 computations (11.2% saved)

regimes1.1s (23.6%)

Accuracy

Total 0.2b remaining (89.8%)

Threshold costs 0.2b (89.8%)

Counts

78 → 3

Compiler

Compiled 15045 to 13903 computations (7.6% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	76
1	34	76
2	37	76
3	39	76
4	40	76
5	39	76

end83.0ms (1.8%)

Compiler: Compiled 145 to 126 computations (13.1% saved)

Details

analyze1.0ms (0%)

sample1.4s (31.7%)

simplify62.0ms (1.4%)

prune2.0ms (0%)

localize7.0ms (0.2%)

series22.0ms (0.5%)

rewrite30.0ms (0.7%)

simplify122.0ms (2.7%)

prune179.0ms (4%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify58.0ms (1.3%)

prune9.0ms (0.2%)

localize9.0ms (0.2%)

series619.0ms (13.7%)

rewrite36.0ms (0.8%)

simplify181.0ms (4%)

prune184.0ms (4.1%)

localize9.0ms (0.2%)

series59.0ms (1.3%)

rewrite22.0ms (0.5%)

simplify112.0ms (2.5%)

prune200.0ms (4.4%)

regimes1.1s (23.6%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end83.0ms (1.8%)

Profiling