Details

analyze98.0ms (2.8%)

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)

sample42.0ms (1.2%)

Algorithm

1×

intervals

Results

17.0ms	67×	body	1024	valid
7.0ms	32×	body	512	valid
6.0ms	130×	body	128	valid
2.0ms	22×	body	256	valid
2.0ms	5×	body	2048	valid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify63.0ms (1.8%)

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 (0.1%)

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

30.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.3b	(-.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))))
✓	3.3b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

series22.0ms (0.6%)

Counts

3 → 20

Calls

3 calls:

10.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
10.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
2.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

rewrite30.0ms (0.8%)

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:

10.0ms	(-.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)))

simplify127.0ms (3.6%)

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

prune158.0ms (4.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	218	3	221

Error

0.0b

Counts

221 → 3

Alt Table

Status	Error	Program
✓	30.3b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
	31.3b	(fma.f64 (pow.f64 x 3) -1/3 x)
▶	30.3b	(expm1.f64 (log.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))))

Compiler

Compiled 5026 to 4578 computations (8.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
✓	0.0b	(expm1.f64 (log.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))))
	0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
✓	3.3b	(log.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))))

series463.0ms (13%)

Counts

2 → 16

Calls

2 calls:

235.0ms	(expm1.f64 (log.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))))
228.0ms	(log.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`log-prod_binary64`
16×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 42

Calls

2 calls:

4.0ms	(log.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))))
0.0ms	(expm1.f64 (log.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))))

simplify113.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
477×	`cancel-sign-sub-inv_binary64`
370×	`unswap-sqr_binary64`
350×	`sub-neg_binary64`
308×	`fma-neg_binary64`

Counts

58 → 82

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	128	1184
1	273	1102
2	586	1054
3	1449	1035
4	3445	1029
5	4686	1029
6	4948	1029
7	4872	1029

prune105.0ms (3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	178	3	181

Error

Counts

181 → 3

Alt Table

Status	Error	Program
✓	30.3b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
	31.3b	(fma.f64 (pow.f64 x 3) -1/3 x)
▶	30.3b	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2)))))

Compiler

Compiled 3093 to 2736 computations (11.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2)))))
✓	0.0b	(log1p.f64 (exp.f64 (*.f64 x -2)))
✓	3.3b	(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))

series662.0ms (18.6%)

Counts

3 → 36

Calls

3 calls:

227.0ms	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2)))))
219.0ms	(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
215.0ms	(log1p.f64 (exp.f64 (*.f64 x -2)))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
8×	`pow1_binary64`

Counts

3 → 61

Calls

3 calls:

4.0ms	(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
0.0ms	(log1p.f64 (exp.f64 (*.f64 x -2)))
0.0ms	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2)))))

simplify85.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

962×	`fma-neg_binary64`
632×	`cancel-sign-sub-inv_binary64`
354×	`fma-def_binary64`
318×	`associate-l_binary64`
281×	`associate-r_binary64`

Counts

97 → 93

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	1628
1	261	1453
2	711	1325
3	2384	1325
4	4080	1316
5	4948	1316

prune60.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	93	3	96

Error

Counts

96 → 3

Alt Table

Status	Error	Program
✓	30.3b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
▶	31.3b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	30.3b	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2)))))

Compiler

Compiled 1764 to 1550 computations (12.1% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 3) -1/3 x)

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(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)

simplify59.0ms (1.7%)

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

prune8.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

19 → 3

Alt Table

Status	Error	Program
✓	30.3b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
✓	31.3b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	30.3b	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2)))))

Compiler

Compiled 180 to 137 computations (23.9% saved)

regimes211.0ms (5.9%)

Accuracy

Total 0.2b remaining (88.8%)

Threshold costs 0.2b (88.8%)

Counts

18 → 2

Compiler

Compiled 1652 to 1423 computations (13.9% saved)

bsearch1.0ms (0%)

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

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	34
1	25	34
2	26	34
3	24	34

end1.0ms (0%)

Compiler: Compiled 25 to 20 computations (20% saved)

sample1.2s (33.8%)

Algorithm

1×

intervals

Results

482.0ms	1963×	body	1024	valid
185.0ms	4296×	body	128	valid
151.0ms	1015×	body	512	valid
58.0ms	212×	body	2048	valid
46.0ms	514×	body	256	valid

Compiler

Compiled 71 to 61 computations (14.1% saved)

Details

analyze98.0ms (2.8%)

sample42.0ms (1.2%)

simplify63.0ms (1.8%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series22.0ms (0.6%)

rewrite30.0ms (0.8%)

simplify127.0ms (3.6%)

prune158.0ms (4.4%)

localize7.0ms (0.2%)

series463.0ms (13%)

rewrite6.0ms (0.2%)

simplify113.0ms (3.2%)

prune105.0ms (3%)

localize8.0ms (0.2%)

series662.0ms (18.6%)

rewrite9.0ms (0.2%)

simplify85.0ms (2.4%)

prune60.0ms (1.7%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify59.0ms (1.7%)

prune8.0ms (0.2%)

regimes211.0ms (5.9%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample1.2s (33.8%)

Profiling