Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample128.0ms (1.9%)

Algorithm

1×

intervals

Results

11.0ms	67×	body	1024	valid
7.0ms	141×	body	128	valid
3.0ms	25×	body	512	valid
2.0ms	10×	body	2048	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

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

28.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	2.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series8.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite221.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

1322×	`*-un-lft-identity_binary64`
1012×	`times-frac_binary64`
869×	`add-sqr-sqrt_binary64`
612×	`prod-diff_binary64`
533×	`add-cube-cbrt_binary64`

Counts

3 → 783

Calls

3 calls:

43.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
4.0ms	(/.f64 x (+.f64 x 1))

simplify940.0ms (13.9%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-neg_binary64`
367×	`unsub-neg_binary64`
299×	`fma-udef_binary64`
213×	`sub-neg_binary64`
202×	`associate-+r-_binary64`

Counts

819 → 619

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	545	54602
1	1290	31108
2	3043	22839
3	4323	22837
4	4983	22837
5	4991	22837
6	4742	22837

prune758.0ms (11.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	615	4	619
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	616	4	620

Error

0.0b

Counts

620 → 4

Alt Table

Status	Error	Program
	30.3b	(+.f64 1 (*.f64 x (+.f64 3 x)))
	33.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	33.4b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))
▶	28.1b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 30424 to 22425 computations (26.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(exp.f64 (/.f64 x (+.f64 x 1)))
✓	2.1b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	2.3b	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))

series10.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
3.0ms	(exp.f64 (/.f64 x (+.f64 x 1)))
3.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))

rewrite312.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Rules

1435×	`*-un-lft-identity_binary64`
1089×	`times-frac_binary64`
985×	`add-sqr-sqrt_binary64`
748×	`prod-diff_binary64`
685×	`log-pow_binary64`

Counts

3 → 884

Calls

3 calls:

52.0ms	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
5.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))
4.0ms	(exp.f64 (/.f64 x (+.f64 x 1)))

simplify715.0ms (10.6%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-neg_binary64`
415×	`unsub-neg_binary64`
393×	`times-frac_binary64`
306×	`fma-udef_binary64`
231×	`exp-prod_binary64`

Counts

920 → 608

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	607	34067
1	1302	22396
2	2772	22185
3	4140	22183
4	4819	22183

prune917.0ms (13.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	676	0	676
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	676	4	680

Error

0.0b

Counts

680 → 4

Alt Table

Status	Error	Program
▶	30.3b	(+.f64 1 (*.f64 x (+.f64 3 x)))
	33.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	33.4b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))
✓	28.1b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 35848 to 26780 computations (25.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 3 x))

series2.0ms (0%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(*.f64 x (+.f64 3 x))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 25

Calls

1 calls:

4.0ms

(*.f64 x (+.f64 3 x))

simplify87.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

982×	`fma-def_binary64`
428×	`unswap-sqr_binary64`
372×	`distribute-rgt-out_binary64`
345×	`+-commutative_binary64`
343×	`associate-+r+_binary64`

Counts

37 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	335
1	122	303
2	392	303
3	1110	303
4	2468	303
5	3561	303
6	4612	303
7	4910	303
8	4853	303

prune29.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	33	4	37

Error

0.0b

Counts

37 → 4

Alt Table

Status	Error	Program
✓	30.3b	(+.f64 1 (*.f64 x (+.f64 3 x)))
▶	33.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	33.4b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))
✓	28.1b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 517 to 374 computations (27.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 3 (pow.f64 x 3))
✓	0.2b	(/.f64 1 (*.f64 x x))
✓	10.8b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
✓	12.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))

series12.0ms (0.2%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
3.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
3.0ms	(/.f64 3 (pow.f64 x 3))
2.0ms	(/.f64 1 (*.f64 x x))

rewrite159.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

521×	`*-un-lft-identity_binary64`
386×	`add-sqr-sqrt_binary64`
347×	`times-frac_binary64`
278×	`prod-diff_binary64`
241×	`add-cube-cbrt_binary64`

Counts

4 → 479

Calls

4 calls:

48.0ms	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
17.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
5.0ms	(/.f64 3 (pow.f64 x 3))
3.0ms	(/.f64 1 (*.f64 x x))

simplify526.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-neg_binary64`
286×	`associate-l_binary64`
263×	`associate-r_binary64`
197×	`associate-/r*_binary64`
170×	`fma-def_binary64`

Counts

515 → 476

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	392	26531
1	913	17934
2	3580	17735
3	4853	17735
4	5052	17735

prune649.0ms (9.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	474	2	476
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	474	6	480

Error

0.0b

Counts

480 → 6

Alt Table

Status	Error	Program
✓	30.3b	(+.f64 1 (*.f64 x (+.f64 3 x)))
✓	33.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	33.4b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))
	57.2b	(/.f64 (fma.f64 (pow.f64 x 4) (-.f64 (/.f64 (/.f64 9 x) x) (pow.f64 (cbrt.f64 (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (.f64 x x)))) 6)) (-.f64 (-.f64 (/.f64 -1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) (/.f64 -3 x))) (.f64 (pow.f64 x 4) (+.f64 (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (.f64 x x))) (/.f64 -3 x))))
	34.1b	(fma.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))))) (cbrt.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))))) (cbrt.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))))) (/.f64 -1 (pow.f64 x 4)))
✓	28.1b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 25898 to 19147 computations (26.1% saved)

regimes116.0ms (1.7%)

Accuracy

Total 0.1b remaining (77.3%)

Threshold costs 0.1b (77.3%)

Counts

33 → 2

Compiler

Compiled 2142 to 1660 computations (22.5% saved)

bsearch2.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
11×	`sub-neg_binary64`
7×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	80
1	42	80
2	59	80
3	79	80
4	91	80
5	96	80
6	97	80
7	94	80

end1.0ms (0%)

Compiler: Compiled 54 to 41 computations (24.1% saved)

sample1.0s (15.3%)

Algorithm

1×

intervals

Results

319.0ms	2005×	body	1024	valid
182.0ms	4305×	body	128	valid
118.0ms	1003×	body	512	valid
41.0ms	476×	body	256	valid
41.0ms	211×	body	2048	valid

Compiler

Compiled 259 to 195 computations (24.7% saved)

Details

analyze5.0ms (0.1%)

sample128.0ms (1.9%)

simplify86.0ms (1.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series8.0ms (0.1%)

rewrite221.0ms (3.3%)

simplify940.0ms (13.9%)

prune758.0ms (11.2%)

localize9.0ms (0.1%)

series10.0ms (0.1%)

rewrite312.0ms (4.6%)

simplify715.0ms (10.6%)

prune917.0ms (13.6%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite5.0ms (0.1%)

simplify87.0ms (1.3%)

prune29.0ms (0.4%)

localize13.0ms (0.2%)

series12.0ms (0.2%)

rewrite159.0ms (2.4%)

simplify526.0ms (7.8%)

prune649.0ms (9.6%)

regimes116.0ms (1.7%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.0s (15.3%)

Profiling