Details

analyze7.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	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 19 to 15 computations (21.1% saved)

sample1.5s (28%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify135.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1041×	`fma-neg_binary64`
807×	`times-frac_binary64`
600×	`associate-/r/_binary64`
564×	`sub-neg_binary64`
392×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	25	19
2	45	19
3	72	19
4	115	19
5	188	19
6	308	19
7	491	19
8	989	19
9	1283	19
10	3056	19
11	4408	19
12	4532	19
13	4794	19
14	4959	19
15	4564	19

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 62 to 46 computations (25.8% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
✓	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	13.3b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series21.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(fma.f64 x 4481/100000 99229/100000)
6.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
5.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
3.0ms	(fma.f64 x 27061/100000 230753/100000)

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 59

Calls

4 calls:

5.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
1.0ms	(fma.f64 x 4481/100000 99229/100000)
1.0ms	(fma.f64 x 27061/100000 230753/100000)
1.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)

simplify161.0ms (3%)

Algorithm

1×	egg-herbie

Rules

496×	`fma-def_binary64`
477×	`associate-l_binary64`
447×	`fma-neg_binary64`
424×	`distribute-rgt-in_binary64`
411×	`distribute-lft-in_binary64`

Counts

107 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1537
1	235	1385
2	582	1380
3	1485	1370
4	4572	1370
5	4900	1370

prune175.0ms (3.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	3	101

Error

0.0b

Counts

101 → 3

Alt Table

Status	Error	Program
	29.5b	(-.f64 x (fma.f64 x (fma.f64 x 1900161040244073/1000000000000000 -20191289437/10000000000) 230753/100000))
	17.8b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
▶	0.8b	(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (*.f64 4481/100000 x) 1)))

Compiler

Compiled 1981 to 1489 computations (24.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (*.f64 4481/100000 x) 1)
	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	0.4b	(*.f64 4481/100000 x)
✓	13.3b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (*.f64 4481/100000 x) 1))

series11.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

5.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (*.f64 4481/100000 x) 1))
3.0ms	(fma.f64 x (*.f64 4481/100000 x) 1)
3.0ms	(*.f64 4481/100000 x)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 59

Calls

3 calls:

3.0ms	(*.f64 4481/100000 x)
2.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (*.f64 4481/100000 x) 1))
2.0ms	(fma.f64 x (*.f64 4481/100000 x) 1)

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-l_binary64`
439×	`associate-r_binary64`
439×	`fma-neg_binary64`
429×	`fma-def_binary64`
238×	`associate-/r*_binary64`

Counts

83 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	1307
1	245	1198
2	605	1194
3	1424	1186
4	4266	1186
5	5027	1186

prune147.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	134	3	137

Error

0.0b

Counts

137 → 3

Alt Table

Status	Error	Program
	29.5b	(-.f64 x (fma.f64 x (fma.f64 x 1900161040244073/1000000000000000 -20191289437/10000000000) 230753/100000))
▶	17.8b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	0.8b	(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (*.f64 4481/100000 x) 1)))

Compiler

Compiled 2638 to 1903 computations (27.9% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x 4481/100000 99229/100000)
	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	1.1b	(expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000)))
✓	5.4b	(/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series10.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
3.0ms	(expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 41

Calls

2 calls:

4.0ms	(/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
1.0ms	(expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000)))

simplify132.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

406×	`fma-def_binary64`
387×	`associate-l_binary64`
305×	`associate-r_binary64`
222×	`sub-neg_binary64`
218×	`associate-/r*_binary64`

Counts

65 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	1161
1	209	1080
2	528	1076
3	1272	1066
4	4037	1066
5	4753	1066
6	5057	1066

prune250.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	118	3	121

Error

Counts

121 → 3

Alt Table

Status	Error	Program
	29.5b	(-.f64 x (fma.f64 x (fma.f64 x 1900161040244073/1000000000000000 -20191289437/10000000000) 230753/100000))
▶	17.8b	(-.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	0.8b	(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (*.f64 4481/100000 x) 1)))

Compiler

Compiled 2740 to 2123 computations (22.5% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(*.f64 (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
	1.1b	(expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000)))
	5.4b	(/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
✓	8.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

series15.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

8.0ms

(cbrt.f64 (*.f64 (*.f64 (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

7.0ms

(*.f64 (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

rewrite48.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

2 → 88

Calls

2 calls:

14.0ms

(*.f64 (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

11.0ms

(cbrt.f64 (*.f64 (*.f64 (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

simplify182.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

721×	`fma-def_binary64`
400×	`associate-/l/_binary64`
269×	`times-frac_binary64`
255×	`distribute-rgt-in_binary64`
245×	`distribute-lft-in_binary64`

Counts

112 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	4756
1	526	3640
2	1637	3155
3	4514	3143
4	5140	3143

prune1.6s (29.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	429	1	430
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	430	3	433

Error

Counts

433 → 3

Alt Table

Status	Error	Program
	29.3b	(-.f64 x (-.f64 (+.f64 230753/100000 (.f64 1900161040244073/1000000000000000 (pow.f64 x 2))) (+.f64 (.f64 20191289437/10000000000 x) (*.f64 179503363065659419717/100000000000000000000 (pow.f64 x 3)))))
✓	0.8b	(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (*.f64 4481/100000 x) 1)))
✓	17.8b	(-.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 x 27061/100000 230753/100000))) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 23250 to 18454 computations (20.6% saved)

regimes549.0ms (10.4%)

Accuracy

Total -0.1b remaining (-101.7%)

Threshold costs -0.1b (-101.7%)

Counts

127 → 1

Compiler

Compiled 6328 to 4942 computations (21.9% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	18	34
2	24	34
3	30	34
4	35	34
5	38	34
6	39	34
7	38	34

end191.0ms (3.6%)

Compiler: Compiled 132 to 102 computations (22.7% saved)

Details

analyze7.0ms (0.1%)

sample1.5s (28%)

simplify135.0ms (2.5%)

prune6.0ms (0.1%)

localize17.0ms (0.3%)

series21.0ms (0.4%)

rewrite12.0ms (0.2%)

simplify161.0ms (3%)

prune175.0ms (3.3%)

localize10.0ms (0.2%)

series11.0ms (0.2%)

rewrite9.0ms (0.2%)

simplify92.0ms (1.7%)

prune147.0ms (2.8%)

localize22.0ms (0.4%)

series10.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify132.0ms (2.5%)

prune250.0ms (4.7%)

localize29.0ms (0.5%)

series15.0ms (0.3%)

rewrite48.0ms (0.9%)

simplify182.0ms (3.4%)

prune1.6s (29.5%)

regimes549.0ms (10.4%)

simplify7.0ms (0.1%)

end191.0ms (3.6%)

Profiling