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)

sample1.1s (21.8%)

Results

905.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify141.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1572×	`fma-neg_binary64`
1419×	`fma-def_binary64`
565×	`sub-neg_binary64`
397×	`div-sub_binary64`
395×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	31	19
2	50	19
3	71	19
4	84	19
5	103	19
6	137	19
7	208	19
8	304	19
9	493	19
10	931	19
11	1441	19
12	2503	19
13	3175	19
14	3604	19
15	4118	19
16	4302	19
17	4751	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 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x)

Compiler

Compiled 62 to 46 computations (25.8% saved)

localize19.0ms (0.4%)

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))

series18.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

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

rewrite13.0ms (0.3%)

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:

6.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
1.0ms	(fma.f64 x 27061/100000 230753/100000)
1.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
1.0ms	(fma.f64 x 4481/100000 99229/100000)

simplify117.0ms (2.4%)

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

prune93.0ms (1.9%)

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

Compiler

Compiled 1981 to 1489 computations (24.8% saved)

localize8.0ms (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))

series8.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

3.0ms	(/.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)
2.0ms	(*.f64 4481/100000 x)

rewrite15.0ms (0.3%)

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:

5.0ms	(*.f64 4481/100000 x)
2.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (*.f64 4481/100000 x) 1))
1.0ms	(fma.f64 x (*.f64 4481/100000 x) 1)

simplify108.0ms (2.2%)

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

prune146.0ms (2.9%)

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

Compiler

Compiled 2638 to 1903 computations (27.9% saved)

localize13.0ms (0.3%)

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))

series8.0ms (0.2%)

Counts

2 → 24

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))
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)))

simplify146.0ms (3%)

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

prune243.0ms (4.9%)

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

Compiler

Compiled 2740 to 2123 computations (22.5% saved)

localize25.0ms (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))))

series9.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms

(*.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)))

4.0ms

(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))))

rewrite40.0ms (0.8%)

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:

15.0ms

(*.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)))

10.0ms

(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))))

simplify213.0ms (4.3%)

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

prune1.7s (34.7%)

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 (-.f64 (+.f64 230753/100000 (.f64 1900161040244073/1000000000000000 (pow.f64 x 2))) (+.f64 (.f64 20191289437/10000000000 x) (*.f64 179503363065659419717/100000000000000000000 (pow.f64 x 3)))) x)
✓	0.8b	(-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (*.f64 4481/100000 x) 1)) x)
✓	17.8b	(-.f64 (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)))) x)

Compiler

Compiled 23250 to 18454 computations (20.6% saved)

regimes560.0ms (11.3%)

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

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	18	34
2	22	34
3	24	34
4	25	34
5	24	34

end183.0ms (3.7%)

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

Details

analyze7.0ms (0.1%)

sample1.1s (21.8%)

simplify141.0ms (2.8%)

prune6.0ms (0.1%)

localize19.0ms (0.4%)

series18.0ms (0.4%)

rewrite13.0ms (0.3%)

simplify117.0ms (2.4%)

prune93.0ms (1.9%)

localize8.0ms (0.2%)

series8.0ms (0.2%)

rewrite15.0ms (0.3%)

simplify108.0ms (2.2%)

prune146.0ms (2.9%)

localize13.0ms (0.3%)

series8.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify146.0ms (3%)

prune243.0ms (4.9%)

localize25.0ms (0.5%)

series9.0ms (0.2%)

rewrite40.0ms (0.8%)

simplify213.0ms (4.3%)

prune1.7s (34.7%)

regimes560.0ms (11.3%)

simplify7.0ms (0.1%)

end183.0ms (3.7%)

Profiling