Details

analyze9.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 19 to 15 computations (21.1% saved)

sample1.0s (28.8%)

Results

879.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify114.0ms (3.2%)

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

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 68 to 52 computations (23.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 99229/100000 (.f64 x 4481/100000)) x)
✓	0.4b	(*.f64 x 27061/100000)
✓	0.4b	(*.f64 x 4481/100000)
✓	16.8b	(/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 (+.f64 99229/100000 (*.f64 x 4481/100000)) x)))

series12.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(*.f64 x 4481/100000)
3.0ms	(/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 (+.f64 99229/100000 (*.f64 x 4481/100000)) x)))
3.0ms	(.f64 (+.f64 99229/100000 (.f64 x 4481/100000)) x)
1.0ms	(*.f64 x 27061/100000)

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

5.0ms	(/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 (+.f64 99229/100000 (*.f64 x 4481/100000)) x)))
4.0ms	(.f64 (+.f64 99229/100000 (.f64 x 4481/100000)) x)
3.0ms	(*.f64 x 4481/100000)
2.0ms	(*.f64 x 27061/100000)

simplify100.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

428×	`fma-def_binary64`
361×	`fma-neg_binary64`
333×	`distribute-rgt-in_binary64`
307×	`distribute-lft-in_binary64`
277×	`*-commutative_binary64`

Counts

143 → 161

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	202	2117
1	465	1686
2	1364	1675
3	3268	1669
4	4817	1665
5	4841	1665

prune187.0ms (5.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	159	3	162

Error

0.0b

Counts

162 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 (+.f64 99229/100000 (*.f64 x 4481/100000)) x))))
	0.5b	(-.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) (/.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
▶	0.0b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 4018 to 3097 computations (22.9% saved)

localize12.0ms (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)
✓	16.8b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series10.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
3.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
2.0ms	(fma.f64 x 27061/100000 230753/100000)
2.0ms	(fma.f64 x 4481/100000 99229/100000)

rewrite6.0ms (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:

2.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
0.0ms	(fma.f64 x 4481/100000 99229/100000)
0.0ms	(fma.f64 x 27061/100000 230753/100000)
0.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)

simplify83.0ms (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

prune115.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	100	3	103

Error

0.0b

Counts

103 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 (+.f64 99229/100000 (*.f64 x 4481/100000)) x))))
▶	0.5b	(-.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) (/.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	0.0b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 2228 to 1730 computations (22.4% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (fma.f64 x 27061/100000 230753/100000))
✓	0.7b	(*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)))
✓	10.1b	(/.f64 (.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
✓	17.3b	(cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series25.0ms (0.7%)

Counts

4 → 48

Calls

4 calls:

8.0ms	(/.f64 (.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
6.0ms	(*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)))
5.0ms	(cbrt.f64 (fma.f64 x 27061/100000 230753/100000))
5.0ms	(cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
18×	`add-exp-log_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(/.f64 (.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
4.0ms	(*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)))
1.0ms	(cbrt.f64 (fma.f64 x 27061/100000 230753/100000))
1.0ms	(cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

simplify154.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
365×	`fma-neg_binary64`
345×	`cancel-sign-sub-inv_binary64`
142×	`distribute-rgt-neg-in_binary64`
139×	`distribute-lft-neg-in_binary64`

Counts

139 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	289	4640
1	751	3883
2	2257	3167
3	4600	3107
4	4993	3107
5	4949	3107

prune706.0ms (19.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	368	3	371

Error

Counts

371 → 3

Alt Table

Status	Error	Program
▶	0.5b	(-.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) (/.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 1/3))))
✓	0.0b	(-.f64 x (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 (+.f64 99229/100000 (*.f64 x 4481/100000)) x))))
✓	0.0b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 21152 to 17018 computations (19.5% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)))
	10.1b	(/.f64 (.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
	17.3b	(cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
✓	18.3b	(pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 1/3)

series7.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

7.0ms

(pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 1/3)

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`pow-unpow_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`unpow-prod-down_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

1.0ms

(pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 1/3)

simplify73.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

773×	`fma-def_binary64`
506×	`times-frac_binary64`
353×	`associate-/l*_binary64`
307×	`fma-neg_binary64`
259×	`associate-/r*_binary64`

Counts

32 → 52

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	805
1	234	765
2	541	625
3	1590	515
4	4815	515
5	5000	515
6	4917	515

prune445.0ms (12.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	263	3	266

Error

Counts

266 → 3

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) (/.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 1/3))))
✓	0.0b	(-.f64 x (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 (+.f64 99229/100000 (*.f64 x 4481/100000)) x))))
✓	0.0b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 14932 to 12041 computations (19.4% saved)

regimes290.0ms (8.2%)

Accuracy

Total 0.0b remaining (44.3%)

Threshold costs 0.0b (44.3%)

Counts

109 → 1

Compiler

Compiled 6508 to 5162 computations (20.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
6×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	22	23
2	28	23
3	37	23
4	50	23
5	55	23
6	58	23
7	59	23
8	56	23

end85.0ms (2.4%)

Compiler: Compiled 117 to 91 computations (22.2% saved)

Details

analyze9.0ms (0.3%)

sample1.0s (28.8%)

simplify114.0ms (3.2%)

prune4.0ms (0.1%)

localize10.0ms (0.3%)

series12.0ms (0.3%)

rewrite19.0ms (0.5%)

simplify100.0ms (2.8%)

prune187.0ms (5.3%)

localize12.0ms (0.3%)

series10.0ms (0.3%)

rewrite6.0ms (0.2%)

simplify83.0ms (2.4%)

prune115.0ms (3.3%)

localize17.0ms (0.5%)

series25.0ms (0.7%)

rewrite17.0ms (0.5%)

simplify154.0ms (4.4%)

prune706.0ms (19.9%)

localize19.0ms (0.5%)

series7.0ms (0.2%)

rewrite2.0ms (0.1%)

simplify73.0ms (2.1%)

prune445.0ms (12.5%)

regimes290.0ms (8.2%)

simplify3.0ms (0.1%)

end85.0ms (2.4%)

Profiling