Details

analyze9.0ms (0.2%)

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)

sample970.0ms (28%)

Results

840.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify106.0ms (3.1%)

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

prune3.0ms (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 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000))))) x)

Compiler

Compiled 68 to 52 computations (23.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (+.f64 99229/100000 (.f64 x 4481/100000)))
✓	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 x (+.f64 99229/100000 (*.f64 x 4481/100000)))))

series10.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

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

rewrite17.0ms (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 → 97

Calls

4 calls:

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

simplify103.0ms (3%)

Algorithm

1×	egg-herbie

Rules

531×	`distribute-rgt-in_binary64`
505×	`distribute-lft-in_binary64`
504×	`fma-def_binary64`
382×	`times-frac_binary64`
354×	`fma-neg_binary64`

Counts

145 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	204	2128
1	481	1708
2	1466	1697
3	4065	1691
4	4831	1691
5	5045	1691

prune172.0ms (5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	161	3	164

Error

0.0b

Counts

164 → 3

Alt Table

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

Compiler

Compiled 4058 to 3127 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))

series9.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

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 (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)

rewrite7.0ms (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)

simplify80.0ms (2.3%)

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

prune104.0ms (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
▶	0.5b	(-.f64 (.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)))) x)
✓	0.0b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) x)
✓	0.0b	(-.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000))))) x)

Compiler

Compiled 2228 to 1730 computations (22.4% saved)

localize15.0ms (0.4%)

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

rewrite18.0ms (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:

6.0ms	(/.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)))
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))

simplify150.0ms (4.3%)

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

prune588.0ms (16.9%)

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

Compiler

Compiled 21152 to 17018 computations (19.5% saved)

localize18.0ms (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)

series5.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

5.0ms

(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)

simplify72.0ms (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

prune493.0ms (14.2%)

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

Compiler

Compiled 14932 to 12041 computations (19.4% saved)

regimes385.0ms (11.1%)

Accuracy

Total 0.0b remaining (44.3%)

Threshold costs 0.0b (44.3%)

Counts

108 → 1

Compiler

Compiled 6478 to 5140 computations (20.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	22	23
2	26	23
3	28	23
4	29	23
5	28	23

end86.0ms (2.5%)

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

Details

analyze9.0ms (0.2%)

sample970.0ms (28%)

simplify106.0ms (3.1%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series10.0ms (0.3%)

rewrite17.0ms (0.5%)

simplify103.0ms (3%)

prune172.0ms (5%)

localize12.0ms (0.3%)

series9.0ms (0.2%)

rewrite7.0ms (0.2%)

simplify80.0ms (2.3%)

prune104.0ms (3%)

localize15.0ms (0.4%)

series25.0ms (0.7%)

rewrite18.0ms (0.5%)

simplify150.0ms (4.3%)

prune588.0ms (16.9%)

localize18.0ms (0.5%)

series5.0ms (0.2%)

rewrite2.0ms (0.1%)

simplify72.0ms (2.1%)

prune493.0ms (14.2%)

regimes385.0ms (11.1%)

simplify3.0ms (0.1%)

end86.0ms (2.5%)

Profiling