Details

analyze7.0ms (0.2%)

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 21 to 17 computations (19% saved)

sample1.1s (32.2%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 62 to 50 computations (19.4% saved)

simplify91.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
684×	`fma-neg_binary64`
640×	`associate-/l*_binary64`
583×	`associate-/r*_binary64`
496×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	34	22
2	59	22
3	94	22
4	131	22
5	171	20
6	250	20
7	423	20
8	810	20
9	1376	20
10	2197	20
11	2355	20
12	3878	20
13	4822	20
14	4656	20

prune4.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 67 to 51 computations (23.9% saved)

localize9.0ms (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 1913510371/10000000000 16316775383/10000000000)
✓	13.3b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series10.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
3.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
2.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
2.0ms	(fma.f64 x 4481/100000 99229/100000)

rewrite5.0ms (0.1%)

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 1913510371/10000000000 16316775383/10000000000) (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 (fma.f64 x 4481/100000 99229/100000) 1)
0.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)

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

prune87.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	3	101

Error

0.1b

Counts

101 → 3

Alt Table

Status	Error	Program
▶	0.7b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))
	30.1b	(fma.f64 x -70711/100000 (fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -1427746267379707/1000000000000000) 16316775383/10000000000))
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 2063 to 1577 computations (23.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 99229/100000 1)
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))
	0.2b	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
✓	0.2b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))

series6.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms

(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))

2.0ms

(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))

2.0ms

(fma.f64 x 99229/100000 1)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

2.0ms

(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))

0.0ms

(fma.f64 x 99229/100000 1)

0.0ms

(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))

simplify81.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-neg_binary64`
635×	`fma-def_binary64`
445×	`associate-l_binary64`
362×	`associate-r_binary64`
297×	`cancel-sign-sub-inv_binary64`

Counts

85 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	1269
1	250	1162
2	615	1146
3	1529	1126
4	4571	1126
5	4908	1126

prune84.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	102	5	107

Error

0.0b

Counts

107 → 5

Alt Table

Status	Error	Program
✓	0.7b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))
	30.1b	(fma.f64 x -70711/100000 (fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -1427746267379707/1000000000000000) 16316775383/10000000000))
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
	14.1b	(*.f64 (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))) (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))
▶	2.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))

Compiler

Compiled 1877 to 1472 computations (21.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
	0.2b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))
✓	0.3b	(cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))
✓	0.7b	(*.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))

series14.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

7.0ms

(cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))

7.0ms

(*.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`cbrt-prod_binary64`
19×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

4.0ms

(*.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))

1.0ms

(cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))

simplify102.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

373×	`associate-l_binary64`
346×	`associate-r_binary64`
319×	`fma-def_binary64`
303×	`unswap-sqr_binary64`
300×	`sub-neg_binary64`

Counts

79 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	3168
1	402	2924
2	1154	2352
3	3894	2160
4	4944	2160

prune495.0ms (14.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	384	3	387
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	385	7	392

Error

0.0b

Counts

392 → 7

Alt Table

Status	Error	Program
	14.1b	(*.f64 (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))) (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))
	14.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))) (cbrt.f64 (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))))
▶	1.6b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))) 5) (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))
✓	0.7b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))
	46.3b	(.f64 (cbrt.f64 (.f64 (*.f64 x x) 5000045521/10000000000)) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))
	30.1b	(fma.f64 x -70711/100000 (fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -1427746267379707/1000000000000000) 16316775383/10000000000))
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 18958 to 15130 computations (20.2% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))
✓	0.3b	(cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))
	0.3b	(cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))
✓	0.5b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))) 5)

series34.0ms (1%)

Counts

2 → 24

Calls

2 calls:

24.0ms

(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))) 5)

9.0ms

(cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod_binary64`
9×	`unpow-prod-down_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

2 → 42

Calls

2 calls:

2.0ms

(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))) 5)

1.0ms

(cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))

simplify95.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

422×	`unswap-sqr_binary64`
337×	`associate-r_binary64`
312×	`associate-l_binary64`
308×	`fma-def_binary64`
287×	`sub-neg_binary64`

Counts

66 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	167	2444
1	409	2300
2	1154	2108
3	3959	1916
4	5144	1916

prune645.0ms (18.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	397	0	397
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	397	7	404

Error

0.0b

Counts

404 → 7

Alt Table

Status	Error	Program
	14.1b	(*.f64 (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))) (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))
	14.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))) (cbrt.f64 (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))))
✓	1.6b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1))))) 5) (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))
✓	0.7b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))
	46.3b	(.f64 (cbrt.f64 (.f64 (*.f64 x x) 5000045521/10000000000)) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x 99229/100000 1)))))
	30.1b	(fma.f64 x -70711/100000 (fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -1427746267379707/1000000000000000) 16316775383/10000000000))
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 21559 to 17588 computations (18.4% saved)

regimes294.0ms (8.5%)

Accuracy

Total 0.0b remaining (35%)

Threshold costs 0.0b (35%)

Counts

68 → 1

Compiler

Compiled 5984 to 4769 computations (20.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	15	20
2	14	20

end155.0ms (4.5%)

Compiler: Compiled 225 to 175 computations (22.2% saved)

Details

analyze7.0ms (0.2%)

sample1.1s (32.2%)

simplify91.0ms (2.6%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

series10.0ms (0.3%)

rewrite5.0ms (0.1%)

simplify83.0ms (2.4%)

prune87.0ms (2.5%)

localize8.0ms (0.2%)

series6.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify81.0ms (2.3%)

prune84.0ms (2.4%)

localize12.0ms (0.3%)

series14.0ms (0.4%)

rewrite9.0ms (0.2%)

simplify102.0ms (2.9%)

prune495.0ms (14.3%)

localize13.0ms (0.4%)

series34.0ms (1%)

rewrite5.0ms (0.2%)

simplify95.0ms (2.7%)

prune645.0ms (18.6%)

regimes294.0ms (8.5%)

simplify2.0ms (0.1%)

end155.0ms (4.5%)

Profiling