Details

analyze4.0ms (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)

sample936.0ms (27.1%)

Infinites

0% of outputs are infinite.

Results

785.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify113.0ms (3.3%)

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

prune3.0ms (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)

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)
✓	0.3b	(fma.f64 x 27061/100000 230753/100000)
✓	14.3b	(/.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	(/.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 4481/100000 99229/100000)
2.0ms	(fma.f64 x 27061/100000 230753/100000)

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)

simplify88.0ms (2.5%)

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

prune102.0ms (2.9%)

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

Counts

101 → 3

Alt Table

Status	Error	Program
	0.5b	(-.f64 x (.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 27061/100000 230753/100000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
	21.5b	(-.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x 27061/100000 230753/100000)) (fma.f64 x 27061/100000 230753/100000)) (.f64 (.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
▶	0.0b	(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 2089 to 1575 computations (24.6% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x 4481/100000 99229/100000)
	0.3b	(fma.f64 x 27061/100000 230753/100000)
✓	14.2b	(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
✓	14.3b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

series15.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

11.0ms

(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

4.0ms

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

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 38

Calls

2 calls:

13.0ms

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

2.0ms

(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

simplify97.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

549×	`cancel-sign-sub-inv_binary64`
499×	`fma-neg_binary64`
337×	`sub-neg_binary64`
274×	`fma-def_binary64`
230×	`neg-mul-1_binary64`

Counts

62 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	1293
1	365	1166
2	1055	1146
3	3203	1139
4	4804	1139
5	4938	1139

prune213.0ms (6.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	173	3	176

Error

Counts

176 → 3

Alt Table

Status	Error	Program
▶	0.5b	(-.f64 x (.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 27061/100000 230753/100000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
	21.5b	(-.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x 27061/100000 230753/100000)) (fma.f64 x 27061/100000 230753/100000)) (.f64 (.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	0.0b	(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 5242 to 4084 computations (22.1% saved)

localize12.0ms (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)))
✓	3.8b	(/.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
✓	10.4b	(.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 27061/100000 230753/100000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

series24.0ms (0.7%)

Counts

4 → 48

Calls

4 calls:

8.0ms	(/.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (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)))
6.0ms	(cbrt.f64 (fma.f64 x 27061/100000 230753/100000))
4.0ms	(.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 27061/100000 230753/100000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

rewrite51.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
41×	`cbrt-prod_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
38×	`times-frac_binary64`

Counts

4 → 143

Calls

4 calls:

13.0ms	(.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 27061/100000 230753/100000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
9.0ms	(*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)))
5.0ms	(/.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
1.0ms	(cbrt.f64 (fma.f64 x 27061/100000 230753/100000))

simplify239.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-def_binary64`
571×	`times-frac_binary64`
373×	`cancel-sign-sub-inv_binary64`
263×	`associate-l_binary64`
251×	`fma-neg_binary64`

Counts

191 → 278

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	318	5683
1	819	5208
2	2699	4844
3	4716	4751
4	4938	4751

prune407.0ms (11.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	351	1	352
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	353	2	355

Error

Counts

355 → 2

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
▶	15.5b	(-.f64 x (*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

Status

Error

Program

✓

0.0b

(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

▶

15.5b

(-.f64 x (*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

Compiler

Compiled 13850 to 11154 computations (19.5% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(cbrt.f64 (fma.f64 x 27061/100000 230753/100000))
✓	0.8b	(pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4)
✓	3.8b	(*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	4.0b	(/.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series31.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

17.0ms

(pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4)

9.0ms

(/.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

5.0ms

(*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

rewrite40.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-sqr-sqrt_binary64`
88×	`times-frac_binary64`
78×	`unpow-prod-down_binary64`
65×	`*-un-lft-identity_binary64`
65×	`add-cube-cbrt_binary64`

Counts

3 → 179

Calls

3 calls:

13.0ms

(*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

5.0ms

(/.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

2.0ms

(pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4)

simplify238.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

533×	`times-frac_binary64`
517×	`fma-def_binary64`
371×	`fma-neg_binary64`
302×	`cancel-sign-sub-inv_binary64`
146×	`neg-mul-1_binary64`

Counts

215 → 302

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	343	8059
1	806	7039
2	2357	6389
3	4316	6143
4	4987	6143
5	4903	6143

prune468.0ms (13.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	376	0	376
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	376	2	378

Error

Counts

378 → 2

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	15.5b	(-.f64 x (*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

Status

Error

Program

✓

0.0b

(-.f64 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

✓

15.5b

(-.f64 x (*.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 27061/100000 230753/100000))) 4) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

Compiler

Compiled 14383 to 11780 computations (18.1% saved)

regimes213.0ms (6.2%)

Accuracy

Total 0.1b remaining (44.4%)

Threshold costs 0.1b (44.4%)

Counts

101 → 1

Compiler

Compiled 3958 to 3042 computations (23.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	18	34
2	24	34
3	28	34
4	31	34
5	32	34
6	31	34

end75.0ms (2.2%)

Compiler: Compiled 100 to 77 computations (23% saved)

Details

analyze4.0ms (0.1%)

sample936.0ms (27.1%)

simplify113.0ms (3.3%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series10.0ms (0.3%)

rewrite6.0ms (0.2%)

simplify88.0ms (2.5%)

prune102.0ms (2.9%)

localize18.0ms (0.5%)

series15.0ms (0.4%)

rewrite19.0ms (0.6%)

simplify97.0ms (2.8%)

prune213.0ms (6.2%)

localize12.0ms (0.4%)

series24.0ms (0.7%)

rewrite51.0ms (1.5%)

simplify239.0ms (6.9%)

prune407.0ms (11.8%)

localize14.0ms (0.4%)

series31.0ms (0.9%)

rewrite40.0ms (1.2%)

simplify238.0ms (6.9%)

prune468.0ms (13.6%)

regimes213.0ms (6.2%)

simplify4.0ms (0.1%)

end75.0ms (2.2%)

Profiling