Details

analyze5.0ms (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)

sample969.0ms (33%)

Results

860.0ms

8256×

body

128

valid

Compiler

Compiled 62 to 50 computations (19.4% saved)

simplify93.0ms (3.2%)

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

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(.f64 70711/100000 (-.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (.f64 x 4481/100000))))) x))
▶	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)))

Status

Error

Program

0.1b

(*.f64 70711/100000 (-.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (*.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000))))) x))

▶

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 107 to 83 computations (22.4% 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 1913510371/10000000000 16316775383/10000000000)
✓	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	15.3b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series18.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

11.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
3.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (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 1913510371/10000000000 16316775383/10000000000)

rewrite5.0ms (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 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
0.0ms	(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 1913510371/10000000000 16316775383/10000000000)

simplify89.0ms (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

prune151.0ms (5.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	4	102

Error

0.0b

Counts

102 → 4

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
	30.9b	(fma.f64 x -70711/100000 (fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -1427746267379707/1000000000000000) 16316775383/10000000000))
	0.9b	(fma.f64 x -70711/100000 (.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (cbrt.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) (cbrt.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
	0.1b	(fma.f64 x -70711/100000 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)))

Compiler

Compiled 2185 to 1673 computations (23.4% saved)

localize27.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	1.5b	(expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	15.3b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
✓	15.8b	(log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series11.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

4.0ms

(expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

3.0ms

(log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

3.0ms

(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

rewrite5.0ms (0.2%)

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 → 51

Calls

3 calls:

2.0ms

(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

0.0ms

(log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

0.0ms

(expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

simplify89.0ms (3%)

Algorithm

1×	egg-herbie

Rules

531×	`fma-neg_binary64`
380×	`distribute-rgt-in_binary64`
357×	`distribute-lft-in_binary64`
342×	`cancel-sign-sub-inv_binary64`
270×	`associate-/r*_binary64`

Counts

87 → 128

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	150	1669
1	350	1505
2	876	1480
3	2258	1472
4	4764	1471
5	4909	1471

prune170.0ms (5.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	144	4	148

Error

0.0b

Counts

148 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
	30.9b	(fma.f64 x -70711/100000 (fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -1427746267379707/1000000000000000) 16316775383/10000000000))
	0.9b	(fma.f64 x -70711/100000 (.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (cbrt.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) (cbrt.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
▶	0.1b	(fma.f64 x -70711/100000 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)))

Compiler

Compiled 3509 to 2754 computations (21.5% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	0.6b	(pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)
	15.3b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
✓	19.5b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms

(pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)

3.0ms

(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
32×	`cbrt-prod_binary64`
32×	`add-cube-cbrt_binary64`

Counts

2 → 92

Calls

2 calls:

5.0ms

(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3))

3.0ms

(pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)

simplify115.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

596×	`times-frac_binary64`
399×	`associate-/l*_binary64`
366×	`fma-def_binary64`
317×	`log-div_binary64`
284×	`unswap-sqr_binary64`

Counts

116 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	3313
1	470	2990
2	1369	2904
3	4493	2892
4	5170	2892

prune218.0ms (7.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	185	3	188

Error

0.0b

Counts

188 → 3

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x -70711/100000 (*.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2)) (cbrt.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	0.1b	(fma.f64 x -70711/100000 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)))
	30.9b	(fma.f64 x -70711/100000 (fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -1427746267379707/1000000000000000) 16316775383/10000000000))

Compiler

Compiled 4907 to 3915 computations (20.2% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	0.6b	(pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2)
	15.3b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
✓	15.8b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2))

series20.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

8.0ms

(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2))

6.0ms

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

6.0ms

(pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2)

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`cbrt-prod_binary64`
27×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`unpow-prod-down_binary64`

Counts

3 → 83

Calls

3 calls:

3.0ms

(pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2)

3.0ms

(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2))

2.0ms

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

simplify106.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-l_binary64`
439×	`fma-def_binary64`
331×	`cancel-sign-sub-inv_binary64`
187×	`times-frac_binary64`
182×	`associate-/r*_binary64`

Counts

119 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	3917
1	662	3737
2	1695	3457
3	4940	3457

prune382.0ms (13%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	259	3	262

Error

0.0b

Counts

262 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x -70711/100000 (*.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 2)) (cbrt.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	0.1b	(fma.f64 x -70711/100000 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)))
	30.9b	(fma.f64 x -70711/100000 (fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -1427746267379707/1000000000000000) 16316775383/10000000000))

Compiler

Compiled 10874 to 8726 computations (19.8% saved)

regimes300.0ms (10.2%)

Accuracy

Total 0.1b remaining (40.3%)

Threshold costs 0.1b (40.3%)

Counts

94 → 1

Compiler

Compiled 5426 to 4262 computations (21.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	17	24
2	16	24

end82.0ms (2.8%)

Compiler: Compiled 99 to 77 computations (22.2% saved)

Details

analyze5.0ms (0.2%)

sample969.0ms (33%)

simplify93.0ms (3.2%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

series18.0ms (0.6%)

rewrite5.0ms (0.2%)

simplify89.0ms (3%)

prune151.0ms (5.2%)

localize27.0ms (0.9%)

series11.0ms (0.4%)

rewrite5.0ms (0.2%)

simplify89.0ms (3%)

prune170.0ms (5.8%)

localize11.0ms (0.4%)

series7.0ms (0.2%)

rewrite15.0ms (0.5%)

simplify115.0ms (3.9%)

prune218.0ms (7.4%)

localize16.0ms (0.5%)

series20.0ms (0.7%)

rewrite16.0ms (0.5%)

simplify106.0ms (3.6%)

prune382.0ms (13%)

regimes300.0ms (10.2%)

simplify2.0ms (0.1%)

end82.0ms (2.8%)

Profiling