Details

analyze13.0ms (0.5%)

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)

sample1.2s (46.5%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify109.0ms (4.4%)

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 (0.4%)

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)
✓	16.7b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series16.0ms (0.7%)

Counts

4 → 48

Calls

4 calls:

10.0ms	(fma.f64 x 27061/100000 230753/100000)
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)
1.0ms	(fma.f64 x 4481/100000 99229/100000)

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

simplify95.0ms (3.8%)

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

prune119.0ms (4.8%)

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
	0.0b	(-.f64 x (/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (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))))
▶	0.0b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 27061/100000 230753/100000))))
	24.0b	(-.f64 x (/.f64 (cbrt.f64 (pow.f64 (fma.f64 x 27061/100000 230753/100000) 3)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 2019 to 1521 computations (24.7% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 27061/100000 230753/100000)))
	0.2b	(fma.f64 x 4481/100000 99229/100000)
	0.3b	(fma.f64 x 27061/100000 230753/100000)
✓	16.7b	(/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 27061/100000 230753/100000))

series7.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

5.0ms

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

2.0ms

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

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms

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

2.0ms

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

simplify114.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

872×	`fma-def_binary64`
477×	`distribute-rgt-in_binary64`
468×	`distribute-lft-in_binary64`
262×	`cancel-sign-sub-inv_binary64`
223×	`fma-neg_binary64`

Counts

131 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	3573
1	347	3248
2	902	3211
3	2308	3197
4	4942	3197

prune217.0ms (8.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	198	2	200

Error

Counts

200 → 2

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 27061/100000 230753/100000))))
▶	20.0b	(-.f64 x (/.f64 1 (exp.f64 (-.f64 (log.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (log.f64 (fma.f64 x 27061/100000 230753/100000))))))

Status

Error

Program

✓

0.0b

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

▶

20.0b

(-.f64 x (/.f64 1 (exp.f64 (-.f64 (log.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (log.f64 (fma.f64 x 27061/100000 230753/100000))))))

Compiler

Compiled 5078 to 3994 computations (21.3% saved)

localize16.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 x 27061/100000 230753/100000)
✓	0.4b	(log.f64 (fma.f64 x 27061/100000 230753/100000))
✓	1.7b	(exp.f64 (-.f64 (log.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (log.f64 (fma.f64 x 27061/100000 230753/100000))))
✓	20.3b	(log.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series12.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

6.0ms

(exp.f64 (-.f64 (log.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (log.f64 (fma.f64 x 27061/100000 230753/100000))))

3.0ms

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

2.0ms

(log.f64 (fma.f64 x 27061/100000 230753/100000))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`exp-sum_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`pow1_binary64`
16×	`prod-diff_binary64`

Counts

3 → 72

Calls

3 calls:

5.0ms

(exp.f64 (-.f64 (log.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (log.f64 (fma.f64 x 27061/100000 230753/100000))))

1.0ms

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

1.0ms

(log.f64 (fma.f64 x 27061/100000 230753/100000))

simplify99.0ms (4%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
562×	`fma-def_binary64`
219×	`cancel-sign-sub-inv_binary64`
217×	`associate--l+_binary64`
213×	`associate-r_binary64`

Counts

108 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	2725
1	548	2149
2	1509	1748
3	4631	1741
4	5054	1741

prune189.0ms (7.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	170	2	172

Error

Counts

172 → 2

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 27061/100000 230753/100000))))
✓	20.0b	(-.f64 x (/.f64 1 (exp.f64 (-.f64 (log.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (log.f64 (fma.f64 x 27061/100000 230753/100000))))))

Status

Error

Program

✓

0.0b

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

✓

20.0b

(-.f64 x (/.f64 1 (exp.f64 (-.f64 (log.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (log.f64 (fma.f64 x 27061/100000 230753/100000))))))

Compiler

Compiled 4877 to 3947 computations (19.1% saved)

regimes207.0ms (8.3%)

Accuracy

Total 0.0b remaining (11.6%)

Threshold costs 0.0b (11.6%)

Counts

71 → 1

Compiler

Compiled 2252 to 1730 computations (23.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	17	22
2	23	22
3	25	22
4	26	22
5	24	22

end66.0ms (2.7%)

Compiler: Compiled 71 to 55 computations (22.5% saved)

Details

analyze13.0ms (0.5%)

sample1.2s (46.5%)

simplify109.0ms (4.4%)

prune3.0ms (0.1%)

localize9.0ms (0.4%)

series16.0ms (0.7%)

rewrite5.0ms (0.2%)

simplify95.0ms (3.8%)

prune119.0ms (4.8%)

localize10.0ms (0.4%)

series7.0ms (0.3%)

rewrite14.0ms (0.5%)

simplify114.0ms (4.6%)

prune217.0ms (8.7%)

localize16.0ms (0.7%)

series12.0ms (0.5%)

rewrite13.0ms (0.5%)

simplify99.0ms (4%)

prune189.0ms (7.5%)

regimes207.0ms (8.3%)

simplify3.0ms (0.1%)

end66.0ms (2.7%)

Profiling