Details

analyze1.3s (9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
28.1%	68.6%	3.3%	10
29.6%	65.5%	4.9%	11
32%	61.7%	6.3%	12
35.5%	56.9%	7.6%	13
48%	38.7%	13.4%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.6s (11%)

Symmetry

(sort d2 d4)

Results

1.0s	8256×	body	128	valid
313.0ms	2481×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify95.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1400×	`fma-neg_binary64`
654×	`fma-def_binary64`
233×	`sub-neg_binary64`
210×	`unsub-neg_binary64`
158×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	32	14
2	94	13
3	263	13
4	655	13
5	1556	13
6	1691	13
7	1500	13
8	1500	13
9	2739	13
10	2707	13
11	2707	13
12	2632	13

prune3.0ms (0%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 92 to 53 computations (42.4% saved)

localize7.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

series15.0ms (0.1%)

Counts

1 → 48

Calls

1 calls:

15.0ms

(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
6×	`associate-r_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`distribute-lft-out--_binary64`
3×	`distribute-lft-out_binary64`

Counts

1 → 27

Calls

1 calls:

8.0ms

(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

617×	`distribute-rgt-in_binary64`
603×	`distribute-lft-in_binary64`
446×	`fma-neg_binary64`
407×	`associate-l_binary64`
313×	`associate-r_binary64`

Counts

75 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	1262
1	195	1056
2	718	940
3	3249	940
4	4599	940
5	4980	940

prune33.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Error

Counts

57 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
▶	28.3b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
	41.7b	(/.f64 (.f64 d1 (fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (.f64 d4 d4))) (-.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
	37.9b	(.f64 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))

Compiler

Compiled 955 to 235 computations (75.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.2b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

series53.0ms (0.4%)

Counts

2 → 80

Calls

2 calls:

32.0ms	(*.f64 (sqrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
21.0ms	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
12×	`associate-l_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

2 → 60

Calls

2 calls:

12.0ms	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
9.0ms	(*.f64 (sqrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

simplify101.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

403×	`fma-def_binary64`
359×	`*-commutative_binary64`
346×	`exp-sum_binary64`
306×	`fma-neg_binary64`
302×	`div-sub_binary64`

Counts

140 → 114

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	114	2759
1	300	2332
2	1117	2067
3	2072	1977
4	3884	1965
5	5268	1965

prune41.0ms (0.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	114	4	118

Error

Counts

118 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	28.3b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
	41.7b	(/.f64 (.f64 d1 (fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (.f64 d4 d4))) (-.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
▶	37.9b	(.f64 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))

Compiler

Compiled 2187 to 430 computations (80.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	0.2b	(.f64 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))
✓	1.1b	(sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

series9.7s (68.5%)

Counts

2 → 68

Calls

2 calls:

9.5s	(.f64 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))
246.0ms	(sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`pow1_binary64`
30×	`sqrt-pow1_binary64`
21×	`pow-prod-down_binary64`
16×	`associate-*r/_binary64`
14×	`sqrt-div_binary64`

Counts

2 → 74

Calls

2 calls:

17.0ms	(.f64 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))
10.0ms	(sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))

simplify117.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

339×	`cancel-sign-sub-inv_binary64`
211×	`fma-def_binary64`
203×	`sub-neg_binary64`
183×	`distribute-neg-in_binary64`
182×	`associate-r_binary64`

Counts

142 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	274	4069
1	832	3718
2	3353	3615
3	4983	3615

prune152.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	320	4	324

Error

Counts

324 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	28.3b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
▶	41.7b	(/.f64 (.f64 d1 (fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (.f64 d4 d4))) (-.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	37.9b	(.f64 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))

Compiler

Compiled 11921 to 3571 computations (70% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	4.5b	(fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (*.f64 d4 d4))
✓	10.4b	(.f64 d1 (fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (.f64 d4 d4)))
✓	28.9b	(/.f64 (.f64 d1 (fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (.f64 d4 d4))) (-.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

series250.0ms (1.8%)

Counts

3 → 144

Calls

3 calls:

154.0ms

(/.f64 (*.f64 d1 (fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (*.f64 d4 d4))) (-.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

62.0ms

(*.f64 d1 (fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (*.f64 d4 d4)))

34.0ms

(fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (*.f64 d4 d4))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`distribute-lft-out--_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 65

Calls

3 calls:

8.0ms

(/.f64 (*.f64 d1 (fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (*.f64 d4 d4))) (-.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

3.0ms

(*.f64 d1 (fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (*.f64 d4 d4)))

0.0ms

(fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (*.f64 d4 d4))

simplify144.0ms (1%)

Algorithm

1×	egg-herbie

Rules

641×	`associate-/l*_binary64`
632×	`times-frac_binary64`
436×	`fma-def_binary64`
202×	`+-commutative_binary64`
165×	`associate-+r+_binary64`

Counts

209 → 203

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	594	11382
1	1988	10440
2	5309	10440

prune127.0ms (0.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	203	4	207

Error

Counts

207 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	28.3b	(.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) (+.f64 d4 (-.f64 (-.f64 d2 d3) d1))))
✓	41.7b	(/.f64 (.f64 d1 (fma.f64 (-.f64 d2 (+.f64 d3 d1)) (-.f64 d1 (-.f64 d2 d3)) (.f64 d4 d4))) (-.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
✓	37.9b	(.f64 (sqrt.f64 (.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))) (sqrt.f64 (*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))))

Compiler

Compiled 11943 to 3689 computations (69.1% saved)

regimes238.0ms (1.7%)

Accuracy

Total 0.0b remaining (42.9%)

Threshold costs 0.0b (42.9%)

Counts

54 → 1

Compiler

Compiled 4478 to 2764 computations (38.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	23	13
3	27	13
4	29	13
5	29	13

end57.0ms (0.4%)

Remove: (sort d2 d4)
Compiler: Compiled 135 to 74 computations (45.2% saved)

Details

analyze1.3s (9%)

sample1.6s (11%)

simplify95.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0%)

series15.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify76.0ms (0.5%)

prune33.0ms (0.2%)

localize8.0ms (0.1%)

series53.0ms (0.4%)

rewrite24.0ms (0.2%)

simplify101.0ms (0.7%)

prune41.0ms (0.3%)

localize9.0ms (0.1%)

series9.7s (68.5%)

rewrite34.0ms (0.2%)

simplify117.0ms (0.8%)

prune152.0ms (1.1%)

localize13.0ms (0.1%)

series250.0ms (1.8%)

rewrite16.0ms (0.1%)

simplify144.0ms (1%)

prune127.0ms (0.9%)

regimes238.0ms (1.7%)

simplify2.0ms (0%)

end57.0ms (0.4%)

Profiling