Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample982.0ms (37.7%)

Symmetry

(sort d2 d3)

Results

868.0ms	7864×	body	128	valid
31.0ms	170×	body	512	valid
29.0ms	137×	body	1024	valid
10.0ms	85×	body	256	valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`distribute-lft-out_binary64`
6×	`associate-+r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	10
2	44	10
3	64	10
4	66	10
5	67	10
6	67	10

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	1.3b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

Compiler

Compiled 69 to 45 computations (34.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 3 (+.f64 d2 d3))
✓	0.0b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

series13.0ms (0.5%)

Counts

2 → 37

Calls

2 calls:

10.0ms	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
3.0ms	(+.f64 3 (+.f64 d2 d3))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-log-exp_binary64`
6×	`distribute-lft-out_binary64`
5×	`associate-r_binary64`

Counts

2 → 46

Calls

2 calls:

7.0ms	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
4.0ms	(+.f64 3 (+.f64 d2 d3))

simplify102.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

937×	`distribute-rgt-in_binary64`
912×	`distribute-lft-in_binary64`
396×	`associate-l_binary64`
335×	`fma-neg_binary64`
295×	`associate-r_binary64`

Counts

83 → 82

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	78	824
1	201	765
2	772	765
3	3781	765
4	4357	765
5	4927	765
6	4994	765
7	4974	765

prune75.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	79	5	84

Error

Counts

84 → 5

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 d1 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (+.f64 d2 d3)))
	17.5b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	33.7b	(/.f64 (.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3))) (+.f64 (.f64 3 3) (-.f64 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)) (.f64 3 (+.f64 d2 d3)))))
	1.3b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
	1.1b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))

Compiler

Compiled 1185 to 659 computations (44.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 d1 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (+.f64 d2 d3)))
✓	0.3b	(fma.f64 (sqrt.f64 3) (sqrt.f64 3) (+.f64 d2 d3))

series42.0ms (1.6%)

Counts

2 → 60

Calls

2 calls:

33.0ms	(*.f64 d1 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (+.f64 d2 d3)))
9.0ms	(fma.f64 (sqrt.f64 3) (sqrt.f64 3) (+.f64 d2 d3))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

3.0ms	(*.f64 d1 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (+.f64 d2 d3)))
0.0ms	(fma.f64 (sqrt.f64 3) (sqrt.f64 3) (+.f64 d2 d3))

simplify66.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

611×	`distribute-rgt-in_binary64`
608×	`distribute-lft-in_binary64`
544×	`associate-+r+_binary64`
543×	`associate-+l+_binary64`
271×	`associate-l_binary64`

Counts

92 → 74

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	897
1	112	840
2	471	840
3	1879	840
4	4668	840
5	5195	840

prune64.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	74	5	79

Error

Counts

79 → 5

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 d1 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (+.f64 d2 d3)))
	17.5b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	33.7b	(/.f64 (.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3))) (+.f64 (.f64 3 3) (-.f64 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)) (.f64 3 (+.f64 d2 d3)))))
	1.3b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
▶	1.1b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))

Compiler

Compiled 1145 to 725 computations (36.7% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
✓	0.5b	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
✓	0.6b	(cbrt.f64 d1)

series238.0ms (9.1%)

Counts

4 → 96

Calls

4 calls:

140.0ms	(*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3)))
40.0ms	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
36.0ms	(cbrt.f64 d1)
22.0ms	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))

rewrite36.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
21×	`*-un-lft-identity_binary64`
20×	`add-exp-log_binary64`

Counts

4 → 115

Calls

4 calls:

12.0ms	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
7.0ms	(*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3)))
5.0ms	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
2.0ms	(cbrt.f64 d1)

simplify141.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

916×	`unswap-sqr_binary64`
548×	`fma-def_binary64`
328×	`exp-prod_binary64`
323×	`log-prod_binary64`
278×	`associate-l_binary64`

Counts

211 → 173

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	155	2396
1	362	2137
2	1676	2084
3	2996	2069
4	4590	2057
5	4913	2057
6	5026	2057

prune119.0ms (4.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	211	5	216

Error

Counts

216 → 5

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 d1 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (+.f64 d2 d3)))
	17.5b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
	33.7b	(/.f64 (.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3))) (+.f64 (.f64 3 3) (-.f64 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)) (.f64 3 (+.f64 d2 d3)))))
▶	1.3b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
✓	1.1b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))

Compiler

Compiled 4078 to 1569 computations (61.5% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 d1 3) (.f64 d1 d2))
✓	1.2b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

series15.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

10.0ms	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
5.0ms	(+.f64 (.f64 d1 3) (.f64 d1 d2))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
5×	`fma-def_binary64`
4×	`sum-log_binary64`
4×	`distribute-lft-out_binary64`
3×	`*-un-lft-identity_binary64`

Counts

2 → 35

Calls

2 calls:

7.0ms	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
3.0ms	(+.f64 (.f64 d1 3) (.f64 d1 d2))

simplify75.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

641×	`fma-def_binary64`
622×	`associate-l_binary64`
565×	`fma-neg_binary64`
499×	`associate-r_binary64`
492×	`distribute-rgt-in_binary64`

Counts

95 → 68

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	934
1	232	892
2	893	888
3	4255	888
4	4992	888
5	5184	888

prune53.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	69	4	73

Error

Counts

73 → 4

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 d1 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (+.f64 d2 d3)))
	33.7b	(/.f64 (.f64 d1 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3))) (+.f64 (.f64 3 3) (-.f64 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)) (.f64 3 (+.f64 d2 d3)))))
	1.3b	(+.f64 (fma.f64 d1 3 (.f64 d1 d2)) (.f64 d1 d3))
✓	1.3b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

Compiler

Compiled 1120 to 562 computations (49.8% saved)

regimes436.0ms (16.7%)

Accuracy

Total 0.0b remaining (82.3%)

Threshold costs 0.0b (82.3%)

Counts

107 → 1

Compiler

Compiled 6056 to 4228 computations (30.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10
2	11	10

end75.0ms (2.9%)

Remove: (sort d2 d3)
Compiler: Compiled 110 to 73 computations (33.6% saved)

Details

analyze2.0ms (0.1%)

sample982.0ms (37.7%)

simplify8.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series13.0ms (0.5%)

rewrite13.0ms (0.5%)

simplify102.0ms (3.9%)

prune75.0ms (2.9%)

localize6.0ms (0.2%)

series42.0ms (1.6%)

rewrite5.0ms (0.2%)

simplify66.0ms (2.5%)

prune64.0ms (2.4%)

localize11.0ms (0.4%)

series238.0ms (9.1%)

rewrite36.0ms (1.4%)

simplify141.0ms (5.4%)

prune119.0ms (4.6%)

localize9.0ms (0.3%)

series15.0ms (0.6%)

rewrite12.0ms (0.4%)

simplify75.0ms (2.9%)

prune53.0ms (2%)

regimes436.0ms (16.7%)

simplify2.0ms (0.1%)

end75.0ms (2.9%)

Profiling