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)

sample718.0ms (18.6%)

Infinites

20.5% of outputs are infinite.

Symmetry

(sort d2 d3)

Results

595.0ms	7871×	body	128	valid
29.0ms	135×	body	1024	valid
27.0ms	158×	body	512	valid
11.0ms	92×	body	256	valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify9.0ms (0.2%)

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

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

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 41 to 27 computations (34.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series10.0ms (0.2%)

Counts

1 → 28

Calls

1 calls:

9.0ms

(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
5×	`associate-r_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`distribute-lft-out_binary64`
3×	`associate-l_binary64`

Counts

1 → 26

Calls

1 calls:

7.0ms

(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

simplify74.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

949×	`distribute-rgt-in_binary64`
943×	`distribute-lft-in_binary64`
503×	`fma-neg_binary64`
394×	`associate-l_binary64`
294×	`associate-r_binary64`

Counts

54 → 48

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	601
1	162	559
2	683	559
3	2795	559
4	3172	559
5	4459	559
6	4975	559

prune36.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Error

Counts

49 → 5

Alt Table

Status	Error	Program
	28.5b	(.f64 (sqrt.f64 (.f64 d1 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3)))))
	34.0b	(/.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)))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
▶	0.8b	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
	16.5b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 813 to 451 computations (44.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 d1 (.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3)))))
✓	0.3b	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	0.3b	(cbrt.f64 (+.f64 3 (+.f64 d2 d3)))
✓	0.4b	(*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))

series657.0ms (17%)

Counts

4 → 120

Calls

4 calls:

539.0ms	(.f64 d1 (.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3)))))
75.0ms	(*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
31.0ms	(cbrt.f64 (+.f64 3 (+.f64 d2 d3)))
12.0ms	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))

rewrite71.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-div_binary64`
70×	`*-un-lft-identity_binary64`
46×	`cbrt-prod_binary64`
44×	`associate-*r/_binary64`
40×	`flip-+_binary64`

Counts

4 → 162

Calls

4 calls:

20.0ms	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
14.0ms	(.f64 d1 (.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3)))))
12.0ms	(*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
3.0ms	(cbrt.f64 (+.f64 3 (+.f64 d2 d3)))

simplify225.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
319×	`*-commutative_binary64`
236×	`fma-neg_binary64`
226×	`associate--l+_binary64`
173×	`+-commutative_binary64`

Counts

282 → 355

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	755	11339
1	2310	10560
2	4992	10558
3	5180	10558

prune542.0ms (14%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	500	1	501
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	501	5	506

Error

Counts

506 → 5

Alt Table

Status	Error	Program
	28.5b	(.f64 (sqrt.f64 (.f64 d1 (+.f64 3 (+.f64 d2 d3)))) (sqrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3)))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	34.0b	(/.f64 (*.f64 d1 (+.f64 27 (pow.f64 (+.f64 d3 d2) 3))) (fma.f64 (+.f64 d3 d2) (+.f64 (+.f64 d3 d2) -3) 9))
✓	0.8b	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
▶	16.5b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 24277 to 16119 computations (33.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))
✓	5.7b	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))
✓	10.7b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

series106.0ms (2.7%)

Counts

3 → 96

Calls

3 calls:

67.0ms	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
33.0ms	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))
6.0ms	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`

Counts

3 → 108

Calls

3 calls:

10.0ms	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))
7.0ms	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))
5.0ms	(.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3))))

simplify109.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

245×	`fma-neg_binary64`
237×	`associate-/l*_binary64`
236×	`associate-r_binary64`
218×	`associate-l_binary64`
196×	`times-frac_binary64`

Counts

204 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	5107
1	958	4615
2	4155	4506
3	4970	4506

prune141.0ms (3.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	2	0	2
Picked	0	1	1
Done	0	2	2
Total	205	4	209

Error

Counts

209 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
▶	15.9b	(/.f64 d1 (/.f64 (-.f64 3 (+.f64 d2 d3)) (-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3)))))
✓	0.8b	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	16.5b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 6088 to 2876 computations (52.8% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 d2 d3) (+.f64 d2 d3))
✓	0.2b	(/.f64 d1 (/.f64 (-.f64 3 (+.f64 d2 d3)) (-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3)))))
✓	24.5b	(/.f64 (-.f64 3 (+.f64 d2 d3)) (-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3))))

series110.0ms (2.9%)

Counts

2 → 60

Calls

2 calls:

66.0ms	(/.f64 d1 (/.f64 (-.f64 3 (+.f64 d2 d3)) (-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3)))))
44.0ms	(/.f64 (-.f64 3 (+.f64 d2 d3)) (-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3))))

rewrite56.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
194×	`*-un-lft-identity_binary64`
162×	`add-sqr-sqrt_binary64`
89×	`add-cube-cbrt_binary64`
52×	`difference-of-squares_binary64`

Counts

2 → 193

Calls

2 calls:

16.0ms	(/.f64 d1 (/.f64 (-.f64 3 (+.f64 d2 d3)) (-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3)))))
9.0ms	(/.f64 (-.f64 3 (+.f64 d2 d3)) (-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3))))

simplify166.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

414×	`associate-/l*_binary64`
351×	`times-frac_binary64`
307×	`fma-def_binary64`
290×	`associate-/r/_binary64`
267×	`associate-/r*_binary64`

Counts

253 → 337

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	586	11265
1	1694	10861
2	5149	10861

prune323.0ms (8.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	397	0	397
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	397	4	401

Error

Counts

401 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
✓	15.9b	(/.f64 d1 (/.f64 (-.f64 3 (+.f64 d2 d3)) (-.f64 9 (*.f64 (+.f64 d2 d3) (+.f64 d2 d3)))))
✓	0.8b	(.f64 (.f64 d1 (*.f64 (cbrt.f64 (+.f64 3 (+.f64 d2 d3))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))) (cbrt.f64 (+.f64 3 (+.f64 d2 d3))))
✓	16.5b	(/.f64 (.f64 d1 (-.f64 9 (.f64 (+.f64 d2 d3) (+.f64 d2 d3)))) (-.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 14885 to 7067 computations (52.5% saved)

regimes366.0ms (9.5%)

Accuracy

Total 0.0b remaining (83.7%)

Threshold costs 0.0b (83.7%)

Counts

87 → 1

Compiler

Compiled 6132 to 4284 computations (30.1% saved)

simplify3.0ms (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

end65.0ms (1.7%)

Remove: (sort d2 d3)
Compiler: Compiled 115 to 73 computations (36.5% saved)

Details

analyze2.0ms (0.1%)

sample718.0ms (18.6%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series10.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify74.0ms (1.9%)

prune36.0ms (0.9%)

localize8.0ms (0.2%)

series657.0ms (17%)

rewrite71.0ms (1.8%)

simplify225.0ms (5.8%)

prune542.0ms (14%)

localize8.0ms (0.2%)

series106.0ms (2.7%)

rewrite31.0ms (0.8%)

simplify109.0ms (2.8%)

prune141.0ms (3.7%)

localize12.0ms (0.3%)

series110.0ms (2.9%)

rewrite56.0ms (1.4%)

simplify166.0ms (4.3%)

prune323.0ms (8.4%)

regimes366.0ms (9.5%)

simplify3.0ms (0.1%)

end65.0ms (1.7%)

Profiling