Details

analyze433.0ms (13.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
37.4%	62.4%	0.1%	8
40.6%	57.7%	1.7%	9
45.2%	51.1%	3.7%	10
57.7%	33.5%	8.7%	11
59.7%	29.4%	10.9%	12
62%	25%	13%	13
68.3%	17.4%	14.4%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.4s (42.9%)

Symmetry

(sort d2 d3)

Results

981.0ms	7717×	body	128	valid
205.0ms	231×	body	512	valid
81.0ms	697×	body	128	invalid
58.0ms	174×	body	1024	valid
24.0ms	134×	body	256	valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify10.0ms (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

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 69 to 45 computations (34.8% 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)))

series9.0ms (0.3%)

Counts

1 → 28

Calls

1 calls:

8.0ms

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

rewrite7.0ms (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:

6.0ms

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

simplify69.0ms (2.1%)

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

prune39.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	44	6	50

Error

Counts

50 → 6

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
▶	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
	32.7b	(/.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)))))
	53.8b	(cbrt.f64 (.f64 (.f64 (.f64 d1 d1) d1) (.f64 (*.f64 (+.f64 3 (+.f64 d2 d3)) (+.f64 3 (+.f64 d2 d3))) (+.f64 3 (+.f64 d2 d3)))))
	1.0b	(.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))))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 849 to 473 computations (44.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series16.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

11.0ms	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
4.0ms	(+.f64 (.f64 d1 3) (.f64 d1 d2))

rewrite9.0ms (0.3%)

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:

5.0ms	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
3.0ms	(+.f64 (.f64 d1 3) (.f64 d1 d2))

simplify75.0ms (2.3%)

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

prune44.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	69	5	74

Error

Counts

74 → 5

Alt Table

Status	Error	Program
	32.7b	(/.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)))))
▶	0.1b	(+.f64 (fma.f64 d1 3 (.f64 d1 d2)) (.f64 d1 d3))
	1.4b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 1194 to 605 computations (49.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 d1 3 (.f64 d1 d2)) (.f64 d1 d3))
✓	0.1b	(fma.f64 d1 3 (*.f64 d1 d2))

series17.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

9.0ms	(+.f64 (fma.f64 d1 3 (.f64 d1 d2)) (.f64 d1 d3))
8.0ms	(fma.f64 d1 3 (*.f64 d1 d2))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(+.f64 (fma.f64 d1 3 (.f64 d1 d2)) (.f64 d1 d3))
0.0ms	(fma.f64 d1 3 (*.f64 d1 d2))

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

488×	`distribute-rgt-out_binary64`
384×	`distribute-lft-out_binary64`
339×	`distribute-rgt-in_binary64`
326×	`distribute-lft-in_binary64`
279×	`sub-neg_binary64`

Counts

87 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	870
1	143	811
2	489	808
3	2242	807
4	4661	807
5	5007	807

prune37.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	57	5	62

Error

Counts

62 → 5

Alt Table

Status	Error	Program
	32.7b	(/.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)))))
✓	0.1b	(+.f64 (fma.f64 d1 3 (.f64 d1 d2)) (.f64 d1 d3))
▶	1.4b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 969 to 458 computations (52.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3)))
✓	0.4b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
✓	0.6b	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
✓	0.6b	(cbrt.f64 d1)

series220.0ms (6.8%)

Counts

4 → 96

Calls

4 calls:

122.0ms	(*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3)))
41.0ms	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
35.0ms	(cbrt.f64 d1)
21.0ms	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))

rewrite28.0ms (0.9%)

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:

10.0ms	(.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)))
4.0ms	(*.f64 (cbrt.f64 d1) (cbrt.f64 d1))
1.0ms	(cbrt.f64 d1)

simplify134.0ms (4.1%)

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	2185
2	1676	2140
3	2996	2125
4	4590	2113
5	4913	2113
6	5026	2113

prune95.0ms (2.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

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

Error

Counts

216 → 5

Alt Table

Status	Error	Program
	32.7b	(/.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)))))
✓	0.1b	(+.f64 (fma.f64 d1 3 (.f64 d1 d2)) (.f64 d1 d3))
✓	1.4b	(.f64 (.f64 (cbrt.f64 d1) (cbrt.f64 d1)) (*.f64 (cbrt.f64 d1) (+.f64 3 (+.f64 d2 d3))))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Compiler

Compiled 4021 to 1525 computations (62.1% saved)

regimes282.0ms (8.7%)

Accuracy

Total 0.0b remaining (79.9%)

Threshold costs 0.0b (79.9%)

Counts

69 → 1

Compiler

Compiled 5342 to 3311 computations (38% 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	9	14
1	12	14
2	12	14

end221.0ms (6.8%)

Compiler: Compiled 136 to 84 computations (38.2% saved)

Details

analyze433.0ms (13.4%)

sample1.4s (42.9%)

simplify10.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series9.0ms (0.3%)

rewrite7.0ms (0.2%)

simplify69.0ms (2.1%)

prune39.0ms (1.2%)

localize7.0ms (0.2%)

series16.0ms (0.5%)

rewrite9.0ms (0.3%)

simplify75.0ms (2.3%)

prune44.0ms (1.4%)

localize6.0ms (0.2%)

series17.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify68.0ms (2.1%)

prune37.0ms (1.1%)

localize13.0ms (0.4%)

series220.0ms (6.8%)

rewrite28.0ms (0.9%)

simplify134.0ms (4.1%)

prune95.0ms (2.9%)

regimes282.0ms (8.7%)

simplify2.0ms (0.1%)

end221.0ms (6.8%)

Profiling