Details

analyze2.0s (31.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample2.0s (31.9%)

Symmetry

(sort y z t)

(sort a b)

Results

1.3s	8256×	body	128	valid
485.0ms	3196×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
641×	`fma-def_binary64`
213×	`cancel-sign-sub-inv_binary64`
172×	`distribute-rgt-neg-in_binary64`
157×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	39	23
2	115	21
3	308	21
4	552	21
5	902	21
6	1201	21
7	1433	21
8	1672	21
9	1787	21
10	1791	21
11	1791	21
12	1791	21
13	1674	21

prune4.0ms (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
▶	1.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	3.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 2 (.f64 (.f64 a 27) b))
✓	0.2b	(.f64 (.f64 a 27) b)
✓	0.2b	(.f64 (.f64 z t) -9)
✓	1.5b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series46.0ms (0.7%)

Counts

4 → 156

Calls

4 calls:

30.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
7.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))
4.0ms	(.f64 (.f64 a 27) b)
4.0ms	(.f64 (.f64 z t) -9)

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
6×	`associate-r_binary64`
6×	`cbrt-unprod_binary64`

Counts

4 → 60

Calls

4 calls:

4.0ms	(.f64 (.f64 z t) -9)
4.0ms	(.f64 (.f64 a 27) b)
0.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
0.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))

simplify113.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

868×	`unswap-sqr_binary64`
419×	`*-commutative_binary64`
321×	`distribute-lft-in_binary64`
321×	`distribute-rgt-in_binary64`
310×	`fma-def_binary64`

Counts

216 → 107

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	122	2976
1	250	2724
2	873	2724
3	1485	2724
4	2922	2724
5	5289	2724

prune89.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	104	5	109

Error

0.0b

Counts

109 → 5

Alt Table

Status	Error	Program
	1.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	3.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
▶	1.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	1.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	32.9b	(fma.f64 y (.f64 (sqrt.f64 (.f64 (.f64 z t) -9)) (sqrt.f64 (.f64 (.f64 z t) -9))) (fma.f64 x 2 (.f64 (*.f64 a 27) b)))

Compiler

Compiled 2332 to 1342 computations (42.5% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
✓	0.3b	(.f64 (.f64 y (*.f64 t z)) -9)
✓	4.3b	(.f64 y (.f64 t z))

series52.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

32.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
12.0ms	(.f64 (.f64 y (*.f64 t z)) -9)
8.0ms	(.f64 y (.f64 t z))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

3 → 53

Calls

3 calls:

5.0ms	(.f64 (.f64 y (*.f64 t z)) -9)
4.0ms	(.f64 y (.f64 t z))
0.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))

simplify100.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

561×	`unsub-neg_binary64`
461×	`distribute-rgt-in_binary64`
455×	`distribute-lft-in_binary64`
409×	`*-commutative_binary64`
312×	`fma-def_binary64`

Counts

161 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	94	2515
1	203	2353
2	714	2353
3	1513	2353
4	3738	2353
5	5113	2353

prune60.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	77	5	82

Error

0.0b

Counts

82 → 5

Alt Table

Status	Error	Program
▶	1.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	3.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	6.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
✓	1.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	1.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

Compiler

Compiled 1752 to 840 computations (52.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x 2 (.f64 (.f64 a 27) b))
	0.2b	(.f64 (.f64 a 27) b)
✓	0.2b	(.f64 z (.f64 t -9))
✓	1.5b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series35.0ms (0.6%)

Counts

2 → 96

Calls

2 calls:

30.0ms	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
4.0ms	(.f64 z (.f64 t -9))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(.f64 z (.f64 t -9))
0.0ms	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

simplify104.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

518×	`distribute-lft-in_binary64`
518×	`distribute-rgt-in_binary64`
508×	`associate-l_binary64`
374×	`fma-neg_binary64`
362×	`associate-r_binary64`

Counts

126 → 60

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	73	2086
1	153	1893
2	434	1893
3	1359	1893
4	3924	1893
5	4790	1893
6	5038	1893

prune86.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	107	5	112

Error

0.0b

Counts

112 → 5

Alt Table

Status	Error	Program
✓	1.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	3.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	6.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
✓	1.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
▶	1.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

Compiler

Compiled 2274 to 1368 computations (39.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 2 (.f64 a (.f64 27 b)))
✓	0.2b	(.f64 a (.f64 27 b))
	0.2b	(.f64 (.f64 z t) -9)
✓	1.5b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

series44.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

29.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
10.0ms	(fma.f64 x 2 (.f64 a (.f64 27 b)))
4.0ms	(.f64 a (.f64 27 b))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 40

Calls

3 calls:

4.0ms	(.f64 a (.f64 27 b))
0.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
0.0ms	(fma.f64 x 2 (.f64 a (.f64 27 b)))

simplify104.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

576×	`distribute-lft-in_binary64`
576×	`distribute-rgt-in_binary64`
548×	`associate-l_binary64`
426×	`fma-def_binary64`
385×	`associate-r_binary64`

Counts

172 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	82	2594
1	159	2378
2	475	2378
3	1528	2378
4	4509	2378
5	5090	2378

prune78.0ms (1.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	107	5	112

Error

0.0b

Counts

112 → 5

Alt Table

Status	Error	Program
✓	1.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	3.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	6.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
✓	1.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
✓	1.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

Compiler

Compiled 2209 to 1254 computations (43.2% saved)

regimes636.0ms (10%)

Accuracy

Total 2.2b remaining (98.9%)

Threshold costs 0b (0%)

Counts

29 → 3

Compiler

Compiled 10563 to 7428 computations (29.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary64`
13×	`+-commutative_binary64`
12×	`distribute-rgt-neg-in_binary64`
11×	`sub-neg_binary64`
10×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	101
1	59	101
2	80	101
3	104	101
4	123	101
5	131	101
6	133	101
7	132	101

end608.0ms (9.6%)

Remove: (sort a b)
Compiler: Compiled 707 to 461 computations (34.8% saved)

Details

analyze2.0s (31.6%)

sample2.0s (31.9%)

simplify71.0ms (1.1%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series46.0ms (0.7%)

rewrite10.0ms (0.2%)

simplify113.0ms (1.8%)

prune89.0ms (1.4%)

localize11.0ms (0.2%)

series52.0ms (0.8%)

rewrite11.0ms (0.2%)

simplify100.0ms (1.6%)

prune60.0ms (0.9%)

localize11.0ms (0.2%)

series35.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify104.0ms (1.6%)

prune86.0ms (1.4%)

localize11.0ms (0.2%)

series44.0ms (0.7%)

rewrite6.0ms (0.1%)

simplify104.0ms (1.6%)

prune78.0ms (1.2%)

regimes636.0ms (10%)

bsearch1.0ms (0%)

simplify7.0ms (0.1%)

end608.0ms (9.6%)

Profiling