Details

analyze1.8s (29.5%)

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)

sample255.0ms (4.2%)

Algorithm

1×

intervals

Symmetry

(sort y z t)

(sort a b)

Results

15.0ms	256×	body	128	valid
5.0ms	86×	body	128	invalid

Compiler

Compiled 53 to 41 computations (22.6% saved)

simplify71.0ms (1.2%)

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	4.1b	(+.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)

localize10.0ms (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 z t) -9)
✓	0.5b	(.f64 (.f64 a 27) b)
✓	2.0b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series51.0ms (0.8%)

Counts

4 → 156

Calls

4 calls:

31.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
8.0ms	(.f64 (.f64 z t) -9)
7.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))
5.0ms	(.f64 (.f64 a 27) b)

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))

simplify101.0ms (1.7%)

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

prune97.0ms (1.6%)

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
	2.8b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (.f64 (.f64 z t) -9)) (cbrt.f64 (.f64 (.f64 z t) -9))) (cbrt.f64 (.f64 (.f64 z t) -9))) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
▶	2.2b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	2.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	4.1b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.9b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

Compiler

Compiled 2346 to 1350 computations (42.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
✓	0.1b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
✓	0.2b	(.f64 (.f64 y (*.f64 t z)) -9)
✓	6.4b	(.f64 y (.f64 t z))

series62.0ms (1%)

Counts

4 → 156

Calls

4 calls:

29.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
13.0ms	(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))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

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

simplify118.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

507×	`distribute-rgt-in_binary64`
501×	`distribute-lft-in_binary64`
416×	`fma-def_binary64`
360×	`*-commutative_binary64`
190×	`associate-+l+_binary64`

Counts

219 → 94

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	3305
1	213	3114
2	739	3114
3	1576	3114
4	4976	3114
5	4981	3114

prune68.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	95	4	99

Error

0.0b

Counts

99 → 4

Alt Table

Status	Error	Program
▶	2.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	5.7b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
	4.1b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.9b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

Compiler

Compiled 2109 to 1002 computations (52.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x 2 (.f64 (.f64 a 27) b))
✓	0.4b	(.f64 z (.f64 t -9))
	0.5b	(.f64 (.f64 a 27) b)
✓	2.0b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series37.0ms (0.6%)

Counts

2 → 96

Calls

2 calls:

33.0ms	(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)))

simplify96.0ms (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

prune77.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	107	4	111

Error

0.0b

Counts

111 → 4

Alt Table

Status	Error	Program
✓	2.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	5.7b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
	4.1b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
▶	2.9b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

Compiler

Compiled 2253 to 1353 computations (39.9% saved)

localize15.0ms (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 (.f64 z t) -9)
✓	0.9b	(.f64 a (.f64 27 b))
✓	2.0b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

series41.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

28.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
7.0ms	(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)))

simplify97.0ms (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

prune73.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	107	4	111

Error

0.0b

Counts

111 → 4

Alt Table

Status	Error	Program
✓	2.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	5.7b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
	4.1b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
✓	2.9b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

Compiler

Compiled 2188 to 1239 computations (43.4% saved)

regimes662.0ms (10.8%)

Accuracy

Total 0.5b remaining (94.2%)

Threshold costs 0.5b (94.2%)

Counts

30 → 2

Compiler

Compiled 10456 to 7523 computations (28.1% saved)

bsearch5.0ms (0.1%)

Steps

Iters	Range		Point
1	4.978535417940739e-81	4.310676231184701e-80	1.4583759884213824e-80

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	52
1	45	52
2	61	52
3	77	52
4	87	52
5	92	52
6	93	52
7	92	52

end65.0ms (1.1%)

Compiler: Compiled 210 to 145 computations (31% saved)

sample2.2s (36.6%)

Algorithm

1×

intervals

Results

547.0ms	8000×	body	128	valid
181.0ms	3047×	body	128	invalid

Compiler

Compiled 158 to 115 computations (27.2% saved)

Details

analyze1.8s (29.5%)

sample255.0ms (4.2%)

simplify71.0ms (1.2%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series51.0ms (0.8%)

rewrite10.0ms (0.2%)

simplify101.0ms (1.7%)

prune97.0ms (1.6%)

localize12.0ms (0.2%)

series62.0ms (1%)

rewrite12.0ms (0.2%)

simplify118.0ms (1.9%)

prune68.0ms (1.1%)

localize15.0ms (0.2%)

series37.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify96.0ms (1.6%)

prune77.0ms (1.3%)

localize15.0ms (0.2%)

series41.0ms (0.7%)

rewrite6.0ms (0.1%)

simplify97.0ms (1.6%)

prune73.0ms (1.2%)

regimes662.0ms (10.8%)

bsearch5.0ms (0.1%)

simplify4.0ms (0.1%)

end65.0ms (1.1%)

sample2.2s (36.6%)

Profiling