Details

analyze2.7s (35.1%)

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)

sample1.9s (24.8%)

Symmetry

(sort y z t)

(sort a b)

Results

1.2s	8256×	body	128	valid
426.0ms	3006×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify70.0ms (0.9%)

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%)

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
▶	2.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.9b	(+.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 (0.1%)

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)
✓	2.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series43.0ms (0.6%)

Counts

4 → 156

Calls

4 calls:

27.0ms	(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 z t) -9)
4.0ms	(.f64 (.f64 a 27) b)

rewrite10.0ms (0.1%)

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 a 27) b)
4.0ms	(.f64 (.f64 z t) -9)
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))

simplify92.0ms (1.2%)

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

prune95.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Error

0.0b

Counts

109 → 6

Alt Table

Status	Error	Program
	2.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	2.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.6b	(+.f64 (.f64 y (.f64 (.f64 z t) -9)) (fma.f64 x 2 (.f64 (*.f64 a 27) b)))
	2.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	12.5b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (.f64 (.f64 z t) -9) (.f64 (.f64 z t) -9)) (.f64 (.f64 z t) -9))) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
▶	2.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

Compiler

Compiled 2386 to 1378 computations (42.2% saved)

localize13.0ms (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)
✓	0.2b	(.f64 a (.f64 27 b))
✓	2.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

series44.0ms (0.6%)

Counts

3 → 132

Calls

3 calls:

32.0ms	(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:

3.0ms	(.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)))

simplify93.0ms (1.2%)

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

prune95.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	106	7	113

Error

0.0b

Counts

113 → 7

Alt Table

Status	Error	Program
	2.6b	(+.f64 (.f64 y (.f64 (.f64 z t) -9)) (fma.f64 x 2 (.f64 (*.f64 a 27) b)))
	2.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (cbrt.f64 a) (.f64 27 b)))))
▶	2.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	2.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	12.2b	(fma.f64 y (cbrt.f64 (pow.f64 (.f64 (.f64 t z) -9) 3)) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	2.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
✓	2.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

Compiler

Compiled 2401 to 1390 computations (42.1% saved)

localize10.0ms (0.1%)

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)
✓	6.1b	(.f64 y (.f64 t z))

series60.0ms (0.8%)

Counts

4 → 156

Calls

4 calls:

26.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
15.0ms	(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))

rewrite11.0ms (0.1%)

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)
3.0ms	(.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)))

simplify102.0ms (1.3%)

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

prune94.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	94	7	101

Error

0.0b

Counts

101 → 7

Alt Table

Status	Error	Program
	2.6b	(+.f64 (.f64 y (.f64 (.f64 z t) -9)) (fma.f64 x 2 (.f64 (*.f64 a 27) b)))
	2.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (cbrt.f64 a) (.f64 27 b)))))
✓	2.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	3.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
✓	2.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
▶	2.6b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t z))) -9)))
	12.2b	(fma.f64 y (cbrt.f64 (pow.f64 (.f64 (.f64 t z) -9) 3)) (fma.f64 x 2 (.f64 a (.f64 27 b))))

Compiler

Compiled 2225 to 1078 computations (51.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)
✓	2.2b	(.f64 (cbrt.f64 y) (.f64 t z))
✓	4.1b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t z)))

series508.0ms (6.7%)

Counts

4 → 96

Calls

4 calls:

413.0ms	(.f64 (cbrt.f64 y) (.f64 t z))
40.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
30.0ms	(cbrt.f64 y)
26.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t z)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 108

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t z)))
4.0ms	(.f64 (cbrt.f64 y) (.f64 t z))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
621×	`distribute-rgt-in_binary64`
467×	`*-commutative_binary64`
327×	`sqr-pow_binary64`
233×	`associate-l_binary64`

Counts

204 → 146

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	118	1885
1	242	1657
2	917	1619
3	1626	1605
4	2956	1511
5	4935	1511

prune162.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	182	7	189

Error

0.0b

Counts

189 → 7

Alt Table

Status	Error	Program
	2.6b	(+.f64 (.f64 y (.f64 (.f64 z t) -9)) (fma.f64 x 2 (.f64 (*.f64 a 27) b)))
	2.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (cbrt.f64 a) (.f64 27 b)))))
✓	2.4b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	3.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
✓	2.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
✓	2.6b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t z))) -9)))
	12.2b	(fma.f64 y (cbrt.f64 (pow.f64 (.f64 (.f64 t z) -9) 3)) (fma.f64 x 2 (.f64 a (.f64 27 b))))

Compiler

Compiled 4980 to 1854 computations (62.8% saved)

regimes789.0ms (10.4%)

Accuracy

Total 1.0b remaining (96.1%)

Threshold costs 0b (0%)

Counts

38 → 2

Compiler

Compiled 13666 to 9831 computations (28.1% saved)

bsearch1.0ms (0%)

Compiler: Compiled 9 to 8 computations (11.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	51
1	35	51
2	35	51

end610.0ms (8%)

Remove: (sort a b)
Compiler: Compiled 501 to 339 computations (32.3% saved)

Details

analyze2.7s (35.1%)

sample1.9s (24.8%)

simplify70.0ms (0.9%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series43.0ms (0.6%)

rewrite10.0ms (0.1%)

simplify92.0ms (1.2%)

prune95.0ms (1.3%)

localize13.0ms (0.2%)

series44.0ms (0.6%)

rewrite6.0ms (0.1%)

simplify93.0ms (1.2%)

prune95.0ms (1.2%)

localize10.0ms (0.1%)

series60.0ms (0.8%)

rewrite11.0ms (0.1%)

simplify102.0ms (1.3%)

prune94.0ms (1.2%)

localize14.0ms (0.2%)

series508.0ms (6.7%)

rewrite28.0ms (0.4%)

simplify86.0ms (1.1%)

prune162.0ms (2.1%)

regimes789.0ms (10.4%)

bsearch1.0ms (0%)

simplify3.0ms (0%)

end610.0ms (8%)

Profiling