Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
99.7%	0%	0.3%	1

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.2s (31.2%)

Infinites

28% of outputs are infinite.

Symmetry

(sort y z t)

(sort a b)

Results

922.0ms

8256×

body

128

valid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify78.0ms (2.1%)

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

prune5.0ms (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
	3.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
▶	2.5b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize10.0ms (0.3%)

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)
✓	2.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series47.0ms (1.3%)

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))
6.0ms	(.f64 (.f64 a 27) b)
4.0ms	(.f64 (.f64 z t) -9)

rewrite11.0ms (0.3%)

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

simplify97.0ms (2.6%)

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

prune117.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	7	109

Error

0.0b

Counts

109 → 7

Alt Table

Status	Error	Program
	3.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.5b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	3.1b	(fma.f64 y (.f64 (.f64 z t) -9) (.f64 (.f64 (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b))) (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b)))))
	2.8b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	30.3b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (sqrt.f64 (.f64 (.f64 a 27) b)) (sqrt.f64 (.f64 (*.f64 a 27) b)))))
▶	2.5b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	27.9b	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))

Compiler

Compiled 2448 to 1428 computations (41.7% saved)

localize13.0ms (0.3%)

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))
✓	2.4b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series34.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

29.0ms	(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)))

simplify98.0ms (2.6%)

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

prune113.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	107	7	114

Error

0.0b

Counts

114 → 7

Alt Table

Status	Error	Program
	3.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
▶	2.5b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	3.1b	(fma.f64 y (.f64 (.f64 z t) -9) (.f64 (.f64 (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b))) (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b)))))
	2.8b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	30.3b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (sqrt.f64 (.f64 (.f64 a 27) b)) (sqrt.f64 (.f64 (*.f64 a 27) b)))))
✓	2.5b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	27.9b	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))

Compiler

Compiled 2427 to 1479 computations (39.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
✓	0.2b	(.f64 (.f64 y (*.f64 t z)) -9)
✓	0.3b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
✓	5.9b	(.f64 y (.f64 t z))

series61.0ms (1.6%)

Counts

4 → 156

Calls

4 calls:

28.0ms	(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))
10.0ms	(.f64 y (.f64 t z))
10.0ms	(.f64 (.f64 y (*.f64 t z)) -9)

rewrite14.0ms (0.4%)

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:

7.0ms	(.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)))

simplify121.0ms (3.2%)

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 → 81

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

prune75.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	81	7	88

Error

0.0b

Counts

88 → 7

Alt Table

Status	Error	Program
	3.1b	(fma.f64 y (.f64 (.f64 z t) -9) (.f64 (.f64 (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b))) (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b)))))
▶	2.8b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	30.3b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (sqrt.f64 (.f64 (.f64 a 27) b)) (sqrt.f64 (.f64 (*.f64 a 27) b)))))
	3.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	3.5b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
✓	2.5b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	27.9b	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))

Compiler

Compiled 1968 to 988 computations (49.8% saved)

localize10.0ms (0.3%)

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)
✓	0.4b	(.f64 a (.f64 27 b))
✓	2.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

series43.0ms (1.1%)

Counts

3 → 132

Calls

3 calls:

30.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
9.0ms	(fma.f64 x 2 (.f64 a (.f64 27 b)))
4.0ms	(.f64 a (.f64 27 b))

rewrite5.0ms (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 (2.5%)

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

prune109.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Error

0.0b

Counts

114 → 7

Alt Table

Status	Error	Program
	3.1b	(fma.f64 y (.f64 (.f64 z t) -9) (.f64 (.f64 (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b))) (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (cbrt.f64 (fma.f64 x 2 (.f64 (.f64 a 27) b)))))
✓	2.8b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	30.3b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (sqrt.f64 (.f64 (.f64 a 27) b)) (sqrt.f64 (.f64 (*.f64 a 27) b)))))
	3.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	3.5b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
✓	2.5b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	27.9b	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))

Compiler

Compiled 2275 to 1302 computations (42.8% saved)

regimes668.0ms (17.7%)

Accuracy

Total 1.5b remaining (94.2%)

Threshold costs 0b (0%)

Counts

28 → 3

Compiler

Compiled 10165 to 7340 computations (27.8% saved)

bsearch1.0ms (0%)

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

simplify6.0ms (0.2%)

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	32	90
1	48	90
2	64	90
3	80	90
4	90	90
5	95	90
6	96	90
7	95	90

end751.0ms (19.9%)

Compiler: Compiled 581 to 389 computations (33% saved)

Details

analyze3.0ms (0.1%)

sample1.2s (31.2%)

simplify78.0ms (2.1%)

prune5.0ms (0.1%)

localize10.0ms (0.3%)

series47.0ms (1.3%)

rewrite11.0ms (0.3%)

simplify97.0ms (2.6%)

prune117.0ms (3.1%)

localize13.0ms (0.3%)

series34.0ms (0.9%)

rewrite5.0ms (0.1%)

simplify98.0ms (2.6%)

prune113.0ms (3%)

localize10.0ms (0.3%)

series61.0ms (1.6%)

rewrite14.0ms (0.4%)

simplify121.0ms (3.2%)

prune75.0ms (2%)

localize10.0ms (0.3%)

series43.0ms (1.1%)

rewrite5.0ms (0.1%)

simplify93.0ms (2.5%)

prune109.0ms (2.9%)

regimes668.0ms (17.7%)

bsearch1.0ms (0%)

simplify6.0ms (0.2%)

end751.0ms (19.9%)

Profiling