Details

analyze1.9s (28.2%)

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 (28%)

Symmetry

(sort y z t)

(sort a b)

Results

1.2s	8256×	body	128	valid
441.0ms	2984×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify74.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.9b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.5b	(+.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 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 z t) -9)
✓	0.2b	(.f64 (.f64 a 27) b)
✓	1.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series41.0ms (0.6%)

Counts

3 → 120

Calls

3 calls:

30.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
6.0ms	(.f64 (.f64 z t) -9)
4.0ms	(.f64 (.f64 a 27) b)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 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)))

simplify106.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

432×	`unswap-sqr_binary64`
410×	`*-commutative_binary64`
279×	`distribute-lft-in_binary64`
279×	`distribute-rgt-in_binary64`
257×	`sqr-pow_binary64`

Counts

170 → 89

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	112	2468
1	240	2239
2	844	2239
3	1418	2239
4	2714	2239
5	4898	2239
6	4989	2239

prune107.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	84	7	91

Error

0.0b

Counts

91 → 7

Alt Table

Status	Error	Program
	2.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
▶	1.9b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
	21.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a 27) b) (.f64 (.f64 a 27) b)) (.f64 (.f64 a 27) b)))))
	3.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b))))) (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))))
	1.9b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))

Compiler

Compiled 2136 to 1244 computations (41.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
✓	0.3b	(.f64 27 (.f64 a b))
✓	0.3b	(.f64 9 (.f64 y (*.f64 t z)))
✓	4.8b	(.f64 y (.f64 t z))

series62.0ms (0.9%)

Counts

4 → 18

Calls

4 calls:

36.0ms	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
12.0ms	(.f64 y (.f64 t z))
10.0ms	(.f64 9 (.f64 y (*.f64 t z)))
4.0ms	(.f64 27 (.f64 a b))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-cbrt-cube_binary64`
23×	`add-exp-log_binary64`
23×	`pow1_binary64`
12×	`cbrt-unprod_binary64`
12×	`prod-exp_binary64`

Counts

4 → 85

Calls

4 calls:

11.0ms	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
5.0ms	(.f64 9 (.f64 y (*.f64 t z)))
4.0ms	(.f64 27 (.f64 a b))
4.0ms	(.f64 y (.f64 t z))

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

535×	`*-commutative_binary64`
493×	`cancel-sign-sub-inv_binary64`
462×	`fma-def_binary64`
344×	`fma-neg_binary64`
215×	`associate-r_binary64`

Counts

103 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	1662
1	345	1372
2	1238	1339
3	3334	1327
4	4946	1327
5	4810	1327

prune106.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	110	7	117

Error

0.0b

Counts

117 → 7

Alt Table

Status	Error	Program
	2.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	2.0b	(-.f64 (+.f64 (.f64 (sqrt.f64 27) (.f64 (sqrt.f64 27) (.f64 a b))) (.f64 2 x)) (.f64 9 (.f64 y (*.f64 t z))))
▶	1.9b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 (.f64 9 y) (.f64 t z)))
	7.4b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 (.f64 y t) z)))
	1.9b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))

Compiler

Compiled 2958 to 1567 computations (47% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 (.f64 9 y) (.f64 t z)))
	0.3b	(.f64 27 (.f64 a b))
✓	4.9b	(.f64 (.f64 9 y) (*.f64 t z))

series44.0ms (0.7%)

Counts

2 → 108

Calls

2 calls:

34.0ms	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 (.f64 9 y) (.f64 t z)))
10.0ms	(.f64 (.f64 9 y) (*.f64 t z))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
8×	`cbrt-unprod_binary64`
8×	`prod-exp_binary64`

Counts

2 → 46

Calls

2 calls:

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

simplify85.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

620×	`distribute-rgt-neg-in_binary64`
553×	`fma-def_binary64`
408×	`*-commutative_binary64`
278×	`fma-neg_binary64`
231×	`cancel-sign-sub-inv_binary64`

Counts

154 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	2758
1	267	2532
2	1038	2500
3	3346	2488
4	4972	2488

prune100.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	98	7	105

Error

0.0b

Counts

105 → 7

Alt Table

Status	Error	Program
	2.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	2.0b	(-.f64 (+.f64 (.f64 (sqrt.f64 27) (.f64 (sqrt.f64 27) (.f64 a b))) (.f64 2 x)) (.f64 9 (.f64 y (*.f64 t z))))
✓	1.9b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 (.f64 9 y) (.f64 t z)))
	7.4b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 (.f64 y t) z)))
▶	1.9b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))

Compiler

Compiled 2661 to 1521 computations (42.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 z (.f64 t -9))
	0.2b	(.f64 (.f64 a 27) b)
✓	1.7b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series35.0ms (0.5%)

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)))

simplify105.0ms (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

prune81.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	89	7	96

Error

0.0b

Counts

96 → 7

Alt Table

Status	Error	Program
	2.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	2.0b	(-.f64 (+.f64 (.f64 (sqrt.f64 27) (.f64 (sqrt.f64 27) (.f64 a b))) (.f64 2 x)) (.f64 9 (.f64 y (*.f64 t z))))
✓	1.9b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 (.f64 9 y) (.f64 t z)))
	7.4b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 (.f64 y t) z)))
✓	1.9b	(fma.f64 y (.f64 z (.f64 t -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	2.5b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (.f64 a 27) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))))

Compiler

Compiled 1890 to 1128 computations (40.3% saved)

regimes986.0ms (14.9%)

Accuracy

Total 0.4b remaining (95.3%)

Threshold costs 0.4b (95.3%)

Counts

48 → 2

Compiler

Compiled 18526 to 13227 computations (28.6% saved)

bsearch13.0ms (0.2%)

Steps

Iters	Range		Point
2	2.0966833998934486e-21	1.808632963508904e-17	1.7986634846681185e-18

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

end748.0ms (11.3%)

Compiler: Compiled 418 to 294 computations (29.7% saved)

Details

analyze1.9s (28.2%)

sample1.9s (28%)

simplify74.0ms (1.1%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series41.0ms (0.6%)

rewrite10.0ms (0.1%)

simplify106.0ms (1.6%)

prune107.0ms (1.6%)

localize11.0ms (0.2%)

series62.0ms (0.9%)

rewrite27.0ms (0.4%)

simplify83.0ms (1.3%)

prune106.0ms (1.6%)

localize13.0ms (0.2%)

series44.0ms (0.7%)

rewrite16.0ms (0.2%)

simplify85.0ms (1.3%)

prune100.0ms (1.5%)

localize10.0ms (0.2%)

series35.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify105.0ms (1.6%)

prune81.0ms (1.2%)

regimes986.0ms (14.9%)

bsearch13.0ms (0.2%)

simplify4.0ms (0.1%)

end748.0ms (11.3%)

Profiling