Details

analyze908.0ms (23.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
23.4%	74.9%	1.8%	11
27.3%	69%	3.7%	12
36.6%	56.5%	6.8%	13
40.5%	52%	7.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (29.2%)

Results

903.0ms	8256×	body	128	valid
212.0ms	1996×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess105.0ms (2.7%)

Algorithm

2×	egg-herbie

Rules

1166×	`fma-def_binary64`
614×	`fma-neg_binary64`
297×	`unsub-neg_binary64`
231×	`distribute-rgt-in_binary64`
209×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	70
1	95	70
2	233	70
3	495	70
4	863	70
5	1688	70
6	2357	70
7	3388	70
8	3607	70
9	3643	70
10	3647	70
11	4249	70
12	4537	70
13	4537	70
14	4537	70
15	4537	70
0	4	4
1	4	4

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort y t)

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify35.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

992×	`fma-def_binary64`
302×	`fma-neg_binary64`
112×	`distribute-rgt-in_binary64`
87×	`associate-l_binary64`
82×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	20	10
2	47	10
3	111	10
4	229	10
5	343	10
6	552	10
7	911	10
8	1666	10
9	2363	10
10	2418	10
11	2424	10
12	2424	10

Stop Event

1×

saturated

Counts

1 → 2

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
▶	6.0b	(.f64 y (.f64 t (-.f64 x z)))
	8.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 t (-.f64 x z))
✓	5.7b	(.f64 y (.f64 t (-.f64 x z)))

series20.0ms (0.5%)

Counts

2 → 84

Calls

21 calls:

3.0ms	(.f64 y (.f64 t (-.f64 x z)))	x	-inf
1.0ms	(.f64 y (.f64 t (-.f64 x z)))	y	-inf
1.0ms	(.f64 y (.f64 t (-.f64 x z)))	t	-inf
1.0ms	(.f64 y (.f64 t (-.f64 x z)))	x	inf
1.0ms	(.f64 y (.f64 t (-.f64 x z)))	t	inf

rewrite44.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

874×	`log1p-expm1-u_binary64`
874×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	170	17
2	2309	17

Stop Event

1×	node limit

Counts

2 → 40

simplify63.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-def_binary64`
384×	`fma-neg_binary64`
131×	`cancel-sign-sub-inv_binary64`
108×	`distribute-rgt-in_binary64`
86×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	708
1	64	708
2	130	708
3	219	708
4	340	708
5	598	708
6	1037	708
7	1545	708
8	2280	708
9	2442	708
10	2454	708
11	2454	708

Stop Event

1×

saturated

Counts

124 → 55

prune29.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	51	4	55
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	52	5	57

Error

0.0b

Counts

57 → 5

Alt Table

Status	Error	Program
	41.4b	(.f64 y (/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)) t) (fma.f64 x x (*.f64 z (+.f64 x z)))))
	34.2b	(pow.f64 (sqrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 2)
	8.6b	(pow.f64 (.f64 t (.f64 (-.f64 x z) y)) 1)
✓	6.0b	(.f64 y (.f64 t (-.f64 x z)))
▶	7.7b	(.f64 (-.f64 x z) (.f64 t y))

Compiler

Compiled 701 to 287 computations (59.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.6b	(.f64 (-.f64 x z) (.f64 t y))

series16.0ms (0.4%)

Counts

1 → 48

Calls

12 calls:

5.0ms	(.f64 (-.f64 x z) (.f64 t y))	y	-inf
1.0ms	(.f64 (-.f64 x z) (.f64 t y))	t	-inf
1.0ms	(.f64 (-.f64 x z) (.f64 t y))	x	-inf
1.0ms	(.f64 (-.f64 x z) (.f64 t y))	x	inf
1.0ms	(.f64 (-.f64 x z) (.f64 t y))	y	inf

rewrite38.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

870×	`log1p-expm1-u_binary64`
870×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	170	10
2	2303	10

Stop Event

1×	node limit

Counts

1 → 21

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-def_binary64`
384×	`fma-neg_binary64`
133×	`cancel-sign-sub-inv_binary64`
108×	`distribute-rgt-in_binary64`
86×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	468
1	59	468
2	129	468
3	225	468
4	347	468
5	605	468
6	1043	468
7	1552	468
8	2287	468
9	2449	468
10	2461	468
11	2461	468

Stop Event

1×

saturated

Counts

69 → 30

prune15.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	30	5	35

Error

0.0b

Counts

35 → 5

Alt Table

Status	Error	Program
	41.4b	(.f64 y (/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)) t) (fma.f64 x x (*.f64 z (+.f64 x z)))))
	34.2b	(pow.f64 (sqrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 2)
▶	8.6b	(pow.f64 (.f64 t (.f64 (-.f64 x z) y)) 1)
✓	6.0b	(.f64 y (.f64 t (-.f64 x z)))
✓	7.7b	(.f64 (-.f64 x z) (.f64 t y))

Compiler

Compiled 441 to 189 computations (57.1% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 x z) y)
✓	8.2b	(.f64 t (.f64 (-.f64 x z) y))

series18.0ms (0.5%)

Counts

2 → 72

Calls

21 calls:

1.0ms	(.f64 t (.f64 (-.f64 x z) y))	t	-inf
1.0ms	(.f64 t (.f64 (-.f64 x z) y))	y	-inf
1.0ms	(.f64 t (.f64 (-.f64 x z) y))	x	-inf
1.0ms	(.f64 t (.f64 (-.f64 x z) y))	x	inf
1.0ms	(.f64 t (.f64 (-.f64 x z) y))	t	0

rewrite55.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

874×	`log1p-expm1-u_binary64`
874×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	170	17
2	2309	17

Stop Event

1×	node limit

Counts

2 → 36

simplify75.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

933×	`fma-def_binary64`
384×	`fma-neg_binary64`
133×	`cancel-sign-sub-inv_binary64`
108×	`distribute-rgt-in_binary64`
86×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	624
1	62	624
2	133	624
3	230	624
4	351	624
5	609	624
6	1046	624
7	1553	624
8	2279	624
9	2441	624
10	2453	624
11	2453	624

Stop Event

1×

saturated

Counts

108 → 50

prune29.0ms (0.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	50	5	55

Error

0.0b

Counts

55 → 5

Alt Table

Status	Error	Program
	41.4b	(.f64 y (/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)) t) (fma.f64 x x (*.f64 z (+.f64 x z)))))
▶	34.2b	(pow.f64 (sqrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 2)
✓	8.6b	(pow.f64 (.f64 t (.f64 (-.f64 x z) y)) 1)
✓	6.0b	(.f64 y (.f64 t (-.f64 x z)))
✓	7.7b	(.f64 (-.f64 x z) (.f64 t y))

Compiler

Compiled 711 to 357 computations (49.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 x z) y)
✓	0.2b	(pow.f64 (sqrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 2)
✓	5.1b	(sqrt.f64 (.f64 t (.f64 (-.f64 x z) y)))
	8.2b	(.f64 t (.f64 (-.f64 x z) y))

series432.0ms (11.1%)

Counts

2 → 16

Calls

24 calls:

46.0ms	(pow.f64 (sqrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 2)	t	0
40.0ms	(pow.f64 (sqrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 2)	t	inf
38.0ms	(pow.f64 (sqrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 2)	t	-inf
35.0ms	(pow.f64 (sqrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 2)	x	0
33.0ms	(pow.f64 (sqrt.f64 (.f64 t (.f64 (-.f64 x z) y))) 2)	y	-inf

rewrite60.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

529×	`log-prod_binary64`
359×	`prod-diff_binary64`
200×	`fma-def_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	235	22
2	2765	22

Stop Event

1×	node limit

Counts

2 → 72

simplify28.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

845×	`times-frac_binary64`
490×	`associate-r_binary64`
413×	`associate-l_binary64`
354×	`associate-/l*_binary64`
308×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	531
1	217	448
2	752	440

Stop Event

1×	node limit

Counts

88 → 92

prune70.0ms (1.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	1	0	1
Picked	1	0	1
Done	0	3	3
Total	141	6	147

Error

0.0b

Counts

147 → 6

Alt Table

Status	Error	Program
✓	8.6b	(pow.f64 (.f64 t (.f64 (-.f64 x z) y)) 1)
✓	6.0b	(.f64 y (.f64 t (-.f64 x z)))
	20.3b	(.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) (*.f64 (-.f64 x z) y)))
	9.4b	(.f64 (pow.f64 (cbrt.f64 (.f64 (-.f64 x z) y)) 2) (.f64 (cbrt.f64 (.f64 (-.f64 x z) y)) t))
✓	7.7b	(.f64 (-.f64 x z) (.f64 t y))
	34.4b	(pow.f64 (pow.f64 (pow.f64 (.f64 t (.f64 (-.f64 x z) y)) 1/4) 2) 2)

Compiler

Compiled 2341 to 896 computations (61.7% saved)

regimes384.0ms (9.9%)

Accuracy

Total 0.6b remaining (94.4%)

Threshold costs 0.6b (94.4%)

Counts

34 → 5

Compiler

Compiled 2920 to 1946 computations (33.4% saved)

bsearch1.0ms (0%)

Algorithm

4×	left-value

Calls

4 calls:

0.0ms	(-.f64 (.f64 x y) (.f64 z y))
0.0ms	(-.f64 (.f64 x y) (.f64 z y))
0.0ms	(-.f64 (.f64 x y) (.f64 z y))
0.0ms	(-.f64 (.f64 x y) (.f64 z y))

Steps

Iters	Point		Range
3.647665142799277e+268	∈ [	3.647665142799277e+268	,	1.9142876871063734e+270	]
3.350296082224214e-201	∈ [	3.350296082224214e-201	,	1.549630550848201e-196	]
-2.532347618419866e-187	∈ [	-2.532347618419866e-187	,	-1.5832854776269552e-193	]
-3.675024877736191e+161	∈ [	-3.675024877736191e+161	,	-6.137316856227488e+152	]

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	110
1	42	110
2	55	110
3	61	110
4	65	110
5	66	110

Stop Event

1×

saturated

end227.0ms (5.9%)

Stop Event

1×

fuel

Compiler

Compiled 404 to 160 computations (60.4% saved)

Details

analyze908.0ms (23.4%)

sample1.1s (29.2%)

preprocess105.0ms (2.7%)

simplify35.0ms (0.9%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series20.0ms (0.5%)

rewrite44.0ms (1.1%)

simplify63.0ms (1.6%)

prune29.0ms (0.8%)

localize5.0ms (0.1%)

series16.0ms (0.4%)

rewrite38.0ms (1%)

simplify59.0ms (1.5%)

prune15.0ms (0.4%)

localize8.0ms (0.2%)

series18.0ms (0.5%)

rewrite55.0ms (1.4%)

simplify75.0ms (1.9%)

prune29.0ms (0.8%)

localize7.0ms (0.2%)

series432.0ms (11.1%)

rewrite60.0ms (1.6%)

simplify28.0ms (0.7%)

prune70.0ms (1.8%)

regimes384.0ms (9.9%)

bsearch1.0ms (0%)

simplify6.0ms (0.2%)

end227.0ms (5.9%)

Profiling