Details

analyze953.0ms (8.1%)

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
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.5s (12.8%)

Results

1.0s	8256×	body	128	valid
441.0ms	3176×	body	128	invalid

Compiler

Compiled 36 to 24 computations (33.3% saved)

preprocess40.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

819×	`fma-def_binary64`
629×	`fma-neg_binary64`
386×	`associate-l_binary64`
328×	`associate-r_binary64`
306×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	133
1	113	119
2	388	119
3	1707	119
4	4575	119
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

850×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
159×	`associate-l_binary64`
152×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	77	17
3	302	17
4	829	17
5	1620	17
6	2745	17
7	3158	17
8	3307	17
9	3349	17
10	3365	17
11	3365	17

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

5.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.1b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))

Compiler

Compiled 61 to 34 computations (44.3% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.8b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))

series29.0ms (0.2%)

Counts

1 → 48

Calls

12 calls:

4.0ms	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))	y	0
3.0ms	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))	t	inf
3.0ms	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))	y	-inf
2.0ms	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))	x	0
2.0ms	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))	y	inf

rewrite44.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`prod-diff_binary64`
233×	`fma-def_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
182×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	230	17
2	2868	17

Stop Event

1×	node limit

Counts

1 → 26

simplify52.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
599×	`fma-neg_binary64`
387×	`cancel-sign-sub-inv_binary64`
310×	`distribute-rgt-neg-in_binary64`
284×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	940
1	81	794
2	229	722
3	597	722
4	1580	722
5	3145	722
6	4638	722

Stop Event

1×	node limit

Counts

74 → 42

prune35.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	5	43

Error

0.0b

Counts

43 → 5

Alt Table

Status	Error	Program
	46.6b	(pow.f64 (pow.f64 (fma.f64 x x (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))) 3) 1/3)
✓	5.1b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))
▶	22.2b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
	32.9b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2)
	42.1b	(/.f64 (+.f64 (pow.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) 3) (pow.f64 (.f64 x x) 3)) (fma.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) (-.f64 (pow.f64 x 4) (.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) (*.f64 x x)))))

Compiler

Compiled 871 to 446 computations (48.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
✓	0.2b	(.f64 z (.f64 z (*.f64 y -4)))

series48.0ms (0.4%)

Counts

2 → 60

Calls

15 calls:

23.0ms	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))	z	0
2.0ms	(.f64 z (.f64 z (*.f64 y -4)))	z	0
2.0ms	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))	x	inf
2.0ms	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))	x	-inf
2.0ms	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))	x	0

rewrite46.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`log1p-expm1-u_binary64`
784×	`expm1-log1p-u_binary64`
198×	`prod-diff_binary64`
90×	`associate-r_binary64`
90×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	181	24
2	2154	24

Stop Event

1×	node limit

Counts

2 → 38

simplify54.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
645×	`unswap-sqr_binary64`
326×	`cancel-sign-sub-inv_binary64`
294×	`fma-neg_binary64`
252×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	738
1	32	684
2	80	684
3	225	684
4	672	684
5	1310	684
6	1997	684
7	3187	684

Stop Event

1×	node limit

Counts

98 → 44

prune34.0ms (0.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	43	6	49

Error

0.0b

Counts

49 → 6

Alt Table

Status	Error	Program
	43.2b	(pow.f64 (hypot.f64 x (.f64 z (sqrt.f64 (.f64 y -4)))) 2)
	42.1b	(/.f64 (+.f64 (pow.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) 3) (pow.f64 (.f64 x x) 3)) (fma.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) (-.f64 (pow.f64 x 4) (.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) (*.f64 x x)))))
✓	22.2b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
▶	32.9b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2)
✓	5.1b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))
	38.5b	(fma.f64 x x (pow.f64 (pow.f64 (.f64 z (.f64 y (*.f64 -4 z))) 3) 1/3))

Compiler

Compiled 858 to 515 computations (40% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))
✓	0.2b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2)
✓	4.8b	(.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))
✓	6.3b	(sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))

series1.5s (12.7%)

Counts

4 → 110

Calls

42 calls:

148.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2)	z	-inf
134.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2)	t	inf
133.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2)	t	-inf
133.0ms	(hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))	y	-inf
127.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))) 2)	z	inf

rewrite67.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

632×	`prod-diff_binary64`
247×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	67
1	297	63
2	3554	63

Stop Event

1×	node limit

Counts

4 → 93

simplify84.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

535×	`cancel-sign-sub-inv_binary64`
279×	`fma-neg_binary64`
199×	`distribute-rgt-neg-in_binary64`
196×	`sub-neg_binary64`
168×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	3729
1	759	3471
2	3043	3443

Stop Event

1×	node limit

Counts

203 → 198

prune154.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	198	6	204

Error

0.0b

Counts

204 → 6

Alt Table

Status	Error	Program
✓	22.2b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
✓	5.1b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))
	43.2b	(pow.f64 (hypot.f64 x (.f64 z (sqrt.f64 (.f64 y -4)))) 2)
	42.0b	(/.f64 (+.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) 3)) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (pow.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) 2) (.f64 (.f64 x x) (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))))
▶	33.1b	(.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))))
	38.5b	(fma.f64 x x (pow.f64 (pow.f64 (.f64 z (.f64 y (*.f64 -4 z))) 3) 1/3))

Compiler

Compiled 6170 to 3888 computations (37% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))))
✓	0.2b	(.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))))
	4.8b	(.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))
	6.3b	(sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))

series4.8s (41%)

Counts

2 → 42

Calls

24 calls:

1.6s	(.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))))	t	-inf
1.5s	(.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))))	t	inf
314.0ms	(.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))))	y	-inf
312.0ms	(.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t)))))	y	inf
130.0ms	(.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))))	t	-inf

rewrite51.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

632×	`prod-diff_binary64`
147×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`
140×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	78
1	315	38
2	3759	38

Stop Event

1×	node limit

Counts

2 → 33

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

588×	`unswap-sqr_binary64`
543×	`fma-neg_binary64`
447×	`fma-def_binary64`
344×	`*-commutative_binary64`
286×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1523
1	369	1337
2	1220	1235
3	3630	1233

Stop Event

1×	node limit

Counts

75 → 75

prune292.0ms (2.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	342	0	342
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	342	6	348

Error

0.0b

Counts

348 → 6

Alt Table

Status	Error	Program
✓	22.2b	(fma.f64 x x (.f64 z (.f64 z (*.f64 y -4))))
✓	5.1b	(fma.f64 y (.f64 (-.f64 (.f64 z z) t) -4) (*.f64 x x))
	43.2b	(pow.f64 (hypot.f64 x (.f64 z (sqrt.f64 (.f64 y -4)))) 2)
	42.0b	(/.f64 (+.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) 3)) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (pow.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t)) 2) (.f64 (.f64 x x) (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))))
✓	33.1b	(.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (.f64 z z) t))))) (hypot.f64 x (sqrt.f64 (.f64 (.f64 y -4) (-.f64 (*.f64 z z) t))))))
	38.5b	(fma.f64 x x (pow.f64 (pow.f64 (.f64 z (.f64 y (*.f64 -4 z))) 3) 1/3))

Compiler

Compiled 15882 to 8714 computations (45.1% saved)

regimes1.7s (14.4%)

Accuracy

Total 0.0b remaining (48.8%)

Threshold costs 0.0b (48.8%)

Counts

84 → 2

Compiler

Compiled 23970 to 15847 computations (33.9% saved)

bsearch6.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(*.f64 z z)

Steps

Iters	Point		Range
1.2910891059276744e+302	∈ [	1.2910891059276744e+302	,	4.897452457819304e+305	]

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	48
1	38	48
2	48	48
3	58	48
4	65	48
5	70	48
6	72	48

Stop Event

1×

saturated

end109.0ms (0.9%)

Stop Event

1×

fuel

Compiler

Compiled 235 to 146 computations (37.9% saved)

Details

analyze953.0ms (8.1%)

sample1.5s (12.8%)

preprocess40.0ms (0.3%)

simplify46.0ms (0.4%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series29.0ms (0.2%)

rewrite44.0ms (0.4%)

simplify52.0ms (0.4%)

prune35.0ms (0.3%)

localize6.0ms (0.1%)

series48.0ms (0.4%)

rewrite46.0ms (0.4%)

simplify54.0ms (0.5%)

prune34.0ms (0.3%)

localize10.0ms (0.1%)

series1.5s (12.7%)

rewrite67.0ms (0.6%)

simplify84.0ms (0.7%)

prune154.0ms (1.3%)

localize13.0ms (0.1%)

series4.8s (41%)

rewrite51.0ms (0.4%)

simplify50.0ms (0.4%)

prune292.0ms (2.5%)

regimes1.7s (14.4%)

bsearch6.0ms (0%)

simplify4.0ms (0%)

end109.0ms (0.9%)

Profiling