Details

analyze1.7s (38.4%)

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
3.1%	96.6%	0.3%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.7s (37.5%)

Results

1.1s	8256×	body	128	valid
529.0ms	3942×	body	128	invalid

Compiler

Compiled 36 to 24 computations (33.3% saved)

preprocess35.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

135×	`fma-def_binary64`
45×	`+-commutative_binary64`
24×	`associate-+l+_binary64`
15×	`*-commutative_binary64`
15×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	224
1	143	192
2	266	192
3	300	192
0	6	6
1	6	6

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort x y)

(sort z t)

(sort a b)

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	20	12
2	36	12
3	46	12

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 x y (fma.f64 a b (*.f64 z t)))

Compiler

Compiled 56 to 31 computations (44.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a b (*.f64 z t))
✓	0.0b	(fma.f64 x y (fma.f64 a b (*.f64 z t)))

series28.0ms (0.6%)

Counts

2 → 120

Calls

30 calls:

4.0ms	(fma.f64 x y (fma.f64 a b (*.f64 z t)))	b	inf
1.0ms	(fma.f64 x y (fma.f64 a b (*.f64 z t)))	x	inf
1.0ms	(fma.f64 x y (fma.f64 a b (*.f64 z t)))	x	-inf
1.0ms	(fma.f64 x y (fma.f64 a b (*.f64 z t)))	t	-inf
1.0ms	(fma.f64 x y (fma.f64 a b (*.f64 z t)))	y	-inf

rewrite46.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

869×	`log1p-expm1-u_binary64`
869×	`expm1-log1p-u_binary64`
240×	`prod-diff_binary64`
102×	`add-sqr-sqrt_binary64`
93×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	196	20
2	2352	20

Stop Event

1×	node limit

Counts

2 → 47

simplify27.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`associate-+r+_binary64`
1×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	1080
1	30	1080
2	42	1080
3	44	1080

Stop Event

1×

saturated

Counts

167 → 59

prune36.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	2	60

Error

Counts

60 → 2

Alt Table

Status	Error	Program
	22.0b	(fma.f64 x y (.f64 (cbrt.f64 (fma.f64 a b (.f64 z t))) (cbrt.f64 (pow.f64 (fma.f64 a b (*.f64 z t)) 2))))
▶	0.0b	(fma.f64 t z (fma.f64 y x (*.f64 a b)))

Compiler

Compiled 850 to 231 computations (72.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 t z (fma.f64 y x (*.f64 a b)))
✓	0.0b	(fma.f64 y x (*.f64 a b))

series31.0ms (0.7%)

Counts

2 → 120

Calls

30 calls:

4.0ms	(fma.f64 y x (*.f64 a b))	x	inf
3.0ms	(fma.f64 t z (fma.f64 y x (*.f64 a b)))	x	-inf
1.0ms	(fma.f64 t z (fma.f64 y x (*.f64 a b)))	b	-inf
1.0ms	(fma.f64 t z (fma.f64 y x (*.f64 a b)))	a	-inf
1.0ms	(fma.f64 t z (fma.f64 y x (*.f64 a b)))	b	0

rewrite46.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

869×	`log1p-expm1-u_binary64`
869×	`expm1-log1p-u_binary64`
240×	`prod-diff_binary64`
102×	`add-sqr-sqrt_binary64`
93×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	196	20
2	2352	20

Stop Event

1×	node limit

Counts

2 → 47

simplify25.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`associate-+r+_binary64`
1×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	1080
1	31	1080
2	42	1080
3	44	1080

Stop Event

1×

saturated

Counts

167 → 58

prune28.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	58	2	60

Error

Counts

60 → 2

Alt Table

Status	Error	Program
▶	22.0b	(fma.f64 x y (.f64 (cbrt.f64 (fma.f64 a b (.f64 z t))) (cbrt.f64 (pow.f64 (fma.f64 a b (*.f64 z t)) 2))))
✓	0.0b	(fma.f64 t z (fma.f64 y x (*.f64 a b)))

Compiler

Compiled 837 to 219 computations (73.8% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (fma.f64 a b (.f64 z t))) (cbrt.f64 (pow.f64 (fma.f64 a b (*.f64 z t)) 2)))
✓	0.3b	(pow.f64 (fma.f64 a b (*.f64 z t)) 2)
✓	1.4b	(cbrt.f64 (fma.f64 a b (*.f64 z t)))
✓	25.1b	(cbrt.f64 (pow.f64 (fma.f64 a b (*.f64 z t)) 2))

series118.0ms (2.7%)

Counts

4 → 128

Calls

48 calls:

9.0ms	(cbrt.f64 (pow.f64 (fma.f64 a b (*.f64 z t)) 2))	a
9.0ms	(cbrt.f64 (pow.f64 (fma.f64 a b (*.f64 z t)) 2))	z
9.0ms	(cbrt.f64 (pow.f64 (fma.f64 a b (*.f64 z t)) 2))	t
7.0ms	(cbrt.f64 (pow.f64 (fma.f64 a b (*.f64 z t)) 2))	b
5.0ms	(pow.f64 (fma.f64 a b (*.f64 z t)) 2)	a

rewrite54.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

855×	`log1p-expm1-u_binary64`
855×	`expm1-log1p-u_binary64`
176×	`prod-diff_binary64`
106×	`add-sqr-sqrt_binary64`
102×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	57
1	237	42
2	2573	42

Stop Event

1×	node limit

Counts

4 → 93

simplify74.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

935×	`fma-def_binary64`
370×	`cancel-sign-sub-inv_binary64`
361×	`unswap-sqr_binary64`
241×	`associate-r_binary64`
174×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	4440
1	551	4176
2	1952	4008

Stop Event

1×	node limit

Counts

221 → 145

prune99.0ms (2.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	145	2	147

Error

Counts

147 → 2

Alt Table

Status	Error	Program
✓	22.0b	(fma.f64 x y (.f64 (cbrt.f64 (fma.f64 a b (.f64 z t))) (cbrt.f64 (pow.f64 (fma.f64 a b (*.f64 z t)) 2))))
✓	0.0b	(fma.f64 t z (fma.f64 y x (*.f64 a b)))

Compiler

Compiled 4636 to 1939 computations (58.2% saved)

regimes282.0ms (6.4%)

Accuracy

Total 0.0b remaining (39.2%)

Threshold costs 0.0b (39.2%)

Counts

22 → 1

Compiler

Compiled 4273 to 2823 computations (33.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	11	12

Stop Event

1×

saturated

end91.0ms (2%)

Stop Event

1×

done

Remove

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 161 to 95 computations (41% saved)

Details

analyze1.7s (38.4%)

sample1.7s (37.5%)

preprocess35.0ms (0.8%)

simplify13.0ms (0.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series28.0ms (0.6%)

rewrite46.0ms (1%)

simplify27.0ms (0.6%)

prune36.0ms (0.8%)

localize7.0ms (0.2%)

series31.0ms (0.7%)

rewrite46.0ms (1%)

simplify25.0ms (0.6%)

prune28.0ms (0.6%)

localize16.0ms (0.4%)

series118.0ms (2.7%)

rewrite54.0ms (1.2%)

simplify74.0ms (1.7%)

prune99.0ms (2.2%)

regimes282.0ms (6.4%)

simplify2.0ms (0%)

end91.0ms (2%)

Profiling