Details

analyze1.3s (22.1%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
16.4%	83.4%	0.2%	11
19.9%	79.9%	0.2%	12
21.6%	77.2%	1.2%	13
24.8%	73.7%	1.4%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.5s (26.3%)

Results

1.1s	8256×	body	128	valid
424.0ms	3094×	body	128	invalid

Compiler

Compiled 30 to 20 computations (33.3% saved)

preprocess53.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

726×	`times-frac_binary64`
527×	`fma-neg_binary64`
372×	`div-sub_binary64`
352×	`cancel-sign-sub-inv_binary64`
314×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	143
1	137	143
2	294	143
3	489	143
4	1106	143
5	2123	143
6	3016	143
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort x y)

(sort z t)

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
389×	`fma-neg_binary64`
131×	`cancel-sign-sub-inv_binary64`
113×	`distribute-rgt-in_binary64`
103×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	21	13
2	46	13
3	77	13
4	161	13
5	292	13
6	483	13
7	733	13
8	1186	13
9	1758	13
10	2658	13
11	2745	13
12	2775	13
13	2780	13

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

7.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.4b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.7b	(-.f64 (.f64 x y) (.f64 z t))
✓	6.9b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

series40.0ms (0.7%)

Counts

2 → 108

Calls

27 calls:

3.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)	x	0
3.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)	a	-inf
3.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)	z	0
3.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)	x	-inf
3.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)	x	inf

rewrite78.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

420×	`fma-def_binary64`
220×	`fma-neg_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`
178×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	227	23
2	3308	23

Stop Event

1×	node limit

Counts

2 → 224

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1168×	`fma-def_binary64`
351×	`fma-neg_binary64`
127×	`cancel-sign-sub-inv_binary64`
93×	`associate-/l*_binary64`
92×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	1140
1	49	1140
2	108	1140
3	245	1140
4	520	1140
5	988	1140
6	1828	1140
7	2773	1140
8	3029	1140
9	3067	1140
10	3072	1140

Stop Event

1×

saturated

Counts

332 → 237

prune154.0ms (2.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	230	7	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	231	7	238

Error

0.0b

Counts

238 → 7

Alt Table

Status	Error	Program
	7.5b	(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
	34.9b	(fma.f64 (/.f64 (sqrt.f64 (.f64 x y)) 1) (/.f64 (sqrt.f64 (.f64 x y)) a) (neg.f64 (/.f64 z (/.f64 a t))))
	8.5b	(-.f64 (/.f64 x (/.f64 a y)) (/.f64 z (/.f64 a t)))
	34.6b	(*.f64 t (/.f64 (neg.f64 z) a))
▶	7.4b	(/.f64 (fma.f64 t (neg.f64 z) (*.f64 y x)) a)
	34.8b	(*.f64 y (/.f64 x a))
	7.7b	(pow.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) -1)

Compiler

Compiled 4759 to 1198 computations (74.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.8b	(fma.f64 t (neg.f64 z) (*.f64 y x))
✓	6.9b	(/.f64 (fma.f64 t (neg.f64 z) (*.f64 y x)) a)

series41.0ms (0.7%)

Counts

2 → 108

Calls

27 calls:

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

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

893×	`log1p-expm1-u_binary64`
893×	`expm1-log1p-u_binary64`
107×	`add-sqr-sqrt_binary64`
105×	`*-un-lft-identity_binary64`
105×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	205	19
2	2638	19

Stop Event

1×	node limit

Counts

2 → 56

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1168×	`fma-def_binary64`
322×	`fma-neg_binary64`
127×	`cancel-sign-sub-inv_binary64`
93×	`associate-/l*_binary64`
92×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	1140
1	49	1140
2	108	1140
3	245	1140
4	521	1140
5	989	1140
6	1797	1140
7	2748	1140
8	3004	1140
9	3042	1140
10	3047	1140

Stop Event

1×

saturated

Counts

164 → 69

prune39.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Error

0.0b

Counts

76 → 7

Alt Table

Status	Error	Program
▶	7.5b	(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
	34.9b	(fma.f64 (/.f64 (sqrt.f64 (.f64 x y)) 1) (/.f64 (sqrt.f64 (.f64 x y)) a) (neg.f64 (/.f64 z (/.f64 a t))))
	8.5b	(-.f64 (/.f64 x (/.f64 a y)) (/.f64 z (/.f64 a t)))
	34.6b	(*.f64 t (/.f64 (neg.f64 z) a))
✓	7.4b	(/.f64 (fma.f64 t (neg.f64 z) (*.f64 y x)) a)
	34.8b	(*.f64 y (/.f64 x a))
	7.7b	(pow.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) -1)

Compiler

Compiled 1086 to 376 computations (65.4% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t))))
✓	6.9b	(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
✓	52.7b	(fma.f64 z (neg.f64 t) (*.f64 z t))

series68.0ms (1.2%)

Counts

3 → 132

Calls

33 calls:

9.0ms	(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)	z	inf
5.0ms	(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)	a	0
4.0ms	(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)	t	-inf
3.0ms	(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)	x	inf
3.0ms	(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)	a	-inf

rewrite61.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

701×	`prod-diff_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
128×	`add-sqr-sqrt_binary64`
126×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	53
1	246	40
2	3175	40

Stop Event

1×	node limit

Counts

3 → 79

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1168×	`fma-def_binary64`
322×	`fma-neg_binary64`
127×	`cancel-sign-sub-inv_binary64`
93×	`associate-/l*_binary64`
92×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	1164
1	50	1164
2	108	1164
3	246	1164
4	519	1164
5	988	1164
6	1804	1164
7	2760	1164
8	3016	1164
9	3054	1164
10	3059	1164

Stop Event

1×

saturated

Counts

211 → 93

prune69.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	93	7	100

Error

0.0b

Counts

100 → 7

Alt Table

Status	Error	Program
✓	7.5b	(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
	34.9b	(fma.f64 (/.f64 (sqrt.f64 (.f64 x y)) 1) (/.f64 (sqrt.f64 (.f64 x y)) a) (neg.f64 (/.f64 z (/.f64 a t))))
	8.5b	(-.f64 (/.f64 x (/.f64 a y)) (/.f64 z (/.f64 a t)))
	34.6b	(*.f64 t (/.f64 (neg.f64 z) a))
✓	7.4b	(/.f64 (fma.f64 t (neg.f64 z) (*.f64 y x)) a)
	34.8b	(*.f64 y (/.f64 x a))
▶	7.7b	(pow.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) -1)

Compiler

Compiled 1868 to 506 computations (72.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) -1)
	0.7b	(-.f64 (.f64 x y) (.f64 z t))
✓	7.0b	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))

series414.0ms (7%)

Counts

2 → 120

Calls

30 calls:

36.0ms	(pow.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) -1)	y	-inf
36.0ms	(pow.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) -1)	x	-inf
31.0ms	(pow.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) -1)	z	inf
29.0ms	(pow.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) -1)	x	0
28.0ms	(pow.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) -1)	t	inf

rewrite64.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

405×	`fma-def_binary64`
237×	`expm1-udef_binary64`
237×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
137×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	266	26
2	3587	26

Stop Event

1×	node limit

Counts

2 → 81

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

825×	`associate-/r*_binary64`
443×	`associate-l_binary64`
325×	`fma-def_binary64`
260×	`associate-*l/_binary64`
245×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	88	2988
1	321	2844
2	1493	2844

Stop Event

1×	node limit

Counts

201 → 110

prune188.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	284	2	286
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	286	7	293

Error

0.0b

Counts

293 → 7

Alt Table

Status	Error	Program
	8.5b	(-.f64 (/.f64 x (/.f64 a y)) (/.f64 z (/.f64 a t)))
	34.5b	(*.f64 (/.f64 (neg.f64 t) a) z)
	7.8b	(pow.f64 (.f64 a (/.f64 1 (-.f64 (.f64 x y) (*.f64 z t)))) -1)
	34.6b	(*.f64 t (/.f64 (neg.f64 z) a))
✓	7.5b	(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
✓	7.4b	(/.f64 (fma.f64 t (neg.f64 z) (*.f64 y x)) a)
	34.8b	(*.f64 y (/.f64 x a))

Compiler

Compiled 6212 to 2016 computations (67.5% saved)

regimes1.1s (18%)

Accuracy

Total 0.9b remaining (97.3%)

Threshold costs 0.9b (97.3%)

Counts

54 → 3

Compiler

Compiled 9784 to 6466 computations (33.9% saved)

bsearch2.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)
0.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

Steps

Iters	Point		Range
1.197418276934376e+292	∈ [	1.197418276934376e+292	,	2.911947319392304e+301	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-6.1739902871792e+305	]

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	81
1	38	81
2	52	81
3	59	81
4	63	81
5	64	81

Stop Event

1×

saturated

end283.0ms (4.8%)

Stop Event

1×

fuel

Remove

(sort x y)

Compiler

Compiled 581 to 250 computations (57% saved)

Details

analyze1.3s (22.1%)

sample1.5s (26.3%)

preprocess53.0ms (0.9%)

simplify33.0ms (0.6%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series40.0ms (0.7%)

rewrite78.0ms (1.3%)

simplify81.0ms (1.4%)

prune154.0ms (2.6%)

localize7.0ms (0.1%)

series41.0ms (0.7%)

rewrite50.0ms (0.9%)

simplify79.0ms (1.3%)

prune39.0ms (0.7%)

localize11.0ms (0.2%)

series68.0ms (1.2%)

rewrite61.0ms (1%)

simplify80.0ms (1.4%)

prune69.0ms (1.2%)

localize8.0ms (0.1%)

series414.0ms (7%)

rewrite64.0ms (1.1%)

simplify65.0ms (1.1%)

prune188.0ms (3.2%)

regimes1.1s (18%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end283.0ms (4.8%)

Profiling