Details

analyze1.5s (10.1%)

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
4.7%	95.1%	0.2%	10
7.2%	92.6%	0.2%	11
16.8%	83%	0.2%	12
19.9%	79.9%	0.2%	13
30.2%	69.6%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.2s (7.5%)

Results

1.1s	8256×	body	128	valid
37.0ms	311×	body	128	invalid

Compiler

Compiled 44 to 28 computations (36.4% saved)

preprocess38.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

513×	`distribute-rgt-in_binary64`
482×	`fma-def_binary64`
472×	`div-sub_binary64`
360×	`fma-neg_binary64`
312×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	175
1	123	175
2	214	175
3	436	175
4	1062	175
5	2449	175
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

507×	`times-frac_binary64`
351×	`fma-def_binary64`
333×	`associate-/l*_binary64`
262×	`div-sub_binary64`
250×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	202	25
5	448	25
6	1376	25

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

7.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.1b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 80 to 46 computations (42.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.7b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	8.4b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series116.0ms (0.8%)

Counts

4 → 114

Calls

42 calls:

9.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	x	0
8.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	z	0
6.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	y	-inf
6.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	y	inf
6.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))	y	inf

rewrite43.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

169×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`
160×	`add-cbrt-cube_binary64`
156×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	325	55

Stop Event

1×	node limit

Counts

4 → 149

simplify101.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

933×	`cancel-sign-sub-inv_binary64`
447×	`sub-neg_binary64`
341×	`times-frac_binary64`
261×	`+-commutative_binary64`
255×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	5495
1	876	5208
2	4054	5103

Stop Event

1×	node limit

Counts

263 → 238

prune247.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	231	7	238
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	232	7	239

Error

Counts

239 → 7

Alt Table

Status	Error	Program
	18.1b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))
	19.5b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	15.9b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (pow.f64 (-.f64 (.f64 z t) x) 3)))) (+.f64 x 1))
▶	1.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	7.1b	(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (fma.f64 z t (neg.f64 x)))) (+.f64 x 1))
	15.3b	(/.f64 (+.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)) 3))) (+.f64 x 1))
	7.2b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)

Compiler

Compiled 8054 to 3446 computations (57.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	1.9b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	5.9b	(/.f64 z (-.f64 (*.f64 t z) x))

series94.0ms (0.6%)

Counts

3 → 120

Calls

30 calls:

7.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))	x	-inf
6.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))	y	-inf
6.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))	y	inf
6.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))	x	0
6.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))	y	0

rewrite37.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

178×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`
167×	`add-cbrt-cube_binary64`
164×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	58
1	344	58

Stop Event

1×	node limit

Counts

3 → 88

simplify92.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

631×	`cancel-sign-sub-inv_binary64`
319×	`times-frac_binary64`
282×	`sub-neg_binary64`
241×	`associate-+r+_binary64`
238×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	5306
1	779	5116
2	3604	4995

Stop Event

1×	node limit

Counts

208 → 168

prune290.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	248	7	255

Error

Counts

255 → 7

Alt Table

Status	Error	Program
	18.1b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))
	19.5b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	15.9b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (pow.f64 (-.f64 (.f64 z t) x) 3)))) (+.f64 x 1))
✓	1.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
▶	7.1b	(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (fma.f64 z t (neg.f64 x)))) (+.f64 x 1))
	15.3b	(/.f64 (+.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)) 3))) (+.f64 x 1))
	7.2b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)

Compiler

Compiled 9590 to 4012 computations (58.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 y z) x)
✓	0.7b	(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (fma.f64 z t (neg.f64 x)))) (+.f64 x 1))
✓	8.4b	(/.f64 (-.f64 (*.f64 y z) x) (fma.f64 z t (neg.f64 x)))

series98.0ms (0.6%)

Counts

2 → 96

Calls

24 calls:

7.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (fma.f64 z t (neg.f64 x)))) (+.f64 x 1))	x	-inf
6.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (fma.f64 z t (neg.f64 x)))) (+.f64 x 1))	y	-inf
6.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (fma.f64 z t (neg.f64 x)))) (+.f64 x 1))	x	0
6.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (fma.f64 z t (neg.f64 x)))) (+.f64 x 1))	y	inf
6.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (fma.f64 z t (neg.f64 x)))) (+.f64 x 1))	t	0

rewrite63.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

269×	`log1p-udef_binary64`
164×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
154×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	317	33
2	4884	33

Stop Event

1×	node limit

Counts

2 → 69

simplify100.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

933×	`cancel-sign-sub-inv_binary64`
447×	`sub-neg_binary64`
341×	`times-frac_binary64`
261×	`+-commutative_binary64`
255×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	5431
1	875	5144
2	4054	5039

Stop Event

1×	node limit

Counts

165 → 153

prune197.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	196	7	203

Error

Counts

203 → 7

Alt Table

Status	Error	Program
	18.1b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))
	19.5b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	15.9b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (pow.f64 (-.f64 (.f64 z t) x) 3)))) (+.f64 x 1))
✓	1.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	7.1b	(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (fma.f64 z t (neg.f64 x)))) (+.f64 x 1))
	15.3b	(/.f64 (+.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)) 3))) (+.f64 x 1))
▶	7.2b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)

Compiler

Compiled 6812 to 3051 computations (55.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 y z) x)
✓	0.1b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)
✓	0.8b	(/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))))
✓	8.4b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))

series7.8s (51%)

Counts

3 → 144

Calls

36 calls:

1.9s	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)	y	inf
1.9s	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)	y	-inf
1.9s	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)	t	0
737.0ms	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)	z	-inf
682.0ms	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)	z	inf

rewrite47.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

188×	`add-sqr-sqrt_binary64`
179×	`log1p-expm1-u_binary64`
179×	`expm1-log1p-u_binary64`
178×	`add-cbrt-cube_binary64`
173×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	69
1	367	66

Stop Event

1×	node limit

Counts

3 → 108

simplify739.0ms (4.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5092	106653

Stop Event

1×	node limit

Counts

252 → 195

prune1.5s (9.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	238	7	245

Error

Counts

245 → 7

Alt Table

Status	Error	Program
	18.1b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))
	19.5b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	15.9b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (pow.f64 (-.f64 (.f64 z t) x) 3)))) (+.f64 x 1))
✓	1.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	7.1b	(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (fma.f64 z t (neg.f64 x)))) (+.f64 x 1))
	15.3b	(/.f64 (+.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)) 3))) (+.f64 x 1))
✓	7.2b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)

Compiler

Compiled 71216 to 45339 computations (36.3% saved)

regimes775.0ms (5.1%)

Accuracy

Total 0.6b remaining (96%)

Threshold costs 0.6b (96%)

Counts

131 → 2

Compiler

Compiled 14465 to 9322 computations (35.6% saved)

bsearch5.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

Steps

Iters	Point		Range
#hash((type . real) (value . +inf))	∈ [	#hash((type . real) (value . +inf))	,	#hash((type . real) (value . NaN))	]

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	81
1	39	81
2	48	81
3	52	81
4	54	81

Stop Event

1×

saturated

end128.0ms (0.8%)

Stop Event

1×

fuel

Compiler

Compiled 277 to 163 computations (41.2% saved)

Details

analyze1.5s (10.1%)

sample1.2s (7.5%)

preprocess38.0ms (0.3%)

simplify18.0ms (0.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series116.0ms (0.8%)

rewrite43.0ms (0.3%)

simplify101.0ms (0.7%)

prune247.0ms (1.6%)

localize12.0ms (0.1%)

series94.0ms (0.6%)

rewrite37.0ms (0.2%)

simplify92.0ms (0.6%)

prune290.0ms (1.9%)

localize10.0ms (0.1%)

series98.0ms (0.6%)

rewrite63.0ms (0.4%)

simplify100.0ms (0.7%)

prune197.0ms (1.3%)

localize11.0ms (0.1%)

series7.8s (51%)

rewrite47.0ms (0.3%)

simplify739.0ms (4.8%)

prune1.5s (9.9%)

regimes775.0ms (5.1%)

bsearch5.0ms (0%)

simplify6.0ms (0%)

end128.0ms (0.8%)

Profiling