Details

analyze1.0s (5.5%)

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
3.1%	96.7%	0.2%	7
6.2%	93.6%	0.2%	8
8.6%	91.2%	0.2%	9
28.1%	71.7%	0.2%	10
31%	68.8%	0.2%	11
40.5%	59.3%	0.2%	12
49.6%	50.2%	0.2%	13
59%	40.8%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.2s (6.4%)

Results

1.1s	8256×	body	128	valid
52.0ms	308×	body	128	invalid

Compiler

Compiled 44 to 28 computations (36.4% saved)

preprocess54.0ms (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)

simplify19.0ms (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

6.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.8b	(/.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)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.0b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	9.8b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series116.0ms (0.6%)

Counts

3 → 105

Calls

33 calls:

13.0ms	(/.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	0
6.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	x	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

rewrite41.0ms (0.2%)

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	48
1	325	48

Stop Event

1×	node limit

Counts

3 → 110

simplify93.0ms (0.5%)

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	5463
1	876	5176
2	4054	5071

Stop Event

1×	node limit

Counts

215 → 198

prune199.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	195	3	198
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	195	4	199

Error

Counts

199 → 4

Alt Table

Status	Error	Program
	2.2b	(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)))
	18.6b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
▶	2.2b	(/.f64 (+.f64 x (-.f64 (/.f64 y (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))
✓	6.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 6945 to 2988 computations (57% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x (-.f64 (/.f64 y (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))
✓	2.7b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	4.3b	(/.f64 y (/.f64 (-.f64 (*.f64 t z) x) z))
✓	8.5b	(/.f64 (-.f64 (*.f64 t z) x) z)

series124.0ms (0.7%)

Counts

4 → 168

Calls

42 calls:

8.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 y (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))	t	0
7.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 y (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))	x	inf
6.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 y (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))	x	0
6.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 y (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))	y	-inf
6.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 y (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))	y	inf

rewrite46.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

192×	`add-sqr-sqrt_binary64`
184×	`log1p-expm1-u_binary64`
184×	`expm1-log1p-u_binary64`
183×	`add-cbrt-cube_binary64`
178×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	67
1	365	67

Stop Event

1×	node limit

Counts

4 → 108

simplify100.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

711×	`cancel-sign-sub-inv_binary64`
337×	`times-frac_binary64`
305×	`sub-neg_binary64`
255×	`associate-+r+_binary64`
248×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	5920
1	825	5609
2	3791	5488

Stop Event

1×	node limit

Counts

276 → 193

prune173.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	194	3	197

Error

Counts

197 → 3

Alt Table

Status	Error	Program
	2.2b	(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)))
▶	0.0b	(/.f64 (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
✓	6.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 7164 to 2825 computations (60.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (/.f64 x z))
✓	0.0b	(/.f64 (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	2.7b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	4.3b	(/.f64 y (-.f64 t (/.f64 x z)))

series105.0ms (0.6%)

Counts

3 → 93

Calls

33 calls:

9.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))	y	inf
7.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))	z	-inf
6.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))	y	-inf
6.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))	x	0
6.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))	t	0

rewrite38.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

206×	`add-sqr-sqrt_binary64`
199×	`log1p-expm1-u_binary64`
199×	`expm1-log1p-u_binary64`
198×	`add-cbrt-cube_binary64`
191×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	48
1	391	48

Stop Event

1×	node limit

Counts

3 → 85

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

708×	`cancel-sign-sub-inv_binary64`
322×	`times-frac_binary64`
296×	`sub-neg_binary64`
237×	`associate-+r+_binary64`
230×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	4498
1	764	4229
2	3575	4150

Stop Event

1×	node limit

Counts

178 → 152

prune166.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	192	3	195

Error

Counts

195 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
▶	0.1b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x))))) -1)
✓	6.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 7019 to 2898 computations (58.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 x 1) (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x)))))
✓	0.1b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x))))) -1)
	2.7b	(/.f64 x (-.f64 (*.f64 t z) x))
	4.3b	(/.f64 y (-.f64 t (/.f64 x z)))

series12.1s (65%)

Counts

2 → 96

Calls

24 calls:

4.3s	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x))))) -1)	y	inf
3.9s	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x))))) -1)	y	-inf
1.8s	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x))))) -1)	t	0
710.0ms	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x))))) -1)	z	-inf
708.0ms	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x))))) -1)	z	inf

rewrite33.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

225×	`add-sqr-sqrt_binary64`
217×	`log1p-expm1-u_binary64`
217×	`expm1-log1p-u_binary64`
216×	`add-cbrt-cube_binary64`
208×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	65
1	433	65

Stop Event

1×	node limit

Counts

2 → 36

simplify800.0ms (4.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6384	126105

Stop Event

1×	node limit

Counts

132 → 106

prune1.5s (8.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	186	3	189

Error

Counts

189 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
✓	0.1b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (-.f64 (/.f64 y (-.f64 t (/.f64 x z))) (/.f64 x (-.f64 (*.f64 t z) x))))) -1)
✓	6.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 84355 to 52277 computations (38% saved)

regimes493.0ms (2.7%)

Accuracy

Total -0.2b remaining (-363.6%)

Threshold costs -0.2b (-363.6%)

Counts

89 → 1

Compiler

Compiled 10075 to 6462 computations (35.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	29	37
2	41	37
3	47	37
4	50	37

Stop Event

1×

saturated

end63.0ms (0.3%)

Stop Event

1×

done

Compiler

Compiled 131 to 81 computations (38.2% saved)

Details

analyze1.0s (5.5%)

sample1.2s (6.4%)

preprocess54.0ms (0.3%)

simplify19.0ms (0.1%)

prune2.0ms (0%)

localize12.0ms (0.1%)

series116.0ms (0.6%)

rewrite41.0ms (0.2%)

simplify93.0ms (0.5%)

prune199.0ms (1.1%)

localize14.0ms (0.1%)

series124.0ms (0.7%)

rewrite46.0ms (0.2%)

simplify100.0ms (0.5%)

prune173.0ms (0.9%)

localize15.0ms (0.1%)

series105.0ms (0.6%)

rewrite38.0ms (0.2%)

simplify77.0ms (0.4%)

prune166.0ms (0.9%)

localize13.0ms (0.1%)

series12.1s (65%)

rewrite33.0ms (0.2%)

simplify800.0ms (4.3%)

prune1.5s (8.1%)

regimes493.0ms (2.7%)

simplify4.0ms (0%)

end63.0ms (0.3%)

Profiling