Details

analyze1.3s (4.8%)

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%	96.6%	3.4%	6
0%	96.6%	3.4%	7
0%	95%	5%	8
0%	85.7%	14.3%	9
0%	64.3%	35.7%	10
0%	64.3%	35.7%	11
0.5%	49.2%	50.3%	12
0.7%	49%	50.3%	13
1%	47.6%	51.4%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample5.7s (21.4%)

Results

4.1s	22534×	body	128	invalid
1.6s	8256×	body	128	valid

Compiler

Compiled 50 to 36 computations (28% saved)

preprocess44.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

573×	`associate-/l*_binary64`
521×	`fma-def_binary64`
272×	`exp-sum_binary64`
215×	`associate-/r/_binary64`
205×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	416
1	315	416
2	833	384
3	2516	384
0	6	6

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l/_binary64`
548×	`associate-/r/_binary64`
488×	`associate-*l/_binary64`
274×	`unswap-sqr_binary64`
184×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	37	26
2	78	24
3	205	24
4	592	24
5	2082	24

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	26.3b	(.f64 x (.f64 (/.f64 (pow.f64 z y) (exp.f64 b)) (/.f64 (pow.f64 a t) (*.f64 y a))))
▶	1.7b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

Compiler

Compiled 132 to 87 computations (34.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (-.f64 t 1) (log.f64 a))
✓	0.3b	(*.f64 y (log.f64 z))
✓	1.0b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	1.0b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series2.0s (7.3%)

Counts

4 → 176

Calls

45 calls:

227.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	x	0
161.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	x	inf
155.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	x	-inf
131.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	z	inf
119.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))	z	0

rewrite42.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

195×	`add-sqr-sqrt_binary64`
183×	`add-cbrt-cube_binary64`
183×	`log1p-expm1-u_binary64`
183×	`expm1-log1p-u_binary64`
181×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	61
1	383	57

Stop Event

1×	node limit

Counts

4 → 98

simplify86.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-def_binary64`
351×	`times-frac_binary64`
320×	`associate-/l*_binary64`
171×	`associate-r_binary64`
156×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	4857
1	569	4089
2	1929	3766

Stop Event

1×	node limit

Counts

274 → 172

prune202.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	170	4	174

Error

Counts

174 → 4

Alt Table

Status	Error	Program
▶	25.6b	(/.f64 (.f64 (.f64 (pow.f64 z y) (/.f64 -1 a)) (pow.f64 a t)) (.f64 (/.f64 y x) (.f64 -1 (exp.f64 b))))
	28.0b	(fma.f64 1/2 (.f64 y (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (pow.f64 (log.f64 z) 2))) (fma.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) x (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y))))))
✓	1.7b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	26.6b	(.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))

Compiler

Compiled 4785 to 1965 computations (58.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 z y) (/.f64 -1 a))
✓	0.3b	(.f64 (.f64 (pow.f64 z y) (/.f64 -1 a)) (pow.f64 a t))
✓	3.0b	(/.f64 (.f64 (.f64 (pow.f64 z y) (/.f64 -1 a)) (pow.f64 a t)) (.f64 (/.f64 y x) (.f64 -1 (exp.f64 b))))
✓	5.0b	(.f64 (/.f64 y x) (.f64 -1 (exp.f64 b)))

series2.2s (8.1%)

Counts

4 → 192

Calls

48 calls:

137.0ms	(/.f64 (.f64 (.f64 (pow.f64 z y) (/.f64 -1 a)) (pow.f64 a t)) (.f64 (/.f64 y x) (.f64 -1 (exp.f64 b))))	x	0
118.0ms	(/.f64 (.f64 (.f64 (pow.f64 z y) (/.f64 -1 a)) (pow.f64 a t)) (.f64 (/.f64 y x) (.f64 -1 (exp.f64 b))))	x	inf
115.0ms	(/.f64 (.f64 (.f64 (pow.f64 z y) (/.f64 -1 a)) (pow.f64 a t)) (.f64 (/.f64 y x) (.f64 -1 (exp.f64 b))))	b	-inf
107.0ms	(/.f64 (.f64 (.f64 (pow.f64 z y) (/.f64 -1 a)) (pow.f64 a t)) (.f64 (/.f64 y x) (.f64 -1 (exp.f64 b))))	x	-inf
105.0ms	(/.f64 (.f64 (.f64 (pow.f64 z y) (/.f64 -1 a)) (pow.f64 a t)) (.f64 (/.f64 y x) (.f64 -1 (exp.f64 b))))	b	inf

rewrite42.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

198×	`add-sqr-sqrt_binary64`
183×	`log1p-expm1-u_binary64`
183×	`expm1-log1p-u_binary64`
182×	`add-log-exp_binary64`
181×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	66
1	388	59

Stop Event

1×	node limit

Counts

4 → 118

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
314×	`times-frac_binary64`
288×	`associate-/l*_binary64`
196×	`associate-r_binary64`
167×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	3930
1	818	3881
2	3350	3857

Stop Event

1×	node limit

Counts

310 → 190

prune177.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	190	4	194

Error

Counts

194 → 4

Alt Table

Status	Error	Program
✓	25.6b	(/.f64 (.f64 (.f64 (pow.f64 z y) (/.f64 -1 a)) (pow.f64 a t)) (.f64 (/.f64 y x) (.f64 -1 (exp.f64 b))))
	28.0b	(fma.f64 1/2 (.f64 y (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (pow.f64 (log.f64 z) 2))) (fma.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) x (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y))))))
✓	1.7b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
▶	26.6b	(.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))

Compiler

Compiled 5363 to 1609 computations (70% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 a (+.f64 t -1))
✓	0.3b	(*.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y))
✓	0.5b	(/.f64 (*.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b))
✓	6.6b	(.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))

series2.8s (10.4%)

Counts

4 → 204

Calls

51 calls:

134.0ms	(.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))	x	0
117.0ms	(.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))	b	inf
109.0ms	(/.f64 (*.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b))	b	inf
105.0ms	(.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))	b	-inf
105.0ms	(/.f64 (*.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b))	b	-inf

rewrite61.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

181×	`add-sqr-sqrt_binary64`
169×	`log1p-expm1-u_binary64`
169×	`expm1-log1p-u_binary64`
167×	`add-cbrt-cube_binary64`
167×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	62
1	349	62

Stop Event

1×	node limit

Counts

4 → 139

simplify103.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-def_binary64`
270×	`associate-/l/_binary64`
253×	`associate-/l*_binary64`
227×	`associate-r_binary64`
198×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	5051
1	753	4951
2	2864	4535

Stop Event

1×	node limit

Counts

343 → 235

prune234.0ms (0.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	235	4	239

Error

Counts

239 → 4

Alt Table

Status	Error	Program
✓	25.6b	(/.f64 (.f64 (.f64 (pow.f64 z y) (/.f64 -1 a)) (pow.f64 a t)) (.f64 (/.f64 y x) (.f64 -1 (exp.f64 b))))
▶	28.0b	(fma.f64 1/2 (.f64 y (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (pow.f64 (log.f64 z) 2))) (fma.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) x (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y))))))
✓	1.7b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
✓	26.6b	(.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))

Compiler

Compiled 6049 to 2534 computations (58.1% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(fma.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) x (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y)))))
✓	1.2b	(fma.f64 1/2 (.f64 y (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (pow.f64 (log.f64 z) 2))) (fma.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) x (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y))))))
✓	3.0b	(/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b))))
✓	5.7b	(.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y))))

series8.4s (31.5%)

Counts

4 → 264

Calls

66 calls:

462.0ms	(fma.f64 1/2 (.f64 y (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (pow.f64 (log.f64 z) 2))) (fma.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) x (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y))))))	x	0
357.0ms	(fma.f64 1/2 (.f64 y (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (pow.f64 (log.f64 z) 2))) (fma.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) x (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y))))))	x	inf
335.0ms	(fma.f64 1/2 (.f64 y (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (pow.f64 (log.f64 z) 2))) (fma.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) x (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y))))))	b	inf
333.0ms	(fma.f64 1/2 (.f64 y (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (pow.f64 (log.f64 z) 2))) (fma.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) x (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y))))))	b	-inf
331.0ms	(fma.f64 1/2 (.f64 y (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (pow.f64 (log.f64 z) 2))) (fma.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) x (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y))))))	x	-inf

rewrite54.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

298×	`log1p-expm1-u_binary64`
298×	`expm1-log1p-u_binary64`
294×	`add-cbrt-cube_binary64`
294×	`add-log-exp_binary64`
293×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	191
1	650	185

Stop Event

1×	node limit

Counts

4 → 65

simplify255.0ms (1%)

Algorithm

1×	egg-herbie

Rules

825×	`associate-/l*_binary64`
733×	`times-frac_binary64`
530×	`fma-def_binary64`
235×	`*-commutative_binary64`
200×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	620	20723
1	2551	19997

Stop Event

1×	node limit

Counts

329 → 195

prune274.0ms (1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

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

Error

Counts

199 → 4

Alt Table

Status	Error	Program
✓	25.6b	(/.f64 (.f64 (.f64 (pow.f64 z y) (/.f64 -1 a)) (pow.f64 a t)) (.f64 (/.f64 y x) (.f64 -1 (exp.f64 b))))
✓	28.0b	(fma.f64 1/2 (.f64 y (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (pow.f64 (log.f64 z) 2))) (fma.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) x (.f64 (.f64 x (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b)))) (+.f64 (log.f64 z) (.f64 (.f64 1/6 (pow.f64 (log.f64 z) 3)) (.f64 y y))))))
✓	1.7b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
✓	26.6b	(.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))

Compiler

Compiled 16797 to 5509 computations (67.2% saved)

regimes2.5s (9.5%)

Accuracy

Total 2.0b remaining (98.5%)

Threshold costs 0b (0%)

Counts

194 → 1

Compiler

Compiled 62059 to 39869 computations (35.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	29	28
2	33	28
3	35	28
4	36	28

Stop Event

1×

saturated

end94.0ms (0.4%)

Stop Event

1×

done

Compiler

Compiled 181 to 113 computations (37.6% saved)

Details

analyze1.3s (4.8%)

sample5.7s (21.4%)

preprocess44.0ms (0.2%)

simplify22.0ms (0.1%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series2.0s (7.3%)

rewrite42.0ms (0.2%)

simplify86.0ms (0.3%)

prune202.0ms (0.8%)

localize17.0ms (0.1%)

series2.2s (8.1%)

rewrite42.0ms (0.2%)

simplify83.0ms (0.3%)

prune177.0ms (0.7%)

localize17.0ms (0.1%)

series2.8s (10.4%)

rewrite61.0ms (0.2%)

simplify103.0ms (0.4%)

prune234.0ms (0.9%)

localize28.0ms (0.1%)

series8.4s (31.5%)

rewrite54.0ms (0.2%)

simplify255.0ms (1%)

prune274.0ms (1%)

regimes2.5s (9.5%)

simplify3.0ms (0%)

end94.0ms (0.4%)

Profiling