Details

analyze1.7s (7.6%)

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)

sample5.5s (24.7%)

Results

3.9s	22230×	body	128	invalid
1.5s	8256×	body	128	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify54.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

615×	`associate-/l/_binary64`
552×	`associate-/r/_binary64`
488×	`associate-*l/_binary64`
352×	`associate-*r/_binary64`
345×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	37	26
2	78	24
3	186	24
4	517	24
5	1664	24
6	4362	24
7	4750	24
8	5045	24

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	23.4b	(.f64 (.f64 (pow.f64 a (-.f64 t 1)) (/.f64 (pow.f64 z y) (exp.f64 b))) (/.f64 x y))
▶	1.9b	(/.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 90 computations (31.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 t 1) (log.f64 a))
✓	0.3b	(*.f64 y (log.f64 z))
✓	0.9b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	1.2b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series1.8s (7.9%)

Counts

4 → 176

Calls

4 calls:

1.0s	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
495.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
172.0ms	(*.f64 y (log.f64 z))
58.0ms	(*.f64 (-.f64 t 1) (log.f64 a))

rewrite93.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

348×	`log1p-udef_binary64`
195×	`add-sqr-sqrt_binary64`
183×	`log1p-expm1-u_binary64`
183×	`expm1-log1p-u_binary64`
181×	`add-log-exp_binary64`

Counts

4 → 100

Calls

4 calls:

91.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
91.0ms	(*.f64 y (log.f64 z))
91.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
91.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	61
1	381	57
2	4837	57
3	5391	57
0	0	0
1	0	0

simplify126.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
399×	`fma-neg_binary64`
351×	`times-frac_binary64`
320×	`associate-/l*_binary64`
270×	`associate-/r*_binary64`

Counts

276 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	4857
1	543	4089
2	1840	3766
3	4936	3764
4	5225	3764

prune200.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	167	7	174
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	168	8	176

Error

0.0b

Counts

176 → 8

Alt Table

Status	Error	Program
▶	20.2b	(/.f64 (.f64 x (.f64 (pow.f64 a t) (/.f64 (pow.f64 z y) a))) y)
	25.9b	(pow.f64 (sqrt.f64 (.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (-.f64 t 1))) (exp.f64 b)))) 2)
	32.4b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (-.f64 t 1))) (exp.f64 b)) (cbrt.f64 (*.f64 y y))) (/.f64 x (cbrt.f64 y)))
	20.8b	(.f64 (.f64 x (/.f64 (*.f64 (pow.f64 z y) (pow.f64 a (-.f64 t 1))) (exp.f64 b))) (/.f64 1 y))
	23.2b	(.f64 (/.f64 (.f64 (pow.f64 a t) (/.f64 (pow.f64 z y) a)) y) (-.f64 x (*.f64 b x)))
	22.7b	(.f64 x (/.f64 1 (.f64 (/.f64 y (*.f64 (pow.f64 z y) (pow.f64 a (-.f64 t 1)))) (exp.f64 b))))
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	31.5b	(fma.f64 (/.f64 (/.f64 (/.f64 (pow.f64 z y) a) (exp.f64 b)) y) x (fma.f64 1/6 (.f64 (/.f64 (pow.f64 (log.f64 a) 3) y) (.f64 (/.f64 (/.f64 (pow.f64 z y) a) (exp.f64 b)) (.f64 x (pow.f64 t 3)))) (fma.f64 1/2 (.f64 (/.f64 (pow.f64 (log.f64 a) 2) y) (.f64 t (.f64 t (.f64 x (/.f64 (/.f64 (pow.f64 z y) a) (exp.f64 b)))))) (.f64 (/.f64 (log.f64 a) y) (.f64 t (.f64 x (/.f64 (/.f64 (pow.f64 z y) a) (exp.f64 b))))))))

Compiler

Compiled 5050 to 2038 computations (59.6% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 z y) a)
✓	0.0b	(*.f64 (pow.f64 a t) (/.f64 (pow.f64 z y) a))
✓	0.0b	(.f64 x (.f64 (pow.f64 a t) (/.f64 (pow.f64 z y) a)))
✓	2.0b	(/.f64 (.f64 x (.f64 (pow.f64 a t) (/.f64 (pow.f64 z y) a))) y)

series3.4s (15.5%)

Counts

4 → 204

Calls

4 calls:

1.7s	(/.f64 (.f64 x (.f64 (pow.f64 a t) (/.f64 (pow.f64 z y) a))) y)
917.0ms	(.f64 x (.f64 (pow.f64 a t) (/.f64 (pow.f64 z y) a)))
579.0ms	(*.f64 (pow.f64 a t) (/.f64 (pow.f64 z y) a))
209.0ms	(/.f64 (pow.f64 z y) a)

rewrite112.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

314×	`prod-diff_binary64`
244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`
241×	`log-pow_binary64`
136×	`add-sqr-sqrt_binary64`

Counts

4 → 129

Calls

4 calls:

109.0ms	(/.f64 (pow.f64 z y) a)
109.0ms	(*.f64 (pow.f64 a t) (/.f64 (pow.f64 z y) a))
109.0ms	(.f64 x (.f64 (pow.f64 a t) (/.f64 (pow.f64 z y) a)))
109.0ms	(/.f64 (.f64 x (.f64 (pow.f64 a t) (/.f64 (pow.f64 z y) a))) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	55
1	262	55
2	3566	55
3	4937	55
4	5471	55
0	0	0
1	0	0

simplify117.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

768×	`times-frac_binary64`
597×	`associate-/r*_binary64`
383×	`associate-/r/_binary64`
327×	`fma-def_binary64`
213×	`associate-/l/_binary64`

Counts

333 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	3722
1	564	3708
2	1865	3680
3	4630	3680
4	5245	3680

prune184.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	207	5	212

Error

Counts

212 → 5

Alt Table

Status	Error	Program
	22.3b	(/.f64 (.f64 (pow.f64 z y) (.f64 (pow.f64 a t) x)) (*.f64 y a))
	32.4b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (-.f64 t 1))) (exp.f64 b)) (cbrt.f64 (*.f64 y y))) (/.f64 x (cbrt.f64 y)))
	22.7b	(.f64 x (/.f64 1 (.f64 (/.f64 y (*.f64 (pow.f64 z y) (pow.f64 a (-.f64 t 1)))) (exp.f64 b))))
▶	20.2b	(/.f64 (/.f64 (*.f64 x (pow.f64 a t)) (/.f64 a (pow.f64 z y))) y)
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

Compiler

Compiled 4686 to 1390 computations (70.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 x (pow.f64 a t)) (/.f64 a (pow.f64 z y)))
✓	0.0b	(/.f64 a (pow.f64 z y))
✓	0.0b	(*.f64 x (pow.f64 a t))
✓	2.0b	(/.f64 (/.f64 (*.f64 x (pow.f64 a t)) (/.f64 a (pow.f64 z y))) y)

series2.6s (11.9%)

Counts

4 → 192

Calls

4 calls:

1.1s	(/.f64 (*.f64 x (pow.f64 a t)) (/.f64 a (pow.f64 z y)))
1.0s	(/.f64 (/.f64 (*.f64 x (pow.f64 a t)) (/.f64 a (pow.f64 z y))) y)
259.0ms	(*.f64 x (pow.f64 a t))
235.0ms	(/.f64 a (pow.f64 z y))

rewrite120.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
153×	`egg-rr`
140×	`add-sqr-sqrt_binary64`
131×	`log1p-expm1-u_binary64`

Counts

4 → 153

Calls

4 calls:

115.0ms	(/.f64 (*.f64 x (pow.f64 a t)) (/.f64 a (pow.f64 z y)))
115.0ms	(/.f64 a (pow.f64 z y))
115.0ms	(*.f64 x (pow.f64 a t))
115.0ms	(/.f64 (/.f64 (*.f64 x (pow.f64 a t)) (/.f64 a (pow.f64 z y))) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	268	49
2	3879	49
3	4972	49
4	4996	49
0	0	0
1	0	0

simplify104.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

893×	`associate-/l*_binary64`
774×	`times-frac_binary64`
426×	`fma-def_binary64`
268×	`associate-/r/_binary64`
177×	`associate-r_binary64`

Counts

345 → 218

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	3195
1	495	3183
2	1756	3167
3	4925	3167
4	4988	3167

prune169.0ms (0.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	218	5	223

Error

Counts

223 → 5

Alt Table

Status	Error	Program
▶	22.3b	(/.f64 (.f64 (pow.f64 z y) (.f64 (pow.f64 a t) x)) (*.f64 y a))
	32.4b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (-.f64 t 1))) (exp.f64 b)) (cbrt.f64 (*.f64 y y))) (/.f64 x (cbrt.f64 y)))
	22.7b	(.f64 x (/.f64 1 (.f64 (/.f64 y (*.f64 (pow.f64 z y) (pow.f64 a (-.f64 t 1)))) (exp.f64 b))))
✓	20.2b	(/.f64 (/.f64 (*.f64 x (pow.f64 a t)) (/.f64 a (pow.f64 z y))) y)
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

Compiler

Compiled 4824 to 1298 computations (73.1% saved)

localize11.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (pow.f64 z y) (.f64 (pow.f64 a t) x))
✓	0.0b	(*.f64 (pow.f64 a t) x)
✓	3.9b	(/.f64 (.f64 (pow.f64 z y) (.f64 (pow.f64 a t) x)) (*.f64 y a))

series3.0s (13.7%)

Counts

3 → 156

Calls

3 calls:

1.9s	(/.f64 (.f64 (pow.f64 z y) (.f64 (pow.f64 a t) x)) (*.f64 y a))
888.0ms	(.f64 (pow.f64 z y) (.f64 (pow.f64 a t) x))
190.0ms	(*.f64 (pow.f64 a t) x)

rewrite225.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

299×	`prod-diff_binary64`
240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
237×	`log-pow_binary64`
134×	`add-sqr-sqrt_binary64`

Counts

3 → 93

Calls

3 calls:

223.0ms	(.f64 (pow.f64 z y) (.f64 (pow.f64 a t) x))
222.0ms	(*.f64 (pow.f64 a t) x)
222.0ms	(/.f64 (.f64 (pow.f64 z y) (.f64 (pow.f64 a t) x)) (*.f64 y a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	259	39
2	3625	39
3	4960	39
4	5460	39
0	0	0
1	0	0

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

873×	`associate-/l*_binary64`
804×	`times-frac_binary64`
694×	`fma-def_binary64`
180×	`associate-/r/_binary64`
161×	`associate-r_binary64`

Counts

249 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	2652
1	436	2620
2	1604	2574
3	4925	2574
4	4985	2574

prune128.0ms (0.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	144	5	149

Error

Counts

149 → 5

Alt Table

Status	Error	Program
✓	22.3b	(/.f64 (.f64 (pow.f64 z y) (.f64 (pow.f64 a t) x)) (*.f64 y a))
	32.4b	(.f64 (/.f64 (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (-.f64 t 1))) (exp.f64 b)) (cbrt.f64 (*.f64 y y))) (/.f64 x (cbrt.f64 y)))
	22.7b	(.f64 x (/.f64 1 (.f64 (/.f64 y (*.f64 (pow.f64 z y) (pow.f64 a (-.f64 t 1)))) (exp.f64 b))))
✓	20.2b	(/.f64 (/.f64 (*.f64 x (pow.f64 a t)) (/.f64 a (pow.f64 z y))) y)
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

Compiler

Compiled 3245 to 865 computations (73.3% saved)

regimes2.3s (10.2%)

Accuracy

Total 1.8b remaining (98.7%)

Threshold costs 0b (0%)

Counts

195 → 1

Compiler

Compiled 48430 to 32070 computations (33.8% 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
5	34	28

end87.0ms (0.4%)

Compiler: Compiled 162 to 111 computations (31.5% saved)

Details

analyze1.7s (7.6%)

sample5.5s (24.7%)

simplify54.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series1.8s (7.9%)

rewrite93.0ms (0.4%)

simplify126.0ms (0.6%)

prune200.0ms (0.9%)

localize10.0ms (0%)

series3.4s (15.5%)

rewrite112.0ms (0.5%)

simplify117.0ms (0.5%)

prune184.0ms (0.8%)

localize13.0ms (0.1%)

series2.6s (11.9%)

rewrite120.0ms (0.5%)

simplify104.0ms (0.5%)

prune169.0ms (0.8%)

localize11.0ms (0%)

series3.0s (13.7%)

rewrite225.0ms (1%)

simplify91.0ms (0.4%)

prune128.0ms (0.6%)

regimes2.3s (10.2%)

simplify3.0ms (0%)

end87.0ms (0.4%)

Profiling