Details

analyze1.3s (4.9%)

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 (21.6%)

Results

4.0s	22219×	body	128	invalid
1.6s	8256×	body	128	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify51.0ms (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
	25.9b	(.f64 (.f64 (pow.f64 a (-.f64 t 1)) (/.f64 (pow.f64 z y) (exp.f64 b))) (/.f64 x y))
▶	1.1b	(/.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)

localize19.0ms (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))
✓	0.3b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
✓	0.8b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))

series2.0s (7.5%)

Counts

4 → 176

Calls

4 calls:

1.1s	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
580.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
193.0ms	(*.f64 y (log.f64 z))
61.0ms	(*.f64 (-.f64 t 1) (log.f64 a))

rewrite32.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
14×	`exp-sum_binary64`
13×	`add-cbrt-cube_binary64`

Counts

4 → 116

Calls

4 calls:

9.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
9.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
6.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
3.0ms	(*.f64 y (log.f64 z))

simplify211.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

510×	`fma-neg_binary64`
314×	`associate-r_binary64`
302×	`associate-l_binary64`
245×	`cancel-sign-sub-inv_binary64`
170×	`times-frac_binary64`

Counts

292 → 248

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	393	7243
1	895	6044
2	3341	5911
3	4549	5911
4	4999	5911
5	4924	5911

prune264.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	243	5	248
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	244	6	250

Error

Counts

250 → 6

Alt Table

Status	Error	Program
	33.5b	(+.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y)) (+.f64 (.f64 (.f64 (log.f64 a) t) (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y))) (fma.f64 1/2 (.f64 (.f64 t (.f64 t (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) x))) (/.f64 (pow.f64 (log.f64 a) 2) y)) (.f64 1/6 (.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (.f64 (pow.f64 t 3) x)) (/.f64 (pow.f64 (log.f64 a) 3) y))))))
	19.5b	(/.f64 (.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y))) (cbrt.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)))) (cbrt.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y))))) y)
▶	19.4b	(/.f64 (.f64 x (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))) (exp.f64 b))) y)
✓	1.1b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	20.7b	(/.f64 x (/.f64 y (*.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y))))
	21.1b	(.f64 x (/.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) y))

Compiler

Compiled 7468 to 3192 computations (57.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 a (+.f64 t -1))
✓	0.3b	(/.f64 (.f64 x (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))) (exp.f64 b))) y)
✓	0.5b	(*.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))
✓	1.0b	(/.f64 (*.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))) (exp.f64 b))

series3.2s (12%)

Counts

4 → 204

Calls

4 calls:

1.3s	(/.f64 (.f64 x (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))) (exp.f64 b))) y)
1.2s	(/.f64 (*.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))) (exp.f64 b))
623.0ms	(*.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))
29.0ms	(pow.f64 a (+.f64 t -1))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-exp-log_binary64`
38×	`prod-exp_binary64`
32×	`div-exp_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`add-cbrt-cube_binary64`

Counts

4 → 133

Calls

4 calls:

7.0ms	(/.f64 (.f64 x (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))) (exp.f64 b))) y)
5.0ms	(/.f64 (*.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))) (exp.f64 b))
5.0ms	(*.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))
4.0ms	(pow.f64 a (+.f64 t -1))

simplify211.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary64`
427×	`associate-/l*_binary64`
400×	`associate-r_binary64`
371×	`times-frac_binary64`
369×	`associate-l_binary64`

Counts

337 → 300

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	410	8351
1	1105	7783
2	4744	7749
3	5499	7749

prune377.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	299	1	300
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	301	5	306

Error

Counts

306 → 5

Alt Table

Status	Error	Program
▶	19.4b	(/.f64 (.f64 x (/.f64 (.f64 (*.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (exp.f64 b))) y)
✓	1.1b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	33.5b	(+.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y)) (+.f64 (.f64 (.f64 (log.f64 a) t) (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y))) (fma.f64 1/2 (.f64 (.f64 t (.f64 t (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) x))) (/.f64 (pow.f64 (log.f64 a) 2) y)) (.f64 1/6 (.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (.f64 (pow.f64 t 3) x)) (/.f64 (pow.f64 (log.f64 a) 3) y))))))
✓	19.4b	(/.f64 (.f64 x (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))) (exp.f64 b))) y)
	21.1b	(.f64 x (/.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) y))

Compiler

Compiled 8303 to 3820 computations (54% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 x (/.f64 (.f64 (*.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (exp.f64 b))) y)
✓	0.4b	(.f64 (.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2)))
✓	0.5b	(*.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2)))
✓	1.0b	(/.f64 (.f64 (.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (exp.f64 b))

series3.7s (13.9%)

Counts

4 → 228

Calls

4 calls:

1.6s	(/.f64 (.f64 x (/.f64 (.f64 (*.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (exp.f64 b))) y)
902.0ms	(/.f64 (.f64 (.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (exp.f64 b))
617.0ms	(.f64 (.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2)))
603.0ms	(*.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2)))

rewrite62.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

262×	`add-exp-log_binary64`
212×	`prod-exp_binary64`
95×	`div-exp_binary64`
90×	`pow-exp_binary64`
90×	`pow-to-exp_binary64`

Counts

4 → 204

Calls

4 calls:

11.0ms	(/.f64 (.f64 x (/.f64 (.f64 (*.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (exp.f64 b))) y)
9.0ms	(/.f64 (.f64 (.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (exp.f64 b))
7.0ms	(.f64 (.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2)))
5.0ms	(*.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2)))

simplify210.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

551×	`associate-r_binary64`
540×	`associate-l_binary64`
482×	`associate-/l*_binary64`
376×	`times-frac_binary64`
207×	`associate-/r*_binary64`

Counts

432 → 336

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	476	14070
1	1295	13154
2	5181	13154

prune408.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	336	5	341

Error

Counts

341 → 5

Alt Table

Status	Error	Program
✓	19.4b	(/.f64 (.f64 x (/.f64 (.f64 (*.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (exp.f64 b))) y)
✓	1.1b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	33.5b	(+.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y)) (+.f64 (.f64 (.f64 (log.f64 a) t) (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y))) (fma.f64 1/2 (.f64 (.f64 t (.f64 t (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) x))) (/.f64 (pow.f64 (log.f64 a) 2) y)) (.f64 1/6 (.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (.f64 (pow.f64 t 3) x)) (/.f64 (pow.f64 (log.f64 a) 3) y))))))
✓	19.4b	(/.f64 (.f64 x (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))) (exp.f64 b))) y)
▶	21.1b	(.f64 x (/.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) y))

Compiler

Compiled 12776 to 7133 computations (44.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(pow.f64 a (+.f64 t -1))
✓	0.7b	(/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b))
✓	0.8b	(*.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y))
✓	1.9b	(.f64 x (/.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) y))

series2.4s (9.2%)

Counts

3 → 168

Calls

3 calls:

1.3s	(.f64 x (/.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) y))
937.0ms	(*.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y))
153.0ms	(/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b))

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-sqr-sqrt_binary64`
68×	`add-exp-log_binary64`
60×	`times-frac_binary64`
40×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`

Counts

3 → 164

Calls

3 calls:

11.0ms	(*.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y))
10.0ms	(.f64 x (/.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) y))
4.0ms	(/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b))

simplify191.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

466×	`fma-def_binary64`
445×	`associate-r_binary64`
412×	`associate-/l*_binary64`
401×	`associate-l_binary64`
332×	`times-frac_binary64`

Counts

332 → 351

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	455	9009
1	1222	8412
2	4762	8402
3	5200	8402

prune500.0ms (1.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	400	0	400
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	400	5	405

Error

Counts

405 → 5

Alt Table

Status	Error	Program
✓	19.4b	(/.f64 (.f64 x (/.f64 (.f64 (*.f64 (pow.f64 z y) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (pow.f64 a (/.f64 (+.f64 t -1) 2))) (exp.f64 b))) y)
✓	1.1b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	33.5b	(+.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y)) (+.f64 (.f64 (.f64 (log.f64 a) t) (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y))) (fma.f64 1/2 (.f64 (.f64 t (.f64 t (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) x))) (/.f64 (pow.f64 (log.f64 a) 2) y)) (.f64 1/6 (.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (.f64 (pow.f64 t 3) x)) (/.f64 (pow.f64 (log.f64 a) 3) y))))))
✓	19.4b	(/.f64 (.f64 x (/.f64 (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))) (exp.f64 b))) y)
✓	21.1b	(.f64 x (/.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) y))

Compiler

Compiled 11264 to 5154 computations (54.2% saved)

regimes5.4s (20.4%)

Accuracy

Total 1.9b remaining (96.2%)

Threshold costs 0b (0%)

Counts

316 → 1

Compiler

Compiled 129891 to 81555 computations (37.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	22	26
2	24	26
3	25	26
4	25	26

end107.0ms (0.4%)

Compiler: Compiled 229 to 138 computations (39.7% saved)

Details

analyze1.3s (4.9%)

sample5.7s (21.6%)

simplify51.0ms (0.2%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series2.0s (7.5%)

rewrite32.0ms (0.1%)

simplify211.0ms (0.8%)

prune264.0ms (1%)

localize14.0ms (0.1%)

series3.2s (12%)

rewrite30.0ms (0.1%)

simplify211.0ms (0.8%)

prune377.0ms (1.4%)

localize15.0ms (0.1%)

series3.7s (13.9%)

rewrite62.0ms (0.2%)

simplify210.0ms (0.8%)

prune408.0ms (1.5%)

localize15.0ms (0.1%)

series2.4s (9.2%)

rewrite41.0ms (0.2%)

simplify191.0ms (0.7%)

prune500.0ms (1.9%)

regimes5.4s (20.4%)

simplify2.0ms (0%)

end107.0ms (0.4%)

Profiling