Details

analyze1.9s (30.3%)

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
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
3.7%	96.1%	0.2%	13
4.2%	94.5%	1.3%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.5s (24.9%)

Results

1.1s	8256×	body	128	valid
306.0ms	2380×	body	128	invalid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify98.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-neg_binary64`
614×	`times-frac_binary64`
480×	`neg-mul-1_binary64`
416×	`div-sub_binary64`
394×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	28	23
2	55	23
3	101	21
4	220	21
5	423	21
6	834	20
7	1845	19
8	3893	19
9	4281	19
10	4633	19
11	4956	19
12	4804	19

prune4.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	8.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 110 to 79 computations (28.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 -2 (/.f64 -2 z))
✓	0.0b	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

series57.0ms (0.9%)

Counts

4 → 108

Calls

4 calls:

30.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
14.0ms	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))
12.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
2.0ms	(+.f64 -2 (/.f64 -2 z))

rewrite70.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

183×	`*-un-lft-identity_binary64`
123×	`add-sqr-sqrt_binary64`
118×	`times-frac_binary64`
118×	`add-cube-cbrt_binary64`
96×	`prod-diff_binary64`

Counts

4 → 232

Calls

4 calls:

21.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
10.0ms	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))
6.0ms	(+.f64 -2 (/.f64 -2 z))
6.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

simplify183.0ms (3%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
571×	`distribute-rgt-in_binary64`
367×	`fma-neg_binary64`
197×	`cancel-sign-sub-inv_binary64`
197×	`times-frac_binary64`

Counts

340 → 293

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	8983
1	774	6168
2	1804	5210
3	4691	5210
4	4836	5210

prune305.0ms (5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	289	4	293
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	290	5	295

Error

Counts

295 → 5

Alt Table

Status	Error	Program
	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	21.8b	(+.f64 (/.f64 x y) (-.f64 -2 (cbrt.f64 (.f64 (.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t) (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	8.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	0.5b	(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 x (cbrt.f64 y)) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 10529 to 7370 computations (30% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 -2 (/.f64 -2 z))
✓	0.0b	(-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t)))
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
✓	0.2b	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))

series52.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

33.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
10.0ms	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))
9.0ms	(-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
13×	`fma-def_binary64`

Counts

3 → 99

Calls

3 calls:

10.0ms	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))
7.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
3.0ms	(-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t)))

simplify155.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

607×	`distribute-rgt-in_binary64`
577×	`distribute-lft-in_binary64`
485×	`fma-def_binary64`
251×	`times-frac_binary64`
230×	`associate-*l/_binary64`

Counts

195 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	3265
1	459	3050
2	1339	2815
3	4343	2815
4	4965	2815
5	4986	2815
6	4864	2815

prune163.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	190	5	195

Error

Counts

195 → 5

Alt Table

Status	Error	Program
	8.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
▶	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	12.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 4 (/.f64 4 (.f64 z z))) (.f64 t (+.f64 -2 (/.f64 2 z))))))
	0.5b	(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 x (cbrt.f64 y)) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 4522 to 3169 computations (29.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 -2 (/.f64 -2 z))
	0.0b	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

series32.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

31.0ms

(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-def_binary64`
492×	`associate-l_binary64`
423×	`associate-+l+_binary64`
379×	`associate-r_binary64`
267×	`associate-*l/_binary64`

Counts

58 → 29

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	43	1177
1	83	1126
2	164	1126
3	357	1126
4	1233	1009
5	4295	1009
6	5040	1009

prune184.0ms (3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	187	5	192

Error

Counts

192 → 5

Alt Table

Status	Error	Program
	8.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
✓	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	12.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 4 (/.f64 4 (.f64 z z))) (.f64 t (+.f64 -2 (/.f64 2 z))))))
▶	0.5b	(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 x (cbrt.f64 y)) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 5923 to 4377 computations (26.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 x (cbrt.f64 y))
✓	0.3b	(/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)

series397.0ms (6.5%)

Counts

4 → 60

Calls

4 calls:

259.0ms	(/.f64 x (cbrt.f64 y))
65.0ms	(/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
38.0ms	(cbrt.f64 y)
35.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
31×	`cbrt-prod_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`

Counts

4 → 133

Calls

4 calls:

4.0ms	(/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
2.0ms	(/.f64 x (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify97.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-def_binary64`
547×	`unswap-sqr_binary64`
530×	`times-frac_binary64`
500×	`fma-neg_binary64`
308×	`associate-l_binary64`

Counts

193 → 186

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	2082
1	254	1760
2	708	1641
3	2161	1540
4	4043	1540
5	5016	1540

prune200.0ms (3.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	222	5	227

Error

Counts

227 → 5

Alt Table

Status	Error	Program
	8.1b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
✓	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	12.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 4 (/.f64 4 (.f64 z z))) (.f64 t (+.f64 -2 (/.f64 2 z))))))
✓	0.5b	(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 x (cbrt.f64 y)) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 5770 to 3019 computations (47.7% saved)

regimes488.0ms (8%)

Accuracy

Total 0.1b remaining (83.3%)

Threshold costs 0.1b (83.3%)

Counts

74 → 1

Compiler

Compiled 9994 to 7607 computations (23.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	16	19
2	23	19
3	32	19
4	39	19
5	42	19
6	43	19
7	42	19

end87.0ms (1.4%)

Compiler: Compiled 142 to 106 computations (25.4% saved)

Details

analyze1.9s (30.3%)

sample1.5s (24.9%)

simplify98.0ms (1.6%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series57.0ms (0.9%)

rewrite70.0ms (1.1%)

simplify183.0ms (3%)

prune305.0ms (5%)

localize10.0ms (0.2%)

series52.0ms (0.8%)

rewrite24.0ms (0.4%)

simplify155.0ms (2.5%)

prune163.0ms (2.7%)

localize13.0ms (0.2%)

series32.0ms (0.5%)

rewrite1.0ms (0%)

simplify73.0ms (1.2%)

prune184.0ms (3%)

localize15.0ms (0.2%)

series397.0ms (6.5%)

rewrite16.0ms (0.3%)

simplify97.0ms (1.6%)

prune200.0ms (3.3%)

regimes488.0ms (8%)

simplify5.0ms (0.1%)

end87.0ms (1.4%)

Profiling