Details

analyze1.2s (19.1%)

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
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.1s (17.5%)

Results

972.0ms	8255×	body	128	valid
88.0ms	774×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify112.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1405×	`fma-def_binary64`
906×	`div-sub_binary64`
613×	`distribute-rgt-in_binary64`
583×	`fma-neg_binary64`
525×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	43	14
3	82	14
4	164	14
5	304	14
6	655	14
7	1590	14
8	3046	14
9	2781	14
10	2954	14
11	3028	14
12	3116	14
13	4289	14
14	5187	14

prune3.0ms (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

2.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

Compiler

Compiled 58 to 31 computations (46.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	2.5b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

series92.0ms (1.4%)

Counts

3 → 144

Calls

3 calls:

41.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
33.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
17.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
28×	`add-cube-cbrt_binary64`

Counts

3 → 122

Calls

3 calls:

11.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
8.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
2.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

simplify129.0ms (2%)

Algorithm

1×	egg-herbie

Rules

766×	`cancel-sign-sub-inv_binary64`
498×	`sub-neg_binary64`
213×	`associate--l+_binary64`
201×	`fma-neg_binary64`
200×	`+-commutative_binary64`

Counts

266 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	6584
1	983	6188
2	3712	6122
3	5248	6122

prune173.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	236	6	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	236	7	243

Error

Counts

243 → 7

Alt Table

Status	Error	Program
✓	2.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
	12.1b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
	12.1b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 (-.f64 z a))))
▶	2.8b	(+.f64 x (.f64 y (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (cbrt.f64 (-.f64 z a)))))
	34.7b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (-.f64 z t))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 z a))))
	6.8b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))))
	18.4b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))

Compiler

Compiled 6423 to 1935 computations (69.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a))))
✓	0.4b	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
✓	0.6b	(cbrt.f64 (-.f64 z a))
✓	2.5b	(.f64 y (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (cbrt.f64 (-.f64 z a))))

series247.0ms (3.9%)

Counts

4 → 132

Calls

4 calls:

155.0ms	(/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a))))
34.0ms	(.f64 y (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (cbrt.f64 (-.f64 z a))))
32.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
24.0ms	(cbrt.f64 (-.f64 z a))

rewrite116.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

187×	`times-frac_binary64`
153×	`add-sqr-sqrt_binary64`
150×	`associate-r_binary64`
137×	`*-un-lft-identity_binary64`
124×	`cbrt-div_binary64`

Counts

4 → 283

Calls

4 calls:

37.0ms	(.f64 y (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (cbrt.f64 (-.f64 z a))))
11.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
10.0ms	(/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a))))
2.0ms	(cbrt.f64 (-.f64 z a))

simplify207.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

377×	`associate-/l*_binary64`
339×	`associate-/l/_binary64`
302×	`fma-def_binary64`
294×	`associate-/r*_binary64`
250×	`times-frac_binary64`

Counts

415 → 476

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	744	13154
1	2019	12596
2	4960	12596

prune475.0ms (7.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	576	0	576
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	576	7	583

Error

Counts

583 → 7

Alt Table

Status	Error	Program
✓	2.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
	12.1b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
	12.1b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 (-.f64 z a))))
✓	2.8b	(+.f64 x (.f64 y (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (cbrt.f64 (-.f64 z a)))))
	34.7b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (-.f64 z t))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 z a))))
▶	6.8b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))))
	18.4b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))

Compiler

Compiled 23025 to 7882 computations (65.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
✓	0.6b	(cbrt.f64 (-.f64 z t))
✓	7.1b	(.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a)))

series152.0ms (2.4%)

Counts

4 → 132

Calls

4 calls:

70.0ms	(/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))
30.0ms	(.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a)))
29.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
23.0ms	(cbrt.f64 (-.f64 z t))

rewrite63.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64`
125×	`*-un-lft-identity_binary64`
88×	`cbrt-prod_binary64`
80×	`times-frac_binary64`
54×	`associate-r_binary64`

Counts

4 → 235

Calls

4 calls:

18.0ms	(.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a)))
9.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
6.0ms	(/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))
2.0ms	(cbrt.f64 (-.f64 z t))

simplify217.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-def_binary64`
337×	`associate-/l*_binary64`
262×	`*-commutative_binary64`
230×	`times-frac_binary64`
162×	`associate-/r*_binary64`

Counts

367 → 438

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	723	11261
1	2070	10207
2	4934	10205
3	4991	10205

prune513.0ms (8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	540	0	540
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	540	7	547

Error

Counts

547 → 7

Alt Table

Status	Error	Program
✓	2.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
▶	12.1b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
	12.1b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 (-.f64 z a))))
✓	2.8b	(+.f64 x (.f64 y (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (cbrt.f64 (-.f64 z a)))))
	34.7b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (-.f64 z t))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 z a))))
✓	6.8b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))))
	18.4b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))

Compiler

Compiled 20599 to 7250 computations (64.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
✓	0.0b	(*.f64 (-.f64 z t) y)
✓	12.5b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))

series101.0ms (1.6%)

Counts

3 → 120

Calls

3 calls:

40.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
35.0ms	(*.f64 (-.f64 z t) y)
26.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

6.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))
6.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
4.0ms	(*.f64 (-.f64 z t) y)

simplify117.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

900×	`fma-def_binary64`
563×	`cancel-sign-sub-inv_binary64`
333×	`sub-neg_binary64`
196×	`div-sub_binary64`
166×	`fma-neg_binary64`

Counts

192 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	258	4561
1	727	4147
2	2695	3786
3	4896	3783
4	4975	3783

prune140.0ms (2.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	185	3	188
Fresh	3	0	3
Picked	0	1	1
Done	1	2	3
Total	189	6	195

Error

Counts

195 → 6

Alt Table

Status	Error	Program
✓	12.1b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
	3.2b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 z a) y)))
✓	2.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
	12.1b	(+.f64 x (/.f64 1 (/.f64 (-.f64 z a) (*.f64 (-.f64 z t) y))))
	3.0b	(+.f64 x (*.f64 (-.f64 z t) (/.f64 y (-.f64 z a))))
✓	2.8b	(+.f64 x (.f64 y (/.f64 (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (cbrt.f64 (-.f64 z a)))))

Compiler

Compiled 4543 to 1338 computations (70.5% saved)

regimes995.0ms (15.5%)

Accuracy

Total 1.3b remaining (99.4%)

Threshold costs 0b (0%)

Counts

87 → 3

Compiler

Compiled 14359 to 8490 computations (40.9% saved)

bsearch35.0ms (0.5%)

Steps

Iters	Range		Point
3	4.7040481619453334e-141	5.867681099870885e-141	5.547445071430195e-141
9	-6.710145116893561e+62	-3.2955716048680465e+57	-7.319216852213493e+57

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	58
1	31	58
2	39	58
3	43	58
4	45	58
5	45	58

end82.0ms (1.3%)

Compiler: Compiled 199 to 107 computations (46.2% saved)

Details

analyze1.2s (19.1%)

sample1.1s (17.5%)

simplify112.0ms (1.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series92.0ms (1.4%)

rewrite30.0ms (0.5%)

simplify129.0ms (2%)

prune173.0ms (2.7%)

localize11.0ms (0.2%)

series247.0ms (3.9%)

rewrite116.0ms (1.8%)

simplify207.0ms (3.2%)

prune475.0ms (7.4%)

localize11.0ms (0.2%)

series152.0ms (2.4%)

rewrite63.0ms (1%)

simplify217.0ms (3.4%)

prune513.0ms (8%)

localize7.0ms (0.1%)

series101.0ms (1.6%)

rewrite19.0ms (0.3%)

simplify117.0ms (1.8%)

prune140.0ms (2.2%)

regimes995.0ms (15.5%)

bsearch35.0ms (0.5%)

simplify6.0ms (0.1%)

end82.0ms (1.3%)

Profiling