Details

analyze870.0ms (8.6%)

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
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (12.1%)

Results

1.1s	8256×	body	128	valid
87.0ms	736×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify95.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1028×	`fma-neg_binary64`
470×	`fma-def_binary64`
271×	`associate-/l*_binary64`
255×	`cancel-sign-sub-inv_binary64`
255×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	24	13
2	53	13
3	109	13
4	185	13
5	336	13
6	549	13
7	870	13
8	1606	13
9	1757	13
10	1912	13
11	1986	13
12	1980	13
13	1985	13
14	1993	13
15	1993	13
16	1872	13

prune3.0ms (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

5.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.0b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
▶	6.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 y t))
✓	0.2b	(/.f64 (/.f64 2 (-.f64 y t)) z)
✓	5.9b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series78.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

45.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
20.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
13.0ms	(/.f64 2 (-.f64 y t))

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

249×	`times-frac_binary64`
180×	`add-sqr-sqrt_binary64`
171×	`*-un-lft-identity_binary64`
121×	`add-cube-cbrt_binary64`
67×	`associate-r_binary64`

Counts

3 → 234

Calls

3 calls:

17.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
8.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
3.0ms	(/.f64 2 (-.f64 y t))

simplify210.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

292×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
234×	`associate-/r*_binary64`
216×	`times-frac_binary64`
212×	`*-commutative_binary64`

Counts

342 → 351

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	422	7256
1	1123	6896
2	3980	6860
3	4623	6847
4	4989	6847

prune302.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	341	10	351
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	343	10	353

Error

0.0b

Counts

353 → 10

Alt Table

Status	Error	Program
	5.3b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))
	6.0b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
	33.2b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	6.3b	(.f64 x (/.f64 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (-.f64 y t))) z))
	2.1b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	5.5b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
▶	1.8b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 z)))
	5.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
	5.4b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	6.5b	(.f64 1 (.f64 2 (/.f64 x (*.f64 (-.f64 y t) z))))

Compiler

Compiled 7723 to 3645 computations (52.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))
✓	0.6b	(cbrt.f64 (/.f64 2 (-.f64 y t)))
✓	0.6b	(cbrt.f64 z)
✓	1.4b	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series1.6s (16.1%)

Counts

4 → 108

Calls

4 calls:

1.5s	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
67.0ms	(*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))
46.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))
41.0ms	(cbrt.f64 z)

rewrite59.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`cbrt-prod_binary64`
117×	`add-sqr-sqrt_binary64`
108×	`*-un-lft-identity_binary64`
95×	`times-frac_binary64`
60×	`add-cube-cbrt_binary64`

Counts

4 → 187

Calls

4 calls:

20.0ms	(*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))
16.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
3.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))
1.0ms	(cbrt.f64 z)

simplify165.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

830×	`associate-r_binary64`
651×	`associate-l_binary64`
312×	`fma-def_binary64`
248×	`times-frac_binary64`
226×	`associate-/r*_binary64`

Counts

295 → 337

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	620	10879
1	1592	10020
2	5754	10020

prune580.0ms (5.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	506	1	507
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	507	10	517

Error

Counts

517 → 10

Alt Table

Status	Error	Program
	33.2b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	6.3b	(.f64 x (/.f64 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (-.f64 y t))) z))
	2.1b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	5.5b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
✓	1.8b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 z)))
	6.0b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
▶	1.7b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 z)))
	5.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
	5.4b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	6.5b	(.f64 1 (.f64 2 (/.f64 x (*.f64 (-.f64 y t) z))))

Compiler

Compiled 24493 to 14184 computations (42.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (/.f64 2 (-.f64 y t)))
	0.6b	(cbrt.f64 z)
✓	1.0b	(cbrt.f64 2)
✓	1.4b	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series1.4s (13.4%)

Counts

2 → 48

Calls

2 calls:

1.4s	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
0.0ms	(cbrt.f64 2)

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
14×	`cbrt-unprod_binary64`
14×	`prod-exp_binary64`
8×	`cbrt-undiv_binary64`

Counts

2 → 48

Calls

2 calls:

18.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
1.0ms	(cbrt.f64 2)

simplify110.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-def_binary64`
484×	`associate-r_binary64`
369×	`associate-l_binary64`
283×	`times-frac_binary64`
267×	`*-commutative_binary64`

Counts

96 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	4881
1	1000	4313
2	4049	4153
3	4995	4153

prune341.0ms (3.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	297	10	307

Error

Counts

307 → 10

Alt Table

Status	Error	Program
	33.2b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	6.3b	(.f64 x (/.f64 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (-.f64 y t))) z))
▶	2.1b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	5.5b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
✓	1.8b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 z)))
	6.0b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
✓	1.7b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 z)))
	5.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
	5.4b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	6.5b	(.f64 1 (.f64 2 (/.f64 x (*.f64 (-.f64 y t) z))))

Compiler

Compiled 14926 to 8836 computations (40.8% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (-.f64 y t))
	0.6b	(cbrt.f64 z)
	1.0b	(cbrt.f64 2)
✓	1.4b	(.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))))

series1.5s (14.3%)

Counts

2 → 72

Calls

2 calls:

1.4s	(.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))))
30.0ms	(cbrt.f64 (-.f64 y t))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-exp-log_binary64`
29×	`add-cbrt-cube_binary64`
24×	`cbrt-unprod_binary64`
24×	`prod-exp_binary64`
18×	`cbrt-undiv_binary64`

Counts

2 → 74

Calls

2 calls:

19.0ms	(.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))))
2.0ms	(cbrt.f64 (-.f64 y t))

simplify134.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

659×	`fma-def_binary64`
528×	`associate-r_binary64`
412×	`associate-l_binary64`
315×	`times-frac_binary64`
235×	`associate-/l*_binary64`

Counts

146 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	480	7162
1	1350	5907
2	4907	5841
3	5341	5841

prune425.0ms (4.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	384	0	384
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	384	10	394

Error

Counts

394 → 10

Alt Table

Status	Error	Program
	33.2b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	6.3b	(.f64 x (/.f64 (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (-.f64 y t))) z))
✓	2.1b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	5.5b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
✓	1.8b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 z)))
	6.0b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
✓	1.7b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 z)))
	5.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
	5.4b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	6.5b	(.f64 1 (.f64 2 (/.f64 x (*.f64 (-.f64 y t) z))))

Compiler

Compiled 19351 to 10115 computations (47.7% saved)

regimes785.0ms (7.7%)

Accuracy

Total 1.8b remaining (98.4%)

Threshold costs 0b (0%)

Counts

113 → 1

Compiler

Compiled 18607 to 12097 computations (35% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	51
1	24	51
2	29	51
3	31	51
4	32	51
5	32	51

end149.0ms (1.5%)

Compiler: Compiled 301 to 191 computations (36.5% saved)

Details

analyze870.0ms (8.6%)

sample1.2s (12.1%)

simplify95.0ms (0.9%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series78.0ms (0.8%)

rewrite53.0ms (0.5%)

simplify210.0ms (2.1%)

prune302.0ms (3%)

localize12.0ms (0.1%)

series1.6s (16.1%)

rewrite59.0ms (0.6%)

simplify165.0ms (1.6%)

prune580.0ms (5.7%)

localize20.0ms (0.2%)

series1.4s (13.4%)

rewrite23.0ms (0.2%)

simplify110.0ms (1.1%)

prune341.0ms (3.4%)

localize19.0ms (0.2%)

series1.5s (14.3%)

rewrite33.0ms (0.3%)

simplify134.0ms (1.3%)

prune425.0ms (4.2%)

regimes785.0ms (7.7%)

simplify4.0ms (0%)

end149.0ms (1.5%)

Profiling