Details

analyze985.0ms (9.8%)

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 (11.9%)

Results

1.0s	8256×	body	128	valid
82.0ms	716×	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

4.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.1b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.2b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 2 (-.f64 y t)) z)
✓	5.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series61.0ms (0.6%)

Counts

2 → 84

Calls

2 calls:

41.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
19.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64`
161×	`add-sqr-sqrt_binary64`
152×	`*-un-lft-identity_binary64`
110×	`add-cube-cbrt_binary64`
67×	`associate-r_binary64`

Counts

2 → 195

Calls

2 calls:

18.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
7.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)

simplify194.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

696×	`fma-def_binary64`
238×	`associate-/l*_binary64`
223×	`associate-/r*_binary64`
212×	`associate-l_binary64`
206×	`associate-r_binary64`

Counts

279 → 298

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	379	6143
1	1008	5846
2	3651	5786
3	4777	5786
4	4976	5786
5	4973	5786

prune277.0ms (2.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	285	13	298
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	287	13	300

Error

Counts

300 → 13

Alt Table

Status	Error	Program
	5.8b	(.f64 x (/.f64 (/.f64 (/.f64 2 (-.f64 y t)) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)))
▶	2.0b	(.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	31.9b	(*.f64 (/.f64 x (sqrt.f64 (-.f64 y t))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) z))
	6.6b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	6.3b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	5.2b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	6.3b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	25.3b	(.f64 (sqrt.f64 (.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))) (sqrt.f64 (.f64 2 (/.f64 x (*.f64 (-.f64 y t) z)))))
	31.8b	(.f64 (.f64 x (sqrt.f64 (/.f64 2 (-.f64 y t)))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) z))
	4.7b	(.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))
	45.6b	(.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (+.f64 (sqrt.f64 y) (sqrt.f64 t)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 y) (sqrt.f64 t))) (cbrt.f64 z)))
	5.4b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	5.1b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))

Compiler

Compiled 6885 to 3203 computations (53.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
✓	0.6b	(cbrt.f64 z)
✓	0.6b	(cbrt.f64 (-.f64 y t))
✓	3.6b	(.f64 x (/.f64 (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series1.5s (14.4%)

Counts

4 → 108

Calls

4 calls:

1.4s	(.f64 x (/.f64 (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
34.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
30.0ms	(cbrt.f64 (-.f64 y t))
30.0ms	(cbrt.f64 z)

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
36×	`cbrt-prod_binary64`
35×	`*-un-lft-identity_binary64`
35×	`add-exp-log_binary64`
30×	`associate-r_binary64`

Counts

4 → 143

Calls

4 calls:

18.0ms	(.f64 x (/.f64 (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
8.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
2.0ms	(cbrt.f64 (-.f64 y t))
1.0ms	(cbrt.f64 z)

simplify172.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
532×	`associate-l_binary64`
324×	`associate-/r*_binary64`
272×	`times-frac_binary64`
193×	`*-commutative_binary64`

Counts

251 → 284

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	581	8349
1	1556	7441
2	4856	7401
3	5235	7401

prune507.0ms (5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	418	0	418
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	418	13	431

Error

Counts

431 → 13

Alt Table

Status	Error	Program
	5.8b	(.f64 x (/.f64 (/.f64 (/.f64 2 (-.f64 y t)) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)))
✓	2.0b	(.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	31.9b	(*.f64 (/.f64 x (sqrt.f64 (-.f64 y t))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) z))
	6.6b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	6.3b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	5.2b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	6.3b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	25.3b	(.f64 (sqrt.f64 (.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))) (sqrt.f64 (.f64 2 (/.f64 x (*.f64 (-.f64 y t) z)))))
	31.8b	(.f64 (.f64 x (sqrt.f64 (/.f64 2 (-.f64 y t)))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) z))
▶	4.7b	(.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))
	45.6b	(.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (+.f64 (sqrt.f64 y) (sqrt.f64 t)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 y) (sqrt.f64 t))) (cbrt.f64 z)))
	5.4b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	5.1b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))

Compiler

Compiled 20026 to 9871 computations (50.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z)
✓	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)))
✓	4.0b	(.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))

series1.7s (17%)

Counts

4 → 132

Calls

4 calls:

1.5s	(/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z)
75.0ms	(.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))
67.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))
65.0ms	(*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))

rewrite118.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

342×	`times-frac_binary64`
276×	`cbrt-prod_binary64`
273×	`add-sqr-sqrt_binary64`
267×	`*-un-lft-identity_binary64`
177×	`add-cube-cbrt_binary64`

Counts

4 → 365

Calls

4 calls:

28.0ms	(.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))
20.0ms	(*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))
7.0ms	(/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z)
3.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))

simplify378.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

518×	`*-commutative_binary64`
380×	`associate-/l*_binary64`
306×	`associate-*r/_binary64`
286×	`fma-def_binary64`
217×	`associate-*l/_binary64`

Counts

497 → 551

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	722	15970
1	1823	15424
2	4854	15321
3	4997	15321
4	4978	15321

prune770.0ms (7.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	686	1	687
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	689	11	700

Error

Counts

700 → 11

Alt Table

Status	Error	Program
	5.1b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
▶	4.7b	(.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 1 (-.f64 y t)))) z))
	31.9b	(*.f64 (/.f64 x (sqrt.f64 (-.f64 y t))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) z))
	6.3b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	5.2b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	6.3b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	25.3b	(.f64 (sqrt.f64 (.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))) (sqrt.f64 (.f64 2 (/.f64 x (*.f64 (-.f64 y t) z)))))
	31.8b	(.f64 (.f64 x (sqrt.f64 (/.f64 2 (-.f64 y t)))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) z))
✓	2.0b	(.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
✓	4.7b	(.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))
	5.4b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))

Compiler

Compiled 26944 to 16109 computations (40.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (/.f64 2 (-.f64 y t)))
✓	0.6b	(cbrt.f64 (/.f64 1 (-.f64 y t)))
✓	1.0b	(cbrt.f64 2)
✓	4.0b	(.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 1 (-.f64 y t)))) z))

series136.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

100.0ms	(.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 1 (-.f64 y t)))) z))
36.0ms	(cbrt.f64 (/.f64 1 (-.f64 y t)))
0.0ms	(cbrt.f64 2)

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-exp-log_binary64`
27×	`add-cbrt-cube_binary64`
24×	`cbrt-prod_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`

Counts

3 → 91

Calls

3 calls:

21.0ms	(.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 1 (-.f64 y t)))) z))
3.0ms	(cbrt.f64 (/.f64 1 (-.f64 y t)))
1.0ms	(cbrt.f64 2)

simplify139.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

431×	`associate-l_binary64`
392×	`associate-r_binary64`
260×	`fma-neg_binary64`
251×	`*-commutative_binary64`
228×	`times-frac_binary64`

Counts

163 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	353	5643
1	977	4531
2	3724	3636
3	4761	3636
4	5015	3636

prune349.0ms (3.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	301	11	312

Error

Counts

312 → 11

Alt Table

Status	Error	Program
	5.1b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
✓	4.7b	(.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 1 (-.f64 y t)))) z))
	31.9b	(*.f64 (/.f64 x (sqrt.f64 (-.f64 y t))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) z))
	6.3b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	5.2b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	6.3b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	25.3b	(.f64 (sqrt.f64 (.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))) (sqrt.f64 (.f64 2 (/.f64 x (*.f64 (-.f64 y t) z)))))
	31.8b	(.f64 (.f64 x (sqrt.f64 (/.f64 2 (-.f64 y t)))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) z))
✓	2.0b	(.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
✓	4.7b	(.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))
	5.4b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))

Compiler

Compiled 12389 to 8131 computations (34.4% saved)

regimes1.2s (11.9%)

Accuracy

Total 1.1b remaining (97.7%)

Threshold costs 0b (0%)

Counts

154 → 3

Compiler

Compiled 25509 to 16808 computations (34.1% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	99
1	45	99
2	56	99
3	62	99
4	66	99
5	67	99
6	67	99

end155.0ms (1.5%)

Compiler: Compiled 370 to 214 computations (42.2% saved)

Details

analyze985.0ms (9.8%)

sample1.2s (11.9%)

simplify95.0ms (0.9%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series61.0ms (0.6%)

rewrite49.0ms (0.5%)

simplify194.0ms (1.9%)

prune277.0ms (2.7%)

localize16.0ms (0.2%)

series1.5s (14.4%)

rewrite45.0ms (0.5%)

simplify172.0ms (1.7%)

prune507.0ms (5%)

localize10.0ms (0.1%)

series1.7s (17%)

rewrite118.0ms (1.2%)

simplify378.0ms (3.7%)

prune770.0ms (7.6%)

localize14.0ms (0.1%)

series136.0ms (1.3%)

rewrite34.0ms (0.3%)

simplify139.0ms (1.4%)

prune349.0ms (3.5%)

regimes1.2s (11.9%)

bsearch6.0ms (0.1%)

simplify5.0ms (0.1%)

end155.0ms (1.5%)

Profiling