Details

analyze1.1s (12.8%)

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)

sample1.3s (15.4%)

Results

1.2s	8256×	body	128	valid
83.0ms	705×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify100.0ms (1.2%)

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

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

4.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.2b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
▶	4.4b	(*.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)
✓	4.3b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series95.0ms (1.1%)

Counts

3 → 108

Calls

3 calls:

66.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
19.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
10.0ms	(/.f64 2 (-.f64 y t))

rewrite60.0ms (0.7%)

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:

21.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
7.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
4.0ms	(/.f64 2 (-.f64 y t))

simplify203.0ms (2.3%)

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

prune288.0ms (3.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	342	9	351
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	342	11	353

Error

0.0b

Counts

353 → 11

Alt Table

Status	Error	Program
	54.6b	(.f64 (/.f64 x (.f64 (sqrt.f64 z) (+.f64 (sqrt.f64 y) (sqrt.f64 t)))) (/.f64 (/.f64 2 (-.f64 (sqrt.f64 y) (sqrt.f64 t))) (sqrt.f64 z)))
	4.3b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
	45.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (sqrt.f64 z))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (sqrt.f64 z)))
	5.2b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	5.5b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	4.1b	(.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)))
	32.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))
▶	3.8b	(.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))
	5.5b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
✓	4.4b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	4.0b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z)))

Compiler

Compiled 7720 to 3638 computations (52.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
✓	0.5b	(cbrt.f64 (-.f64 y t))
✓	3.0b	(.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))

series190.0ms (2.2%)

Counts

4 → 120

Calls

4 calls:

76.0ms	(.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))
45.0ms	(/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t)))
38.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
31.0ms	(cbrt.f64 (-.f64 y t))

rewrite127.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

354×	`times-frac_binary64`
255×	`add-sqr-sqrt_binary64`
253×	`*-un-lft-identity_binary64`
187×	`add-cube-cbrt_binary64`
174×	`associate-r_binary64`

Counts

4 → 359

Calls

4 calls:

38.0ms	(.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))
8.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
5.0ms	(/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t)))
2.0ms	(cbrt.f64 (-.f64 y t))

simplify304.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-*l/_binary64`
486×	`associate-/l*_binary64`
336×	`times-frac_binary64`
286×	`associate-/r*_binary64`
263×	`associate-/l/_binary64`

Counts

479 → 508

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	716	16747
1	2099	14684
2	5552	14684

prune602.0ms (6.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	606	2	608
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	610	9	619

Error

Counts

619 → 9

Alt Table

Status	Error	Program
	4.7b	(/.f64 (.f64 2 x) (.f64 (-.f64 y t) z))
	32.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))
	5.7b	(/.f64 (/.f64 (*.f64 2 x) (-.f64 y t)) z)
	4.3b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
	45.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (sqrt.f64 z))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (sqrt.f64 z)))
	5.5b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	4.1b	(.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)))
✓	4.4b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
▶	4.0b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z)))

Compiler

Compiled 23852 to 11562 computations (51.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	3.2b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z)))

series248.0ms (2.9%)

Counts

4 → 108

Calls

4 calls:

115.0ms	(/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z))
58.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z)))
38.0ms	(cbrt.f64 z)
37.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))

rewrite118.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

467×	`times-frac_binary64`
337×	`add-sqr-sqrt_binary64`
297×	`*-un-lft-identity_binary64`
219×	`add-cube-cbrt_binary64`
152×	`cbrt-prod_binary64`

Counts

4 → 404

Calls

4 calls:

40.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z)))
11.0ms	(/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify242.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-/r*_binary64`
509×	`associate-/l*_binary64`
477×	`associate-*l/_binary64`
373×	`times-frac_binary64`
338×	`associate-/l/_binary64`

Counts

512 → 603

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	565	13791
1	1630	11819
2	5334	11819

prune460.0ms (5.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	635	2	637
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	638	8	646

Error

Counts

646 → 8

Alt Table

Status	Error	Program
	4.7b	(/.f64 (.f64 2 x) (.f64 (-.f64 y t) z))
	32.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))
▶	1.6b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 z)) (*.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z))))
	45.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (sqrt.f64 z))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (sqrt.f64 z)))
	5.5b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	3.9b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 2 (/.f64 (cbrt.f64 (/.f64 1 z)) (-.f64 y t))))
✓	4.4b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	5.7b	(/.f64 (/.f64 (*.f64 2 x) (-.f64 y t)) z)

Compiler

Compiled 18012 to 6731 computations (62.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series798.0ms (9.2%)

Counts

3 → 108

Calls

3 calls:

698.0ms

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

70.0ms

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

29.0ms

(cbrt.f64 x)

rewrite241.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

308×	`times-frac_binary64`
265×	`add-sqr-sqrt_binary64`
165×	`*-un-lft-identity_binary64`
135×	`cbrt-prod_binary64`
132×	`add-exp-log_binary64`

Counts

3 → 306

Calls

3 calls:

109.0ms

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

20.0ms

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

1.0ms

(cbrt.f64 x)

simplify294.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

571×	`associate-*l/_binary64`
545×	`associate-/l*_binary64`
401×	`fma-def_binary64`
284×	`associate-/l/_binary64`
248×	`associate-/r*_binary64`

Counts

414 → 484

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	582	13408
1	1796	11422
2	4948	11324
3	5275	11324

prune394.0ms (4.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	569	0	569
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	569	8	577

Error

Counts

577 → 8

Alt Table

Status	Error	Program
	4.7b	(/.f64 (.f64 2 x) (.f64 (-.f64 y t) z))
	32.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))
✓	1.6b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 z)) (*.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z))))
	45.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (sqrt.f64 z))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (sqrt.f64 z)))
	5.5b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	3.9b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 2 (/.f64 (cbrt.f64 (/.f64 1 z)) (-.f64 y t))))
✓	4.4b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	5.7b	(/.f64 (/.f64 (*.f64 2 x) (-.f64 y t)) z)

Compiler

Compiled 19600 to 5790 computations (70.5% saved)

regimes1.3s (14.9%)

Accuracy

Total 1.7b remaining (98.7%)

Threshold costs 0b (0%)

Counts

151 → 1

Compiler

Compiled 23087 to 15212 computations (34.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-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	16	49
1	20	49
2	25	49
3	27	49
4	28	49
5	28	49

end113.0ms (1.3%)

Compiler: Compiled 215 to 137 computations (36.3% saved)

Details

analyze1.1s (12.8%)

sample1.3s (15.4%)

simplify100.0ms (1.2%)

prune4.0ms (0%)

localize6.0ms (0.1%)

series95.0ms (1.1%)

rewrite60.0ms (0.7%)

simplify203.0ms (2.3%)

prune288.0ms (3.3%)

localize14.0ms (0.2%)

series190.0ms (2.2%)

rewrite127.0ms (1.5%)

simplify304.0ms (3.5%)

prune602.0ms (6.9%)

localize12.0ms (0.1%)

series248.0ms (2.9%)

rewrite118.0ms (1.4%)

simplify242.0ms (2.8%)

prune460.0ms (5.3%)

localize13.0ms (0.2%)

series798.0ms (9.2%)

rewrite241.0ms (2.8%)

simplify294.0ms (3.4%)

prune394.0ms (4.5%)

regimes1.3s (14.9%)

simplify4.0ms (0%)

end113.0ms (1.3%)

Profiling