Details

analyze888.0ms (10.6%)

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)

sample102.0ms (1.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	23×	body	128	invalid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify98.0ms (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

4.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.1b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.3b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize7.0ms (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)
✓	4.9b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series64.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

35.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
19.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
9.0ms	(/.f64 2 (-.f64 y t))

rewrite52.0ms (0.6%)

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:

15.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
9.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
4.0ms	(/.f64 2 (-.f64 y t))

simplify218.0ms (2.6%)

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

prune318.0ms (3.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	340	11	351
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	341	12	353

Error

Counts

353 → 12

Alt Table

Status	Error	Program
	30.7b	(.f64 (/.f64 x (.f64 (sqrt.f64 (-.f64 y t)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) (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)))
	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	5.1b	(*.f64 (/.f64 (/.f64 2 (-.f64 y t)) z) x)
	3.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
	4.8b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	5.6b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	6.3b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	5.3b	(*.f64 x (/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z))
	35.0b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	26.1b	(.f64 x (cbrt.f64 (pow.f64 (/.f64 2 (.f64 (-.f64 y t) z)) 3)))
	2.3b	(.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)))

Compiler

Compiled 7793 to 3681 computations (52.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series1.4s (17.1%)

Counts

4 → 108

Calls

4 calls:

1.3s	(.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))))
36.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
33.0ms	(cbrt.f64 z)
28.0ms	(cbrt.f64 (-.f64 y t))

rewrite43.0ms (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:

16.0ms	(.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))))
11.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
2.0ms	(cbrt.f64 (-.f64 y t))
1.0ms	(cbrt.f64 z)

simplify276.0ms (3.3%)

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

prune435.0ms (5.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	418	0	418
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	418	12	430

Error

Counts

430 → 12

Alt Table

Status	Error	Program
	30.7b	(.f64 (/.f64 x (.f64 (sqrt.f64 (-.f64 y t)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) (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)))
	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	5.1b	(*.f64 (/.f64 (/.f64 2 (-.f64 y t)) z) x)
	3.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
	4.8b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	5.6b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	6.3b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	5.3b	(*.f64 x (/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z))
	35.0b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	26.1b	(.f64 x (cbrt.f64 (pow.f64 (/.f64 2 (.f64 (-.f64 y t) z)) 3)))
▶	2.3b	(.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)))

Compiler

Compiled 19984 to 9839 computations (50.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(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))))

series1.4s (17.1%)

Counts

2 → 48

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))))
0.0ms	(cbrt.f64 2)

rewrite41.0ms (0.5%)

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 → 70

Calls

2 calls:

31.0ms	(.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))))
1.0ms	(cbrt.f64 2)

simplify130.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-def_binary64`
427×	`associate-r_binary64`
348×	`associate-l_binary64`
264×	`*-commutative_binary64`
251×	`times-frac_binary64`

Counts

118 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	378	6155
1	1058	4922
2	4043	4688
3	5014	4688

prune433.0ms (5.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	384	0	384
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	384	12	396

Error

Counts

396 → 12

Alt Table

Status	Error	Program
	30.7b	(.f64 (/.f64 x (.f64 (sqrt.f64 (-.f64 y t)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) (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)))
	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	5.1b	(*.f64 (/.f64 (/.f64 2 (-.f64 y t)) z) x)
▶	3.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
	4.8b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	5.6b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	6.3b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	5.3b	(*.f64 x (/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z))
	35.0b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	26.1b	(.f64 x (cbrt.f64 (pow.f64 (/.f64 2 (.f64 (-.f64 y t) z)) 3)))
✓	2.3b	(.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)))

Compiler

Compiled 19537 to 10342 computations (47.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.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))
✓	2.9b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))

series80.0ms (1%)

Counts

2 → 72

Calls

2 calls:

41.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
38.0ms	(/.f64 2 (cbrt.f64 (-.f64 y t)))

rewrite78.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

203×	`times-frac_binary64`
149×	`add-sqr-sqrt_binary64`
123×	`*-un-lft-identity_binary64`
97×	`add-cube-cbrt_binary64`
94×	`associate-r_binary64`

Counts

2 → 200

Calls

2 calls:

38.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
4.0ms	(/.f64 2 (cbrt.f64 (-.f64 y t)))

simplify198.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

623×	`associate-*r/_binary64`
436×	`associate-*l/_binary64`
395×	`associate-/l*_binary64`
292×	`times-frac_binary64`
289×	`associate-/r*_binary64`

Counts

272 → 319

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	485	8987
1	1478	7839
2	4890	7809
3	5014	7809

prune399.0ms (4.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	554	1	555
Fresh	2	7	9
Picked	1	0	1
Done	2	0	2
Total	559	8	567

Error

Counts

567 → 8

Alt Table

Status	Error	Program
	4.8b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	5.6b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	6.3b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	5.3b	(*.f64 x (/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z))
	35.0b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	30.7b	(.f64 (/.f64 x (.f64 (sqrt.f64 (-.f64 y t)) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	5.1b	(*.f64 (/.f64 (/.f64 2 (-.f64 y t)) z) x)
	4.7b	(/.f64 (/.f64 (*.f64 x 2) (-.f64 y t)) z)

Compiler

Compiled 19045 to 7622 computations (60% saved)

regimes760.0ms (9.1%)

Accuracy

Total 1.0b remaining (98%)

Threshold costs 0b (0%)

Counts

90 → 3

Compiler

Compiled 14957 to 9666 computations (35.4% saved)

bsearch3.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-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	33	108
1	47	108
2	57	108
3	63	108
4	67	108
5	68	108
6	67	108

end1.0ms (0%)

Compiler: Compiled 75 to 35 computations (53.3% saved)

sample811.0ms (9.7%)

Algorithm

1×

intervals

Results

354.0ms	8000×	body	128	valid
30.0ms	663×	body	128	invalid

Compiler

Compiled 238 to 146 computations (38.7% saved)

Details

analyze888.0ms (10.6%)

sample102.0ms (1.2%)

simplify98.0ms (1.2%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series64.0ms (0.8%)

rewrite52.0ms (0.6%)

simplify218.0ms (2.6%)

prune318.0ms (3.8%)

localize15.0ms (0.2%)

series1.4s (17.1%)

rewrite43.0ms (0.5%)

simplify276.0ms (3.3%)

prune435.0ms (5.2%)

localize17.0ms (0.2%)

series1.4s (17.1%)

rewrite41.0ms (0.5%)

simplify130.0ms (1.6%)

prune433.0ms (5.2%)

localize9.0ms (0.1%)

series80.0ms (1%)

rewrite78.0ms (0.9%)

simplify198.0ms (2.4%)

prune399.0ms (4.8%)

regimes760.0ms (9.1%)

bsearch3.0ms (0%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample811.0ms (9.7%)

Profiling