Details

analyze1.1s (16.3%)

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
0%	99.8%	0.2%	9
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample103.0ms (1.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	23×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify126.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1539×	`fma-neg_binary64`
1346×	`fma-def_binary64`
1046×	`div-sub_binary64`
750×	`associate-/r/_binary64`
420×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	49	16
3	96	16
4	183	16
5	339	16
6	657	16
7	1726	16
8	2830	16
9	2687	16
10	2951	16
11	3172	16
12	3258	16
13	4297	16
14	5213	16

prune2.0ms (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

11.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.8b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 33 computations (44.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	11.4b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series69.0ms (1%)

Counts

2 → 69

Calls

2 calls:

63.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
6.0ms	(-.f64 x (*.f64 y z))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 54

Calls

2 calls:

5.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
2.0ms	(-.f64 x (*.f64 y z))

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

807×	`fma-def_binary64`
729×	`cancel-sign-sub-inv_binary64`
205×	`sub-neg_binary64`
190×	`div-sub_binary64`
182×	`fma-neg_binary64`

Counts

123 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	3797
1	628	3572
2	2362	3442
3	4895	3442
4	5108	3442

prune120.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	115	11	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	11	127

Error

3.3b

Counts

127 → 11

Alt Table

Status	Error	Program
	12.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 a z)))))
	29.3b	(/.f64 x (-.f64 t (*.f64 a z)))
	34.9b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 a z)))))
	38.6b	(-.f64 (fma.f64 (/.f64 y (.f64 a a)) (/.f64 t z) (/.f64 y a)) (/.f64 x (.f64 z a)))
	38.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	40.0b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
	12.6b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	36.6b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
	44.7b	(-.f64 (fma.f64 (/.f64 a t) (/.f64 (.f64 z x) t) (fma.f64 (/.f64 (.f64 a a) (pow.f64 t 3)) (.f64 z (.f64 z x)) (/.f64 x t))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y (.f64 z z)) t) (fma.f64 (/.f64 y t) z (/.f64 y (/.f64 (pow.f64 (/.f64 t z) 3) (*.f64 a a))))))
▶	11.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	42.2b	(/.f64 y a)

Compiler

Compiled 3860 to 1208 computations (68.7% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.1b	(/.f64 1 (-.f64 t (*.f64 a z)))
✓	11.4b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))

series89.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

69.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
20.0ms	(/.f64 1 (-.f64 t (*.f64 a z)))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`

Counts

2 → 79

Calls

2 calls:

8.0ms	(/.f64 1 (-.f64 t (*.f64 a z)))
8.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))

simplify145.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

717×	`cancel-sign-sub-inv_binary64`
335×	`fma-neg_binary64`
295×	`distribute-rgt-in_binary64`
210×	`times-frac_binary64`
205×	`sub-neg_binary64`

Counts

175 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	5382
1	682	4890
2	2696	4652
3	4643	4651
4	4987	4651

prune159.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	203	11	214

Error

2.1b

Counts

214 → 11

Alt Table

Status	Error	Program
	12.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 a z)))))
	29.3b	(/.f64 x (-.f64 t (*.f64 a z)))
	36.6b	(/.f64 (.f64 (-.f64 x (.f64 y z)) (fma.f64 y z x)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
▶	12.6b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
✓	11.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	34.8b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	34.9b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 a z)))))
	38.6b	(-.f64 (fma.f64 (/.f64 y (.f64 a a)) (/.f64 t z) (/.f64 y a)) (/.f64 x (.f64 z a)))
	38.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	40.0b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
	42.2b	(/.f64 y a)

Compiler

Compiled 5594 to 1958 computations (65% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z))))
✓	2.3b	(/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a)))
✓	5.0b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
✓	9.6b	(cbrt.f64 (-.f64 x (*.f64 y z)))

series355.0ms (5.1%)

Counts

4 → 192

Calls

4 calls:

147.0ms	(/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a)))
85.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
65.0ms	(.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z))))
57.0ms	(cbrt.f64 (-.f64 x (*.f64 y z)))

rewrite52.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
41×	`cbrt-prod_binary64`
41×	`add-cube-cbrt_binary64`
40×	`cbrt-div_binary64`

Counts

4 → 175

Calls

4 calls:

17.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
7.0ms	(.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z))))
5.0ms	(/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a)))
2.0ms	(cbrt.f64 (-.f64 x (*.f64 y z)))

simplify328.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-def_binary64`
319×	`*-commutative_binary64`
229×	`sub-neg_binary64`
189×	`cancel-sign-sub-inv_binary64`
178×	`fma-neg_binary64`

Counts

367 → 480

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	868	17175
1	2873	15541
2	4873	15522
3	5299	15522

prune472.0ms (6.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	626	0	626
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	626	11	637

Error

2.1b

Counts

637 → 11

Alt Table

Status	Error	Program
▶	12.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 a z)))))
	29.3b	(/.f64 x (-.f64 t (*.f64 a z)))
	36.6b	(/.f64 (.f64 (-.f64 x (.f64 y z)) (fma.f64 y z x)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
✓	12.6b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
✓	11.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	34.8b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	34.9b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 a z)))))
	38.6b	(-.f64 (fma.f64 (/.f64 y (.f64 a a)) (/.f64 t z) (/.f64 y a)) (/.f64 x (.f64 z a)))
	38.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	40.0b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
	42.2b	(/.f64 y a)

Compiler

Compiled 31512 to 10761 computations (65.9% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))
✓	4.5b	(/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 a z))))
✓	6.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 a z)))))
✓	7.7b	(cbrt.f64 (-.f64 t (*.f64 a z)))

series498.0ms (7.1%)

Counts

4 → 192

Calls

4 calls:

307.0ms	(/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 a z))))
67.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 a z)))))
67.0ms	(.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))
56.0ms	(cbrt.f64 (-.f64 t (*.f64 a z)))

rewrite69.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
53×	`add-exp-log_binary64`
51×	`times-frac_binary64`
46×	`*-un-lft-identity_binary64`
43×	`cbrt-prod_binary64`

Counts

4 → 193

Calls

4 calls:

22.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 a z)))))
7.0ms	(.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (*.f64 a z))))
5.0ms	(/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 a z))))
2.0ms	(cbrt.f64 (-.f64 t (*.f64 a z)))

simplify354.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-def_binary64`
321×	`*-commutative_binary64`
262×	`sub-neg_binary64`
211×	`cancel-sign-sub-inv_binary64`
155×	`distribute-neg-in_binary64`

Counts

385 → 513

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	905	18612
1	2988	17553
2	4992	17553
3	5000	17553

prune553.0ms (7.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	653	0	653
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	653	11	664

Error

2.1b

Counts

664 → 11

Alt Table

Status	Error	Program
✓	12.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 a z)))))
	29.3b	(/.f64 x (-.f64 t (*.f64 a z)))
	36.6b	(/.f64 (.f64 (-.f64 x (.f64 y z)) (fma.f64 y z x)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
✓	12.6b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
✓	11.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	34.8b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	34.9b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 a z)))))
	38.6b	(-.f64 (fma.f64 (/.f64 y (.f64 a a)) (/.f64 t z) (/.f64 y a)) (/.f64 x (.f64 z a)))
	38.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	40.0b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
	42.2b	(/.f64 y a)

Compiler

Compiled 34662 to 12860 computations (62.9% saved)

regimes1.3s (18%)

Accuracy

Total 3.3b remaining (64.2%)

Threshold costs 0b (0%)

Counts

121 → 3

Compiler

Compiled 17980 to 10040 computations (44.2% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	73
1	39	73
2	60	73
3	72	73
4	79	73
5	80	73
6	80	73

end1.0ms (0%)

Compiler: Compiled 54 to 21 computations (61.1% saved)

sample889.0ms (12.8%)

Algorithm

1×

intervals

Results

385.0ms	8000×	body	128	valid
32.0ms	702×	body	128	invalid

Compiler

Compiled 330 to 171 computations (48.2% saved)

Details

analyze1.1s (16.3%)

sample103.0ms (1.5%)

simplify126.0ms (1.8%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series69.0ms (1%)

rewrite10.0ms (0.1%)

simplify109.0ms (1.6%)

prune120.0ms (1.7%)

localize11.0ms (0.2%)

series89.0ms (1.3%)

rewrite21.0ms (0.3%)

simplify145.0ms (2.1%)

prune159.0ms (2.3%)

localize12.0ms (0.2%)

series355.0ms (5.1%)

rewrite52.0ms (0.7%)

simplify328.0ms (4.7%)

prune472.0ms (6.8%)

localize18.0ms (0.3%)

series498.0ms (7.1%)

rewrite69.0ms (1%)

simplify354.0ms (5.1%)

prune553.0ms (7.9%)

regimes1.3s (18%)

bsearch4.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample889.0ms (12.8%)

Profiling