Details

analyze1.1s (14.1%)

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)

sample106.0ms (1.3%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify116.0ms (1.5%)

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

11.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.2b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 33 computations (44.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	11.0b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series65.0ms (0.8%)

Counts

2 → 69

Calls

2 calls:

60.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
5.0ms	(-.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))

simplify117.0ms (1.5%)

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

prune111.0ms (1.4%)

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

2.6b

Counts

127 → 11

Alt Table

Status	Error	Program
▶	11.2b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	35.2b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
	12.1b	(.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))))
	41.4b	(-.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))))))
	33.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
	11.4b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	12.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))))
	43.0b	(/.f64 y a)
	37.2b	(cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z))) (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))) (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))))
	31.1b	(/.f64 x (-.f64 t (*.f64 a z)))
	39.7b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))

Compiler

Compiled 3916 to 1206 computations (69.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
✓	4.8b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	11.8b	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))

series164.0ms (2.1%)

Counts

3 → 114

Calls

3 calls:

91.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
37.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))
36.0ms	(/.f64 x (-.f64 t (*.f64 a z)))

rewrite64.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`times-frac_binary64`
135×	`prod-diff_binary64`
120×	`add-sqr-sqrt_binary64`
117×	`*-un-lft-identity_binary64`
115×	`add-cube-cbrt_binary64`

Counts

3 → 236

Calls

3 calls:

16.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
6.0ms	(/.f64 x (-.f64 t (*.f64 a z)))
4.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))

simplify358.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

441×	`fma-neg_binary64`
243×	`unsub-neg_binary64`
216×	`associate-/l*_binary64`
216×	`times-frac_binary64`
203×	`associate-l_binary64`

Counts

350 → 439

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	436	21196
1	1104	16095
2	4152	15759
3	4952	15759
4	5052	15759

prune384.0ms (4.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	433	6	439
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	440	10	450

Error

0.0b

Counts

450 → 10

Alt Table

Status	Error	Program
	11.3b	(-.f64 (/.f64 1 (/.f64 (-.f64 t (.f64 a z)) x)) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	34.4b	(/.f64 (-.f64 y (/.f64 x z)) a)
	11.7b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 t (.f64 z a)))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	35.2b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
	41.4b	(-.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))))))
	33.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
	11.4b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	9.7b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
	11.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (*.f64 y z))))
▶	9.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))

Compiler

Compiled 22099 to 3607 computations (83.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
✓	4.1b	(.f64 y (/.f64 z (-.f64 t (.f64 z a))))
	4.8b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	8.5b	(/.f64 z (-.f64 t (*.f64 z a)))

series138.0ms (1.7%)

Counts

3 → 144

Calls

3 calls:

73.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
41.0ms	(.f64 y (/.f64 z (-.f64 t (.f64 z a))))
24.0ms	(/.f64 z (-.f64 t (*.f64 z a)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
15×	`fma-neg_binary64`

Counts

3 → 112

Calls

3 calls:

7.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
6.0ms	(.f64 y (/.f64 z (-.f64 t (.f64 z a))))
5.0ms	(/.f64 z (-.f64 t (*.f64 z a)))

simplify219.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

382×	`fma-neg_binary64`
271×	`distribute-rgt-neg-in_binary64`
245×	`sub-neg_binary64`
210×	`associate-/l*_binary64`
210×	`times-frac_binary64`

Counts

256 → 254

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	327	8156
1	892	7648
2	3421	6954
3	4795	6953
4	4999	6953
5	4928	6953

prune278.0ms (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	323	1	324
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	324	10	334

Error

0.0b

Counts

334 → 10

Alt Table

Status	Error	Program
▶	4.6b	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
	41.4b	(-.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))))))
	11.3b	(-.f64 (/.f64 1 (/.f64 (-.f64 t (.f64 a z)) x)) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	34.4b	(/.f64 (-.f64 y (/.f64 x z)) a)
	11.7b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 t (.f64 z a)))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	35.2b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
	33.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
	11.4b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	11.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (*.f64 y z))))
✓	9.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))

Compiler

Compiled 10058 to 2353 computations (76.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 t z) a)
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
✓	4.3b	(/.f64 y (-.f64 (/.f64 t z) a))
	4.8b	(/.f64 x (-.f64 t (*.f64 a z)))

series142.0ms (1.8%)

Counts

3 → 87

Calls

3 calls:

79.0ms	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
55.0ms	(/.f64 y (-.f64 (/.f64 t z) a))
7.0ms	(-.f64 (/.f64 t z) a)

rewrite166.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

668×	`add-sqr-sqrt_binary64`
628×	`times-frac_binary64`
508×	`*-un-lft-identity_binary64`
399×	`prod-diff_binary64`
391×	`add-cube-cbrt_binary64`

Counts

3 → 534

Calls

3 calls:

32.0ms	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
6.0ms	(-.f64 (/.f64 t z) a)
6.0ms	(/.f64 y (-.f64 (/.f64 t z) a))

simplify671.0ms (8.5%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-def_binary64`
339×	`fma-udef_binary64`
269×	`unsub-neg_binary64`
237×	`associate-/l*_binary64`
230×	`associate-l_binary64`

Counts

621 → 664

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	760	50504
1	1822	30992
2	4465	30846
3	5141	30846

prune549.0ms (6.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	731	3	734
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	735	9	744

Error

0.0b

Counts

744 → 9

Alt Table

Status	Error	Program
	35.2b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
	4.7b	(-.f64 (/.f64 1 (/.f64 (-.f64 t (*.f64 z a)) x)) (/.f64 y (-.f64 (/.f64 t z) a)))
	5.1b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 t (*.f64 z a)))) (/.f64 y (-.f64 (/.f64 t z) a)))
	33.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
	11.4b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	34.4b	(/.f64 (-.f64 y (/.f64 x z)) a)
	37.9b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (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))))))
	11.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (*.f64 y z))))
✓	9.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))

Compiler

Compiled 40543 to 5811 computations (85.7% saved)

regimes2.1s (27.1%)

Accuracy

Total 3.7b remaining (99.5%)

Threshold costs 0b (0%)

Counts

196 → 4

Compiler

Compiled 31006 to 16874 computations (45.6% saved)

bsearch8.0ms (0.1%)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
19×	`sub-neg_binary64`
15×	`*-commutative_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	169
1	62	169
2	101	169
3	126	169
4	141	169
5	144	169
6	144	169

end5.0ms (0.1%)

Compiler: Compiled 118 to 35 computations (70.3% saved)

sample925.0ms (11.7%)

Algorithm

1×

intervals

Results

393.0ms	8000×	body	128	valid
38.0ms	717×	body	128	invalid

Compiler

Compiled 359 to 177 computations (50.7% saved)

Details

analyze1.1s (14.1%)

sample106.0ms (1.3%)

simplify116.0ms (1.5%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series65.0ms (0.8%)

rewrite10.0ms (0.1%)

simplify117.0ms (1.5%)

prune111.0ms (1.4%)

localize8.0ms (0.1%)

series164.0ms (2.1%)

rewrite64.0ms (0.8%)

simplify358.0ms (4.5%)

prune384.0ms (4.8%)

localize11.0ms (0.1%)

series138.0ms (1.7%)

rewrite26.0ms (0.3%)

simplify219.0ms (2.8%)

prune278.0ms (3.5%)

localize9.0ms (0.1%)

series142.0ms (1.8%)

rewrite166.0ms (2.1%)

simplify671.0ms (8.5%)

prune549.0ms (6.9%)

regimes2.1s (27.1%)

bsearch8.0ms (0.1%)

simplify8.0ms (0.1%)

end5.0ms (0.1%)

sample925.0ms (11.7%)

Profiling