Details

analyze1.2s (21.8%)

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
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)

sample1.2s (21.8%)

Results

1.0s	8256×	body	128	valid
100.0ms	772×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify117.0ms (2.1%)

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

10.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.7b	(/.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 a z))
✓	0.0b	(-.f64 x (*.f64 y z))
✓	10.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series74.0ms (1.3%)

Counts

3 → 78

Calls

3 calls:

61.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
7.0ms	(-.f64 x (*.f64 y z))
5.0ms	(-.f64 t (*.f64 a z))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 74

Calls

3 calls:

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

simplify118.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

886×	`fma-def_binary64`
731×	`cancel-sign-sub-inv_binary64`
207×	`sub-neg_binary64`
192×	`fma-neg_binary64`
173×	`times-frac_binary64`

Counts

152 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	4118
1	671	3825
2	2454	3679
3	4965	3679
4	4935	3679

prune122.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	155	8	163
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	155	9	164

Error

2.6b

Counts

164 → 9

Alt Table

Status	Error	Program
	11.1b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	11.3b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (cbrt.f64 t) (neg.f64 (*.f64 a z))))
	36.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	29.8b	(/.f64 x (-.f64 t (*.f64 a z)))
	37.3b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 (.f64 t t) (.f64 (.f64 a z) (.f64 a z)))) (+.f64 t (*.f64 a z)))
	44.5b	(-.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))))))
▶	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	42.9b	(/.f64 y a)

Compiler

Compiled 4303 to 1247 computations (71% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 t (*.f64 a z))
	0.0b	(-.f64 x (*.f64 y z))
✓	0.4b	(/.f64 1 (-.f64 t (*.f64 a z)))
✓	10.3b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))

series82.0ms (1.4%)

Counts

2 → 96

Calls

2 calls:

61.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
21.0ms	(/.f64 1 (-.f64 t (*.f64 a z)))

rewrite16.0ms (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 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
3.0ms	(/.f64 1 (-.f64 t (*.f64 a z)))

simplify139.0ms (2.5%)

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

prune179.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	238	2	240
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	241	8	249

Error

1.9b

Counts

249 → 8

Alt Table

Status	Error	Program
▶	11.1b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	11.3b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (cbrt.f64 t) (neg.f64 (*.f64 a z))))
	36.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	35.1b	(.f64 (.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (/.f64 1 (-.f64 t (.f64 a z))))) (sqrt.f64 (/.f64 1 (-.f64 t (*.f64 a z)))))
✓	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	33.7b	(-.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))))
	42.9b	(/.f64 y a)

Compiler

Compiled 6089 to 2065 computations (66.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 t (*.f64 a z))
	0.0b	(-.f64 x (*.f64 y z))
✓	0.8b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	10.3b	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))

series124.0ms (2.2%)

Counts

2 → 120

Calls

2 calls:

62.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
61.0ms	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

2 → 120

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
5.0ms	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))

simplify208.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

398×	`sub-neg_binary64`
351×	`times-frac_binary64`
310×	`fma-neg_binary64`
262×	`associate-/l*_binary64`
231×	`associate-/r*_binary64`

Counts

240 → 261

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	8921
1	1048	8344
2	4130	8272
3	4944	8272
4	4953	8272

prune214.0ms (3.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	324	1	325
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	326	7	333

Error

1.9b

Counts

333 → 7

Alt Table

Status	Error	Program
✓	11.1b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	36.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
✓	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
▶	10.9b	(/.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 x (.f64 y z))))
	33.7b	(-.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))))
	42.9b	(/.f64 y a)

Compiler

Compiled 9435 to 2886 computations (69.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.2b	(/.f64 1 (-.f64 x (*.f64 y z)))
	0.4b	(/.f64 1 (-.f64 t (*.f64 a z)))
✓	10.2b	(/.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 x (.f64 y z))))

series91.0ms (1.6%)

Counts

2 → 96

Calls

2 calls:

72.0ms	(/.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 x (.f64 y z))))
19.0ms	(/.f64 1 (-.f64 x (*.f64 y z)))

rewrite76.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

522×	`times-frac_binary64`
234×	`*-un-lft-identity_binary64`
234×	`add-sqr-sqrt_binary64`
234×	`add-cube-cbrt_binary64`
67×	`associate-/r/_binary64`

Counts

2 → 324

Calls

2 calls:

13.0ms	(/.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 x (.f64 y z))))
3.0ms	(/.f64 1 (-.f64 x (*.f64 y z)))

simplify297.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

754×	`cancel-sign-sub-inv_binary64`
220×	`associate-/r*_binary64`
220×	`times-frac_binary64`
212×	`sub-neg_binary64`
204×	`unswap-sqr_binary64`

Counts

420 → 434

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	353	16581
1	1020	15249
2	3835	14708
3	5481	14708

prune340.0ms (6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	528	0	528
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	528	7	535

Error

1.9b

Counts

535 → 7

Alt Table

Status	Error	Program
✓	11.1b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	36.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
✓	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
✓	10.9b	(/.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 x (.f64 y z))))
	33.7b	(-.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))))
	42.9b	(/.f64 y a)

Compiler

Compiled 17146 to 6371 computations (62.8% saved)

regimes832.0ms (14.6%)

Accuracy

Total 3.3b remaining (62.7%)

Threshold costs 0b (0%)

Counts

89 → 5

Compiler

Compiled 13394 to 7722 computations (42.3% saved)

bsearch5.0ms (0.1%)

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

simplify7.0ms (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	28	146
1	42	146
2	62	146
3	74	146
4	81	146
5	82	146
6	82	146

end93.0ms (1.6%)

Compiler: Compiled 342 to 135 computations (60.5% saved)

Details

analyze1.2s (21.8%)

sample1.2s (21.8%)

simplify117.0ms (2.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series74.0ms (1.3%)

rewrite13.0ms (0.2%)

simplify118.0ms (2.1%)

prune122.0ms (2.1%)

localize9.0ms (0.2%)

series82.0ms (1.4%)

rewrite16.0ms (0.3%)

simplify139.0ms (2.5%)

prune179.0ms (3.1%)

localize9.0ms (0.2%)

series124.0ms (2.2%)

rewrite22.0ms (0.4%)

simplify208.0ms (3.7%)

prune214.0ms (3.8%)

localize14.0ms (0.2%)

series91.0ms (1.6%)

rewrite76.0ms (1.3%)

simplify297.0ms (5.2%)

prune340.0ms (6%)

regimes832.0ms (14.6%)

bsearch5.0ms (0.1%)

simplify7.0ms (0.1%)

end93.0ms (1.6%)

Profiling