Details

analyze1.3s (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)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	21×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify118.0ms (2%)

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

9.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.6b	(/.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))
✓	9.3b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series95.0ms (1.6%)

Counts

2 → 69

Calls

2 calls:

89.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
5.0ms	(-.f64 x (*.f64 y z))

rewrite11.0ms (0.2%)

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:

6.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
2.0ms	(-.f64 x (*.f64 y z))

simplify109.0ms (1.9%)

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

prune89.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	118	8	126
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	118	9	127

Error

2.3b

Counts

127 → 9

Alt Table

Status	Error	Program
	42.9b	(/.f64 y a)
▶	9.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	26.6b	(/.f64 x (-.f64 t (*.f64 a z)))
	33.1b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 t (.f64 a z)))) (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))))
	35.8b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
	45.7b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (.f64 y z) 3)) (.f64 (-.f64 t (.f64 a z)) (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z))))))
	10.0b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	10.5b	(.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)))))
✓	9.6b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 3670 to 1130 computations (69.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.4b	(/.f64 1 (-.f64 t (*.f64 a z)))
✓	9.4b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))

series82.0ms (1.4%)

Counts

2 → 96

Calls

2 calls:

63.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
19.0ms	(/.f64 1 (-.f64 t (*.f64 a z)))

rewrite17.0ms (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))))
4.0ms	(/.f64 1 (-.f64 t (*.f64 a z)))

simplify142.0ms (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

prune144.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	199	4	203
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	202	10	212

Error

1.5b

Counts

212 → 10

Alt Table

Status	Error	Program
	45.7b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (.f64 y z) 3)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 (.f64 y z) (fma.f64 y z x) (*.f64 x x))))
	35.8b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
	42.9b	(/.f64 y a)
	32.9b	(-.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))))
✓	9.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
▶	10.0b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	26.6b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	9.6b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	31.9b	(.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)))))
	36.0b	(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (/.f64 1 (-.f64 t (.f64 a z)))) (+.f64 x (*.f64 y z)))

Compiler

Compiled 5508 to 1942 computations (64.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	9.2b	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))

series131.0ms (2.3%)

Counts

2 → 120

Calls

2 calls:

68.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
63.0ms	(/.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)))

simplify227.0ms (3.9%)

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

prune219.0ms (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	285	3	288
Fresh	3	4	7
Picked	1	0	1
Done	0	2	2
Total	289	9	298

Error

1.5b

Counts

298 → 9

Alt Table

Status	Error	Program
	43.1b	(/.f64 1 (/.f64 a y))
	35.8b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
	42.9b	(/.f64 y a)
▶	9.8b	(/.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 x (.f64 y z))))
	32.9b	(-.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))))
✓	9.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	26.6b	(/.f64 x (-.f64 t (*.f64 a z)))
	10.0b	(/.f64 1 (.f64 (-.f64 t (.f64 a z)) (/.f64 1 (-.f64 x (*.f64 y z)))))
✓	9.6b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 8818 to 2748 computations (68.8% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.4b	(/.f64 1 (-.f64 x (*.f64 y z)))
	0.4b	(/.f64 1 (-.f64 t (*.f64 a z)))
✓	9.1b	(/.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 x (.f64 y z))))

series97.0ms (1.7%)

Counts

2 → 96

Calls

2 calls:

74.0ms	(/.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 x (.f64 y z))))
23.0ms	(/.f64 1 (-.f64 x (*.f64 y z)))

rewrite73.0ms (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:

15.0ms	(/.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 x (.f64 y z))))
3.0ms	(/.f64 1 (-.f64 x (*.f64 y z)))

simplify309.0ms (5.4%)

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

prune374.0ms (6.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	528	0	528
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	528	9	537

Error

1.5b

Counts

537 → 9

Alt Table

Status	Error	Program
	43.1b	(/.f64 1 (/.f64 a y))
	35.8b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
	42.9b	(/.f64 y a)
✓	9.8b	(/.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 x (.f64 y z))))
	32.9b	(-.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))))
✓	9.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	26.6b	(/.f64 x (-.f64 t (*.f64 a z)))
	10.0b	(/.f64 1 (.f64 (-.f64 t (.f64 a z)) (/.f64 1 (-.f64 x (*.f64 y z)))))
✓	9.6b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 17173 to 6392 computations (62.8% saved)

regimes1.3s (21.9%)

Accuracy

Total 3.4b remaining (64.5%)

Threshold costs 0b (0%)

Counts

133 → 3

Compiler

Compiled 18813 to 11915 computations (36.7% saved)

bsearch5.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	64
1	34	64
2	51	64
3	61	64
4	67	64
5	68	64
6	68	64

end1.0ms (0%)

Compiler: Compiled 48 to 18 computations (62.5% saved)

sample898.0ms (15.6%)

Algorithm

1×

intervals

Results

381.0ms	8000×	body	128	valid
32.0ms	727×	body	128	invalid

Compiler

Compiled 231 to 138 computations (40.3% saved)

Details

analyze1.3s (21.8%)

sample26.0ms (0.5%)

simplify118.0ms (2%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series95.0ms (1.6%)

rewrite11.0ms (0.2%)

simplify109.0ms (1.9%)

prune89.0ms (1.5%)

localize10.0ms (0.2%)

series82.0ms (1.4%)

rewrite17.0ms (0.3%)

simplify142.0ms (2.5%)

prune144.0ms (2.5%)

localize9.0ms (0.2%)

series131.0ms (2.3%)

rewrite22.0ms (0.4%)

simplify227.0ms (3.9%)

prune219.0ms (3.8%)

localize17.0ms (0.3%)

series97.0ms (1.7%)

rewrite73.0ms (1.3%)

simplify309.0ms (5.4%)

prune374.0ms (6.5%)

regimes1.3s (21.9%)

bsearch5.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample898.0ms (15.6%)

Profiling