Details

analyze2.8s (22.2%)

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
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
14.9%	84.9%	0.2%	13
16.2%	83.5%	0.3%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample68.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms	209×	body	128	valid
7.0ms	16×	body	1024	valid
5.0ms	17×	body	512	valid
5.0ms	41×	body	128	invalid
2.0ms	13×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 42 to 28 computations (33.3% saved)

simplify111.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

825×	`unsub-neg_binary64`
766×	`fma-def_binary64`
693×	`div-sub_binary64`
637×	`sub-neg_binary64`
587×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	21	19
2	52	17
3	144	17
4	421	17
5	1090	17
6	2642	17
7	3865	17
8	4364	17
9	4936	17
10	4941	17

prune9.0ms (0.1%)

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

12.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.6b	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)
	25.4b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 100 to 55 computations (45% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	3.1b	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)

series167.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

119.0ms	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)
47.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

13.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
1.0ms	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify238.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

615×	`cancel-sign-sub-inv_binary64`
513×	`sub-neg_binary64`
366×	`associate-+r+_binary64`
300×	`+-commutative_binary64`
270×	`associate-+l+_binary64`

Counts

160 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	378	5871
1	1049	5776
2	3942	5716
3	5417	5716

prune257.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	146	8	154
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	147	9	156

Error

0.8b

Counts

156 → 9

Alt Table

Status	Error	Program
	37.7b	(fma.f64 (-.f64 y x) (*.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 a t))) x)
	42.8b	(*.f64 (-.f64 (/.f64 y (-.f64 a t)) (/.f64 x (-.f64 a t))) z)
▶	13.7b	(fma.f64 (-.f64 y x) (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
	14.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)))
	31.9b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) x)
✓	13.6b	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)
	21.4b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x)) (+.f64 (/.f64 (.f64 z x) (-.f64 a t)) (/.f64 (.f64 y t) (-.f64 a t))))
	37.7b	(fma.f64 (-.f64 y x) (/.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (-.f64 a t) (sqrt.f64 (-.f64 z t)))) x)
	38.4b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 a y) t))) (+.f64 (/.f64 (.f64 a x) t) (/.f64 (.f64 y z) t)))

Compiler

Compiled 5342 to 1669 computations (68.8% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.3b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
✓	5.1b	(fma.f64 (-.f64 y x) (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

series197.0ms (1.6%)

Counts

3 → 120

Calls

3 calls:

132.0ms	(fma.f64 (-.f64 y x) (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
43.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
20.0ms	(/.f64 1 (-.f64 a t))

rewrite64.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

23.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
8.0ms	(/.f64 1 (-.f64 a t))
1.0ms	(fma.f64 (-.f64 y x) (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

simplify311.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

513×	`sub-neg_binary64`
384×	`associate-+r+_binary64`
321×	`+-commutative_binary64`
288×	`associate-+l+_binary64`
224×	`fma-neg_binary64`

Counts

225 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	409	6650
1	1099	6387
2	4267	6327
3	5077	6327

prune339.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	237	9	246

Error

0.8b

Counts

246 → 9

Alt Table

Status	Error	Program
	37.7b	(fma.f64 (-.f64 y x) (*.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 a t))) x)
	42.8b	(*.f64 (-.f64 (/.f64 y (-.f64 a t)) (/.f64 x (-.f64 a t))) z)
	49.9b	(fma.f64 (-.f64 y x) (*.f64 (-.f64 z t) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 a) (sqrt.f64 t))) (-.f64 (sqrt.f64 a) (sqrt.f64 t)))) x)
✓	13.6b	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)
	31.9b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) x)
▶	21.4b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x)) (+.f64 (/.f64 (.f64 z x) (-.f64 a t)) (/.f64 (.f64 y t) (-.f64 a t))))
	37.7b	(fma.f64 (-.f64 y x) (/.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (-.f64 a t) (sqrt.f64 (-.f64 z t)))) x)
✓	13.7b	(fma.f64 (-.f64 y x) (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
	38.4b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 a y) t))) (+.f64 (/.f64 (.f64 a x) t) (/.f64 (.f64 y z) t)))

Compiler

Compiled 7132 to 2500 computations (64.9% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.1b	(/.f64 (*.f64 y z) (-.f64 a t))
✓	8.1b	(/.f64 (*.f64 z x) (-.f64 a t))
✓	9.1b	(/.f64 (*.f64 y t) (-.f64 a t))
✓	11.9b	(/.f64 (*.f64 t x) (-.f64 a t))

series193.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

62.0ms	(/.f64 (*.f64 z x) (-.f64 a t))
58.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
40.0ms	(/.f64 (*.f64 y t) (-.f64 a t))
34.0ms	(/.f64 (*.f64 t x) (-.f64 a t))

rewrite55.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
24×	`add-cbrt-cube_binary64`
24×	`add-exp-log_binary64`
20×	`associate-/r*_binary64`

Counts

4 → 116

Calls

4 calls:

12.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
11.0ms	(/.f64 (*.f64 z x) (-.f64 a t))
11.0ms	(/.f64 (*.f64 y t) (-.f64 a t))
11.0ms	(/.f64 (*.f64 t x) (-.f64 a t))

simplify281.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
361×	`associate-/l*_binary64`
330×	`times-frac_binary64`
171×	`associate-l_binary64`
164×	`cancel-sign-sub-inv_binary64`

Counts

212 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	330	4544
1	866	4292
2	3352	3952
3	4895	3952
4	4979	3952
5	4975	3952

prune463.0ms (3.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	222	4	226
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	224	11	235

Error

0.8b

Counts

235 → 11

Alt Table

Status	Error	Program
	37.7b	(fma.f64 (-.f64 y x) (*.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 a t))) x)
	42.8b	(*.f64 (-.f64 (/.f64 y (-.f64 a t)) (/.f64 x (-.f64 a t))) z)
	31.9b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) x)
	21.4b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 1 (/.f64 (-.f64 a t) (.f64 y z))) x)) (+.f64 (/.f64 (.f64 z x) (-.f64 a t)) (/.f64 (.f64 y t) (-.f64 a t))))
✓	13.6b	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	21.4b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x)) (+.f64 (/.f64 1 (/.f64 (-.f64 a t) (.f64 z x))) (/.f64 (.f64 y t) (-.f64 a t))))
	37.7b	(fma.f64 (-.f64 y x) (/.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (-.f64 a t) (sqrt.f64 (-.f64 z t)))) x)
	21.5b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x)) (+.f64 (/.f64 (.f64 z x) (-.f64 a t)) (/.f64 1 (/.f64 (-.f64 a t) (.f64 y t)))))
	38.4b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 a y) t))) (+.f64 (/.f64 (.f64 a x) t) (/.f64 (.f64 y z) t)))
	28.2b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x)) (+.f64 (/.f64 (.f64 z x) (-.f64 a t)) (cbrt.f64 (pow.f64 (/.f64 (.f64 t y) (-.f64 a t)) 3))))
✓	13.7b	(fma.f64 (-.f64 y x) (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

Compiler

Compiled 9958 to 1837 computations (81.6% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.1b	(/.f64 (*.f64 y z) (-.f64 a t))
✓	8.1b	(/.f64 (-.f64 a t) (*.f64 z x))
	9.1b	(/.f64 (*.f64 y t) (-.f64 a t))
	11.9b	(/.f64 (*.f64 t x) (-.f64 a t))

series41.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

41.0ms

(/.f64 (-.f64 a t) (*.f64 z x))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`associate-/l*_binary64`

Counts

1 → 30

Calls

1 calls:

11.0ms

(/.f64 (-.f64 a t) (*.f64 z x))

simplify72.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

838×	`distribute-rgt-in_binary64`
478×	`fma-def_binary64`
351×	`div-sub_binary64`
240×	`times-frac_binary64`
206×	`associate-/l*_binary64`

Counts

54 → 39

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	687
1	179	624
2	580	622
3	2139	622
4	5201	622

prune445.0ms (3.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	206	11	217

Error

0.8b

Counts

217 → 11

Alt Table

Status	Error	Program
	37.7b	(fma.f64 (-.f64 y x) (*.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 a t))) x)
	42.8b	(*.f64 (-.f64 (/.f64 y (-.f64 a t)) (/.f64 x (-.f64 a t))) z)
	31.9b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) x)
	21.4b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 1 (/.f64 (-.f64 a t) (.f64 y z))) x)) (+.f64 (/.f64 (.f64 z x) (-.f64 a t)) (/.f64 (.f64 y t) (-.f64 a t))))
✓	13.6b	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	21.4b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x)) (+.f64 (/.f64 1 (/.f64 (-.f64 a t) (.f64 z x))) (/.f64 (.f64 y t) (-.f64 a t))))
	37.7b	(fma.f64 (-.f64 y x) (/.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (-.f64 a t) (sqrt.f64 (-.f64 z t)))) x)
	21.5b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x)) (+.f64 (/.f64 (.f64 z x) (-.f64 a t)) (/.f64 1 (/.f64 (-.f64 a t) (.f64 y t)))))
	38.4b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 a y) t))) (+.f64 (/.f64 (.f64 a x) t) (/.f64 (.f64 y z) t)))
	28.2b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x)) (+.f64 (/.f64 (.f64 z x) (-.f64 a t)) (cbrt.f64 (pow.f64 (/.f64 (.f64 t y) (-.f64 a t)) 3))))
✓	13.7b	(fma.f64 (-.f64 y x) (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

Compiler

Compiled 9164 to 2041 computations (77.7% saved)

regimes3.9s (31.5%)

Accuracy

Total 5.6b remaining (83.3%)

Threshold costs 0b (0%)

Counts

146 → 4

Compiler

Compiled 29802 to 15012 computations (49.6% saved)

bsearch15.0ms (0.1%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify20.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

27×	`+-commutative_binary64`
23×	`*-commutative_binary64`
20×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	198
1	76	198
2	98	198
3	126	198
4	165	198
5	183	198
6	193	198
7	196	198
8	195	198

end2.0ms (0%)

Compiler: Compiled 139 to 50 computations (64% saved)

sample2.3s (18.2%)

Algorithm

1×

intervals

Results

671.0ms	6663×	body	128	valid
162.0ms	520×	body	512	valid
160.0ms	358×	body	1024	valid
120.0ms	1231×	body	128	invalid
71.0ms	388×	body	256	valid
32.0ms	71×	body	2048	valid

Compiler

Compiled 474 to 233 computations (50.8% saved)

Iter	Nodes	Cost
0	51	198
1	76	198
2	98	198
3	126	198
4	165	198
5	183	198
6	193	198
7	196	198
8	195	198

Iter	Nodes	Cost
0	51	198
1	76	198
2	98	198
3	126	198
4	165	198
5	183	198
6	193	198
7	196	198
8	195	198

Details

analyze2.8s (22.2%)

sample68.0ms (0.5%)

simplify111.0ms (0.9%)

prune9.0ms (0.1%)

localize16.0ms (0.1%)

series167.0ms (1.3%)

rewrite30.0ms (0.2%)

simplify238.0ms (1.9%)

prune257.0ms (2.1%)

localize18.0ms (0.1%)

series197.0ms (1.6%)

rewrite64.0ms (0.5%)

simplify311.0ms (2.5%)

prune339.0ms (2.7%)

localize34.0ms (0.3%)

series193.0ms (1.5%)

rewrite55.0ms (0.4%)

simplify281.0ms (2.2%)

prune463.0ms (3.7%)

localize39.0ms (0.3%)

series41.0ms (0.3%)

rewrite15.0ms (0.1%)

simplify72.0ms (0.6%)

prune445.0ms (3.6%)

regimes3.9s (31.5%)

bsearch15.0ms (0.1%)

simplify20.0ms (0.2%)

end2.0ms (0%)

sample2.3s (18.2%)

Profiling

Iter	Nodes	Cost
0	51	198
1	76	198
2	98	198
3	126	198
4	165	198
5	183	198
6	193	198
7	196	198
8	195	198