Details

analyze1.1s (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
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
22.2%	77.6%	0.2%	11
40.4%	59.5%	0.2%	12
47.4%	52.4%	0.2%	13
55.3%	44.5%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.2s (23.6%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
504×	`associate-*l/_binary64`
466×	`div-sub_binary64`
450×	`cancel-sign-sub-inv_binary64`
403×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	30	25
2	70	25
3	177	22
4	486	19
5	1087	19
6	2534	19
7	4434	19
8	5156	19

prune4.0ms (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

3.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.8b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	12.2b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
✓	4.9b	(/.f64 (.f64 y t) (.f64 2 z))
✓	5.4b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

series119.0ms (2.4%)

Counts

4 → 156

Calls

4 calls:

57.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
30.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
20.0ms	(/.f64 (.f64 y t) (.f64 2 z))
11.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

rewrite49.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`add-sqr-sqrt_binary64`
118×	`*-un-lft-identity_binary64`
82×	`add-cube-cbrt_binary64`
81×	`times-frac_binary64`
78×	`prod-diff_binary64`

Counts

4 → 203

Calls

4 calls:

11.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
7.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
4.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
4.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify243.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

335×	`fma-neg_binary64`
273×	`exp-prod_binary64`
232×	`times-frac_binary64`
230×	`associate-/l*_binary64`
215×	`associate-*r/_binary64`

Counts

359 → 312

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	11732
1	1154	9150
2	3814	7711
3	4584	7711
4	4860	7711

prune246.0ms (4.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	309	3	312
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	311	3	314

Error

0.0b

Counts

314 → 3

Alt Table

Status	Error	Program
	24.0b	(fma.f64 2 (/.f64 z t) x)
▶	2.8b	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
	3.9b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))

Compiler

Compiled 11557 to 5775 computations (50% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
✓	4.7b	(*.f64 (/.f64 y z) t)
✓	5.4b	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))

series101.0ms (2%)

Counts

4 → 156

Calls

4 calls:

45.0ms	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
30.0ms	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
14.0ms	(*.f64 (/.f64 y z) t)
12.0ms	(-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
68×	`*-un-lft-identity_binary64`
66×	`add-cube-cbrt_binary64`
56×	`times-frac_binary64`
48×	`prod-diff_binary64`

Counts

4 → 164

Calls

4 calls:

8.0ms	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
6.0ms	(*.f64 (/.f64 y z) t)
4.0ms	(/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t))))
3.0ms	(-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))

simplify206.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

290×	`cancel-sign-sub-inv_binary64`
290×	`fma-neg_binary64`
225×	`distribute-neg-frac_binary64`
181×	`exp-prod_binary64`
172×	`*-commutative_binary64`

Counts

320 → 243

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	379	9211
1	991	7354
2	3036	6455
3	4686	6445
4	4788	6445

prune180.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	243	3	246

Error

0.0b

Counts

246 → 3

Alt Table

Status	Error	Program
	24.0b	(fma.f64 2 (/.f64 z t) x)
✓	2.8b	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
▶	3.9b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))

Compiler

Compiled 8810 to 3946 computations (55.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
✓	0.7b	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
	4.9b	(/.f64 (.f64 y t) (.f64 2 z))
✓	5.0b	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)

series101.0ms (2%)

Counts

3 → 120

Calls

3 calls:

52.0ms	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
29.0ms	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
20.0ms	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)

rewrite126.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

546×	`times-frac_binary64`
438×	`add-sqr-sqrt_binary64`
429×	`*-un-lft-identity_binary64`
320×	`add-cube-cbrt_binary64`
186×	`prod-diff_binary64`

Counts

3 → 413

Calls

3 calls:

26.0ms	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))
8.0ms	(/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y))
6.0ms	(/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)

simplify485.0ms (9.7%)

Algorithm

1×	egg-herbie

Rules

368×	`cancel-sign-sub-inv_binary64`
253×	`fma-neg_binary64`
245×	`div-sub_binary64`
241×	`distribute-neg-frac_binary64`
188×	`*-commutative_binary64`

Counts

533 → 503

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	405	25783
1	1042	19853
2	3218	16279
3	4569	15775
4	4768	15775

prune501.0ms (10%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	540	0	540
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	540	3	543

Error

0.0b

Counts

543 → 3

Alt Table

Status	Error	Program
▶	24.0b	(fma.f64 2 (/.f64 z t) x)
✓	2.8b	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
✓	3.9b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))

Compiler

Compiled 27326 to 15495 computations (43.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (/.f64 z t) x)

series9.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(fma.f64 2 (/.f64 z t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 2 (/.f64 z t) x)

simplify79.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-*l/_binary64`
542×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
443×	`associate-+l+_binary64`
396×	`fma-def_binary64`

Counts

46 → 14

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	376
1	23	359
2	49	359
3	126	359
4	432	359
5	1628	359
6	4283	359
7	4686	359
8	4929	359
9	4999	359

prune8.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	14	3	17

Error

0.0b

Counts

17 → 3

Alt Table

Status	Error	Program
✓	24.0b	(fma.f64 2 (/.f64 z t) x)
✓	2.8b	(-.f64 x (/.f64 y (-.f64 z (.f64 1/2 (.f64 (/.f64 y z) t)))))
✓	3.9b	(-.f64 x (/.f64 1 (/.f64 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))) y)))

Compiler

Compiled 185 to 99 computations (46.5% saved)

regimes96.0ms (1.9%)

Accuracy

Total 0.1b remaining (88.9%)

Threshold costs 0.1b (88.9%)

Counts

15 → 1

Compiler

Compiled 1414 to 994 computations (29.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	19	19
2	25	19
3	27	19
4	28	19
5	26	19

end52.0ms (1%)

Compiler: Compiled 80 to 55 computations (31.3% saved)

Details

analyze1.1s (21.8%)

sample1.2s (23.6%)

simplify56.0ms (1.1%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series119.0ms (2.4%)

rewrite49.0ms (1%)

simplify243.0ms (4.9%)

prune246.0ms (4.9%)

localize9.0ms (0.2%)

series101.0ms (2%)

rewrite36.0ms (0.7%)

simplify206.0ms (4.1%)

prune180.0ms (3.6%)

localize11.0ms (0.2%)

series101.0ms (2%)

rewrite126.0ms (2.5%)

simplify485.0ms (9.7%)

prune501.0ms (10%)

localize6.0ms (0.1%)

series9.0ms (0.2%)

rewrite1.0ms (0%)

simplify79.0ms (1.6%)

prune8.0ms (0.2%)

regimes96.0ms (1.9%)

simplify3.0ms (0.1%)

end52.0ms (1%)

Profiling