Details

analyze912.0ms (8.8%)

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
3.1%	96.7%	0.2%	7
6.2%	93.6%	0.2%	8
8.6%	91.2%	0.2%	9
28.1%	71.7%	0.2%	10
31%	68.8%	0.2%	11
40.5%	59.3%	0.2%	12
49.6%	50.2%	0.2%	13
59%	40.8%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample91.0ms (0.9%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 47 to 31 computations (34% saved)

simplify96.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

573×	`neg-mul-1_binary64`
569×	`unsub-neg_binary64`
509×	`times-frac_binary64`
460×	`neg-sub0_binary64`
418×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	185	25
5	383	25
6	1133	25
7	3784	25
8	4245	25
9	4554	25
10	4899	25
11	4864	25

prune3.0ms (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

5.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.6b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 80 to 46 computations (42.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.2b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	7.7b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series202.0ms (1.9%)

Counts

4 → 153

Calls

4 calls:

94.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
54.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
48.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 y z) x)

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

4 → 115

Calls

4 calls:

11.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
11.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
6.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 y z) x)

simplify149.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
290×	`associate--l+_binary64`
201×	`fma-def_binary64`

Counts

268 → 300

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	436	10267
1	1359	9717
2	5100	9717

prune306.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	295	5	300
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	296	5	301

Error

Counts

301 → 5

Alt Table

Status	Error	Program
	5.6b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	5.9b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
▶	3.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	36.5b	(/.f64 (+.f64 x (.f64 (sqrt.f64 (-.f64 (.f64 z y) x)) (/.f64 (sqrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))
	23.6b	(-.f64 (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (.f64 (+.f64 1 x) t))) (/.f64 x (.f64 (+.f64 1 x) (*.f64 t z))))

Compiler

Compiled 10850 to 3983 computations (63.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.f64 x 1))
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	1.4b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.1b	(/.f64 z (-.f64 (*.f64 t z) x))

series141.0ms (1.4%)

Counts

4 → 144

Calls

4 calls:

87.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
22.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
20.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
11.0ms	(/.f64 y (+.f64 x 1))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
30×	`times-frac_binary64`
29×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
10×	`associate-/r*_binary64`

Counts

4 → 107

Calls

4 calls:

4.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
3.0ms	(/.f64 y (+.f64 x 1))
0.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))

simplify157.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

408×	`times-frac_binary64`
329×	`associate-/l*_binary64`
276×	`fma-neg_binary64`
255×	`associate-/r*_binary64`
250×	`+-commutative_binary64`

Counts

251 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	7626
1	1119	7175
2	4600	7050
3	4982	7050

prune273.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	262	1	263
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	263	5	268

Error

Counts

268 → 5

Alt Table

Status	Error	Program
	16.8b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
▶	5.6b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	5.9b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
✓	3.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	36.5b	(/.f64 (+.f64 x (.f64 (sqrt.f64 (-.f64 (.f64 z y) x)) (/.f64 (sqrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 10280 to 3910 computations (62% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 y z) x)
✓	0.2b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	0.4b	(/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))
✓	7.6b	(/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x))

series183.0ms (1.8%)

Counts

3 → 144

Calls

3 calls:

90.0ms

(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))) (+.f64 x 1))

48.0ms

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

45.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))

rewrite65.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`times-frac_binary64`
93×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

3 → 167

Calls

3 calls:

18.0ms

(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))) (+.f64 x 1))

12.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))

7.0ms

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

simplify232.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

513×	`times-frac_binary64`
389×	`associate-/l*_binary64`
324×	`associate-/r*_binary64`
266×	`associate--l+_binary64`
179×	`sub-neg_binary64`

Counts

311 → 360

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	480	13006
1	1499	12060
2	5108	12060

prune446.0ms (4.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	394	0	394
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	394	5	399

Error

Counts

399 → 5

Alt Table

Status	Error	Program
	16.8b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
✓	5.6b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
▶	5.9b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
✓	3.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	36.5b	(/.f64 (+.f64 x (.f64 (sqrt.f64 (-.f64 (.f64 z y) x)) (/.f64 (sqrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 14615 to 5596 computations (61.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
✓	0.3b	(.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))))
✓	4.0b	(cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
	7.7b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series1.4s (13.1%)

Counts

3 → 144

Calls

3 calls:

720.0ms

(*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))))

523.0ms

(cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x)))

121.0ms

(/.f64 (+.f64 x (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x)))) (cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))))) (+.f64 x 1))

rewrite59.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`cbrt-prod_binary64`
75×	`add-sqr-sqrt_binary64`
63×	`times-frac_binary64`
59×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`

Counts

3 → 149

Calls

3 calls:

22.0ms

(*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))))

6.0ms

(/.f64 (+.f64 x (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x)))) (cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))))) (+.f64 x 1))

5.0ms

(cbrt.f64 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x)))

simplify302.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

599×	`*-commutative_binary64`
253×	`associate-r_binary64`
238×	`associate-+r+_binary64`
223×	`fma-def_binary64`
178×	`associate-/r*_binary64`

Counts

293 → 422

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1560	27736
1	5159	27736

prune1.5s (14.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	927	0	927
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	927	5	932

Error

Counts

932 → 5

Alt Table

Status	Error	Program
	16.8b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
✓	5.6b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	5.9b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))) (cbrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
✓	3.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	36.5b	(/.f64 (+.f64 x (.f64 (sqrt.f64 (-.f64 (.f64 z y) x)) (/.f64 (sqrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 83578 to 28543 computations (65.8% saved)

regimes2.8s (26.9%)

Accuracy

Total 1.5b remaining (98.6%)

Threshold costs 0b (0%)

Counts

292 → 3

Compiler

Compiled 41443 to 24123 computations (41.8% saved)

bsearch47.0ms (0.4%)

Steps

Iters	Range		Point
6	8.378681345494192e+37	5.702915593124847e+41	3.633970818777441e+41
9	-1.7069034648846957e+88	-2.6250722693753414e+80	-2.0677804913452024e+84

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
7×	`*-commutative_binary64`
6×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	118
1	47	118
2	59	118
3	65	118
4	68	118
5	67	118

end1.0ms (0%)

Compiler: Compiled 84 to 46 computations (45.2% saved)

sample1.0s (9.6%)

Algorithm

1×

intervals

Results

587.0ms	8000×	body	128	valid
21.0ms	325×	body	128	invalid

Compiler

Compiled 257 to 138 computations (46.3% saved)

Details

analyze912.0ms (8.8%)

sample91.0ms (0.9%)

simplify96.0ms (0.9%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series202.0ms (1.9%)

rewrite39.0ms (0.4%)

simplify149.0ms (1.4%)

prune306.0ms (2.9%)

localize12.0ms (0.1%)

series141.0ms (1.4%)

rewrite17.0ms (0.2%)

simplify157.0ms (1.5%)

prune273.0ms (2.6%)

localize11.0ms (0.1%)

series183.0ms (1.8%)

rewrite65.0ms (0.6%)

simplify232.0ms (2.2%)

prune446.0ms (4.3%)

localize14.0ms (0.1%)

series1.4s (13.1%)

rewrite59.0ms (0.6%)

simplify302.0ms (2.9%)

prune1.5s (14.1%)

regimes2.8s (26.9%)

bsearch47.0ms (0.4%)

simplify5.0ms (0%)

end1.0ms (0%)

sample1.0s (9.6%)

Profiling