Details

analyze582.0ms (14.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
26.5%	73.3%	0.1%	8
33.5%	66.3%	0.1%	9
49.1%	50.7%	0.1%	10
56.9%	42.9%	0.1%	11
60.8%	39%	0.1%	12
69%	30.9%	0.1%	13
72.5%	27.3%	0.1%	14

Compiler

Compiled 16 to 10 computations (37.5% saved)

sample42.0ms (1%)

Algorithm

1×

intervals

Results

17.0ms	96×	body	1024	valid
6.0ms	31×	body	2048	valid
5.0ms	42×	body	512	valid
3.0ms	66×	body	128	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

simplify78.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

202×	`cancel-sign-sub-inv_binary64`
170×	`sub-neg_binary64`
91×	`associate--r+_binary64`
82×	`associate-+l-_binary64`
77×	`associate--l+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	21	17
2	48	17
3	129	17
4	231	17
5	425	17
6	500	17
7	515	17
8	534	17
9	535	17
10	504	17

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

47.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	47.4b	(-.f64 (fma.f64 x y z) (+.f64 1 (+.f64 (*.f64 x y) z)))

Compiler

Compiled 45 to 27 computations (40% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

8.8b	(-.f64 (fma.f64 x y z) (+.f64 1 (+.f64 (*.f64 x y) z)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

46.9b

Rules

10×	`add-log-exp_binary64`
9×	`*-un-lft-identity_binary64`
4×	`cancel-sign-sub-inv_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`diff-log_binary64`

Counts

1 → 21

Calls

1 calls:

6.0ms

(-.f64 (fma.f64 x y z) (+.f64 1 (+.f64 (*.f64 x y) z)))

Compiler

Compiled 431 to 155 computations (64% saved)

series31.0ms (0.8%)

Error

46.1b

Counts

1 → 18

Calls

1 calls:

26.0ms

(-.f64 (fma.f64 x y z) (+.f64 1 (+.f64 (*.f64 x y) z)))

Compiler

Compiled 390 to 237 computations (39.2% saved)

simplify73.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

435×	`cancel-sign-sub-inv_binary64`
381×	`distribute-rgt-in_binary64`
371×	`distribute-lft-in_binary64`
338×	`neg-mul-1_binary64`
314×	`distribute-rgt-out_binary64`

Counts

39 → 37

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	729
1	159	684
2	475	684
3	2519	675
4	4345	675
5	4958	675

prune15.0ms (0.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	32	5	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	5	38

Error

46.1b

Counts

38 → 5

Alt Table

Status	Error	Program
	48.4b	(-.f64 (fma.f64 x y z) (+.f64 z 1))
▶	48.1b	(-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y)))
	49.3b	(/.f64 (-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (pow.f64 (sqrt.f64 (+.f64 (+.f64 z 1) (.f64 x y))) 4)) (+.f64 (fma.f64 x y z) (+.f64 (+.f64 z 1) (*.f64 x y))))
	61.9b	(neg.f64 (*.f64 x y))
	62.0b	(neg.f64 z)

Compiler

Compiled 439 to 208 computations (52.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (*.f64 x y))
7.9b	(-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y)))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

46.1b

Rules

9×	`add-log-exp_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`cancel-sign-sub-inv_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 29

Calls

2 calls:

4.0ms	(-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y)))
2.0ms	(+.f64 1 (*.f64 x y))

Compiler

Compiled 543 to 228 computations (58% saved)

series74.0ms (1.8%)

Error

46.1b

Counts

2 → 27

Calls

2 calls:

61.0ms	(-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y)))
10.0ms	(+.f64 1 (*.f64 x y))

Compiler

Compiled 534 to 325 computations (39.1% saved)

simplify78.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

496×	`associate-+l+_binary64`
427×	`associate-+r+_binary64`
304×	`cancel-sign-sub-inv_binary64`
246×	`associate-l_binary64`
209×	`distribute-rgt-out_binary64`

Counts

56 → 36

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	743
1	179	706
2	439	706
3	1566	700
4	4501	700
5	5050	700

prune14.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	33	8	41

Error

46.1b

Counts

41 → 8

Alt Table

Status	Error	Program
	62.0b	(neg.f64 z)
	48.7b	(-.f64 (fma.f64 x y z) (cbrt.f64 (pow.f64 (+.f64 1 (*.f64 x y)) 3)))
▶	48.4b	(-.f64 (fma.f64 x y z) (+.f64 z 1))
✓	48.1b	(-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y)))
	50.1b	(-.f64 (fma.f64 x y z) (/.f64 (+.f64 1 (pow.f64 (.f64 x y) 3)) (+.f64 1 (.f64 x (-.f64 (.f64 x (.f64 y y)) y)))))
	49.3b	(/.f64 (-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (pow.f64 (sqrt.f64 (+.f64 (+.f64 z 1) (.f64 x y))) 4)) (+.f64 (fma.f64 x y z) (+.f64 (+.f64 z 1) (*.f64 x y))))
	61.9b	(neg.f64 (*.f64 x y))
	48.7b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y))) 3))

Compiler

Compiled 446 to 237 computations (46.9% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

3.5b	(-.f64 (fma.f64 x y z) (+.f64 z 1))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

22.0b

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-log-exp_binary64`
4×	`cancel-sign-sub-inv_binary64`
4×	`add-sqr-sqrt_binary64`
2×	`distribute-lft-out--_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(-.f64 (fma.f64 x y z) (+.f64 z 1))

Compiler

Compiled 290 to 145 computations (50% saved)

series15.0ms (0.4%)

Error

46.1b

Counts

1 → 12

Calls

1 calls:

14.0ms

(-.f64 (fma.f64 x y z) (+.f64 z 1))

Compiler

Compiled 239 to 153 computations (36% saved)

simplify70.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-+l+_binary64`
418×	`neg-mul-1_binary64`
307×	`sub-neg_binary64`
268×	`distribute-rgt-out_binary64`
237×	`distribute-neg-in_binary64`

Counts

32 → 21

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	442
1	124	409
2	263	408
3	1096	406
4	2388	406
5	4492	406
6	4950	406

prune20.0ms (0.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	20	9	29

Error

46.1b

Counts

29 → 9

Alt Table

Status	Error	Program
	62.0b	(neg.f64 z)
	48.7b	(-.f64 (fma.f64 x y z) (cbrt.f64 (pow.f64 (+.f64 1 (*.f64 x y)) 3)))
▶	48.7b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y))) 3))
	49.7b	(/.f64 (-.f64 (*.f64 (fma.f64 x y z) (fma.f64 x y z)) (pow.f64 (sqrt.f64 (+.f64 z 1)) 4)) (+.f64 (fma.f64 x y z) (+.f64 z 1)))
✓	48.4b	(-.f64 (fma.f64 x y z) (+.f64 z 1))
✓	48.1b	(-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y)))
	50.1b	(-.f64 (fma.f64 x y z) (/.f64 (+.f64 1 (pow.f64 (.f64 x y) 3)) (+.f64 1 (.f64 x (-.f64 (.f64 x (.f64 y y)) y)))))
	49.3b	(/.f64 (-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (pow.f64 (sqrt.f64 (+.f64 (+.f64 z 1) (.f64 x y))) 4)) (+.f64 (fma.f64 x y z) (+.f64 (+.f64 z 1) (*.f64 x y))))
	61.9b	(neg.f64 (*.f64 x y))

Compiler

Compiled 394 to 228 computations (42.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (*.f64 x y))
0.0b	(pow.f64 (-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y))) 3)
7.9b	(-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y)))
18.3b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y))) 3))

rewrite123.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

46.1b

Rules

21×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(pow.f64 (-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y))) 3)
4.0ms	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y))) 3))
4.0ms	(-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y)))
2.0ms	(+.f64 1 (*.f64 x y))

Compiler

Compiled 1718 to 842 computations (51% saved)

series118.0ms (2.9%)

Error

45.9b

Counts

4 → 65

Calls

4 calls:

59.0ms	(pow.f64 (-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y))) 3)
20.0ms	(-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y)))
17.0ms	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y))) 3))
12.0ms	(+.f64 1 (*.f64 x y))

Compiler

Compiled 2452 to 1592 computations (35.1% saved)

simplify175.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

479×	`distribute-rgt-in_binary64`
447×	`distribute-lft-in_binary64`
362×	`cancel-sign-sub-inv_binary64`
268×	`unswap-sqr_binary64`
167×	`exp-prod_binary64`

Counts

150 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	3617
1	440	3329
2	1439	3195
3	4810	3195
4	5027	3195

prune41.0ms (1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	108	7	115
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	109	15	124

Error

45.9b

Counts

124 → 15

Alt Table

Status	Error	Program
	48.4b	(-.f64 (fma.f64 x y z) (+.f64 z 1))
	49.5b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y z) (/.f64 (+.f64 1 (pow.f64 (.f64 x y) 3)) (+.f64 1 (.f64 x (-.f64 (.f64 y (.f64 x y)) y))))) 3))
	49.3b	(/.f64 (-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (pow.f64 (sqrt.f64 (+.f64 (+.f64 z 1) (.f64 x y))) 4)) (+.f64 (fma.f64 x y z) (+.f64 (+.f64 z 1) (*.f64 x y))))
	48.7b	(cbrt.f64 (.f64 (pow.f64 (-.f64 (fma.f64 x y z) (+.f64 1 (.f64 x y))) 2) (-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y)))))
	62.0b	(neg.f64 z)
	48.7b	(-.f64 (fma.f64 x y z) (cbrt.f64 (pow.f64 (+.f64 1 (*.f64 x y)) 3)))
	62.5b	(cbrt.f64 (-.f64 (.f64 (fma.f64 x y z) (+.f64 (.f64 (.f64 y 6) x) (.f64 (.f64 x y) (.f64 (.f64 x y) 3)))) (+.f64 (.f64 3 (.f64 (.f64 x y) (+.f64 (pow.f64 (fma.f64 x y z) 2) (+.f64 1 (.f64 x y))))) (pow.f64 (.f64 x y) 3))))
	49.7b	(/.f64 (-.f64 (*.f64 (fma.f64 x y z) (fma.f64 x y z)) (pow.f64 (sqrt.f64 (+.f64 z 1)) 4)) (+.f64 (fma.f64 x y z) (+.f64 z 1)))
	48.1b	(-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y)))
	50.1b	(-.f64 (fma.f64 x y z) (/.f64 (+.f64 1 (pow.f64 (.f64 x y) 3)) (+.f64 1 (.f64 x (-.f64 (.f64 x (.f64 y y)) y)))))
	61.9b	(neg.f64 (*.f64 x y))
	48.7b	(cbrt.f64 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y z) (+.f64 1 (.f64 x y))) 2)) (cbrt.f64 (-.f64 (fma.f64 x y z) (+.f64 1 (*.f64 x y))))) 3))
	49.8b	(cbrt.f64 (-.f64 (+.f64 (.f64 6 (.f64 y (.f64 x (fma.f64 x y z)))) (+.f64 (pow.f64 (fma.f64 x y z) 3) (.f64 (fma.f64 x y z) (+.f64 3 (.f64 (.f64 x y) (.f64 (.f64 x y) 3)))))) (+.f64 1 (+.f64 (pow.f64 (.f64 x y) 3) (.f64 3 (+.f64 (.f64 (+.f64 1 (.f64 x y)) (pow.f64 (fma.f64 x y z) 2)) (.f64 (.f64 x y) (+.f64 1 (*.f64 x y)))))))))
	62.2b	(cbrt.f64 (-.f64 (.f64 3 (.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (fma.f64 x y z) 1))) (pow.f64 (.f64 x y) 3)))
	62.3b	(cbrt.f64 (pow.f64 (neg.f64 (*.f64 x y)) 3))

Compiler

Compiled 1244 to 627 computations (49.6% saved)

regimes406.0ms (10.1%)

Accuracy

Total -19.5b remaining (-80%)

Threshold costs -19.5b (-80%)

Compiler

Compiled 8082 to 4836 computations (40.2% saved)

bsearch41.0ms (1%)

Steps

Iters	Range		Point
10	1046826.4431399766	2.020566610106697e+20	32767434791329.156
6	-3.0907627267697655	-0.22792934956836094	-2.1021206699534236

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	42
1	34	42
2	44	42
3	54	42
4	68	42
5	75	42
6	80	42
7	82	42
8	80	42

end1.0ms (0%)

Compiler: Compiled 32 to 19 computations (40.6% saved)

sample1.9s (47.8%)

Algorithm

1×

intervals

Results

624.0ms	2734×	body	1024	valid
302.0ms	2288×	body	128	valid
247.0ms	1143×	body	2048	valid
142.0ms	1266×	body	512	valid
75.0ms	568×	body	256	valid
0.0ms	1×	body	4096	valid

Compiler

Compiled 438 to 256 computations (41.6% saved)

Iter	Nodes	Cost
0	10	17
1	21	17
2	48	17
3	129	17
4	231	17
5	425	17
6	500	17
7	515	17
8	534	17
9	535	17
10	504	17

Iter	Nodes	Cost
0	10	17
1	21	17
2	48	17
3	129	17
4	231	17
5	425	17
6	500	17
7	515	17
8	534	17
9	535	17
10	504	17

Details

analyze582.0ms (14.5%)

sample42.0ms (1%)

simplify78.0ms (1.9%)

prune2.0ms (0%)

localize7.0ms (0.2%)

rewrite20.0ms (0.5%)

series31.0ms (0.8%)

simplify73.0ms (1.8%)

prune15.0ms (0.4%)

localize6.0ms (0.2%)

rewrite28.0ms (0.7%)

series74.0ms (1.8%)

simplify78.0ms (1.9%)

prune14.0ms (0.4%)

localize6.0ms (0.2%)

rewrite18.0ms (0.5%)

series15.0ms (0.4%)

simplify70.0ms (1.7%)

prune20.0ms (0.5%)

localize9.0ms (0.2%)

rewrite123.0ms (3.1%)

series118.0ms (2.9%)

simplify175.0ms (4.4%)

prune41.0ms (1%)

regimes406.0ms (10.1%)

bsearch41.0ms (1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.9s (47.8%)

Profiling

Iter	Nodes	Cost
0	10	17
1	21	17
2	48	17
3	129	17
4	231	17
5	425	17
6	500	17
7	515	17
8	534	17
9	535	17
10	504	17