Details

analyze358.0ms (7.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample27.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
5.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 38 to 27 computations (28.9% saved)

simplify123.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

724×	`associate-/r/_binary64`
530×	`unsub-neg_binary64`
520×	`distribute-rgt-in_binary64`
518×	`div-sub_binary64`
438×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	16
3	72	16
4	207	16
5	430	16
6	715	16
7	1126	16
8	955	16
9	1077	16
10	1417	16
11	1909	16
12	2195	16
13	3288	16
14	3288	16
15	3681	16
16	4740	16

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

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
0.0b	(*.f64 m (-.f64 1 m))
0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

rewrite184.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 96

Calls

4 calls:

11.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

Compiler

Compiled 1708 to 1122 computations (34.3% saved)

series103.0ms (2.2%)

Error

0.1b

Counts

4 → 45

Calls

4 calls:

36.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
25.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
21.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
8.0ms	(*.f64 m (-.f64 1 m))

Compiler

Compiled 1013 to 684 computations (32.5% saved)

simplify103.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

440×	`div-sub_binary64`
374×	`distribute-rgt-in_binary64`
354×	`distribute-lft-in_binary64`
341×	`associate-*l/_binary64`
215×	`associate-/r*_binary64`

Counts

141 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	1957
1	373	1773
2	1181	1757
3	3853	1752
4	5199	1752

prune80.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	9	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	9	120

Error

Counts

120 → 9

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (+.f64 -1 (/.f64 (-.f64 m (*.f64 m m)) v)) (sqrt.f64 m)) (sqrt.f64 m))
	53.6b	(neg.f64 (/.f64 (pow.f64 m 3) v))
	9.6b	(.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (.f64 m (+.f64 -1 (sqrt.f64 (/.f64 (-.f64 m (.f64 m m)) v)))))
	19.1b	(-.f64 (/.f64 (*.f64 m m) v) m)
	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (.f64 1 1) (.f64 m m))) (*.f64 v (+.f64 m 1))) 1) m)
	0.7b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (.f64 m m))))) 1) m)
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 m (+.f64 -1 (/.f64 (-.f64 m (.f64 m m)) v)))) (cbrt.f64 (.f64 m (+.f64 -1 (/.f64 (-.f64 m (.f64 m m)) v))))) (cbrt.f64 (.f64 m (+.f64 -1 (/.f64 (-.f64 m (.f64 m m)) v)))))
▶	0.2b	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
	20.7b	(.f64 (/.f64 (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3)) (+.f64 1 (.f64 (/.f64 (-.f64 m (.f64 m m)) v) (+.f64 (/.f64 (-.f64 m (*.f64 m m)) v) 1)))) m)

Compiler

Compiled 1499 to 718 computations (52.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
0.0b	(/.f64 (-.f64 1 m) v)
0.2b	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
0.2b	(*.f64 m (/.f64 (-.f64 1 m) v))

rewrite202.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

57×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`
25×	`associate-r_binary64`

Counts

4 → 117

Calls

4 calls:

10.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
9.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
8.0ms	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
5.0ms	(/.f64 (-.f64 1 m) v)

Compiler

Compiled 2138 to 1380 computations (35.5% saved)

series105.0ms (2.3%)

Error

Counts

4 → 48

Calls

4 calls:

32.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
26.0ms	(-.f64 (*.f64 m (/.f64 (-.f64 1 m) v)) 1)
18.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
15.0ms	(/.f64 (-.f64 1 m) v)

Compiler

Compiled 1155 to 775 computations (32.9% saved)

simplify135.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

416×	`associate-*l/_binary64`
411×	`distribute-rgt-in_binary64`
395×	`distribute-lft-in_binary64`
331×	`times-frac_binary64`
316×	`associate-/l*_binary64`

Counts

165 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	2367
1	403	2187
2	1248	2176
3	4492	2164
4	4973	2164
5	4942	2164

prune82.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	116	9	125

Error

Counts

125 → 9

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (+.f64 -1 (/.f64 (-.f64 m (*.f64 m m)) v)) (sqrt.f64 m)) (sqrt.f64 m))
	53.6b	(neg.f64 (/.f64 (pow.f64 m 3) v))
	9.6b	(.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (.f64 m (+.f64 -1 (sqrt.f64 (/.f64 (-.f64 m (.f64 m m)) v)))))
	19.1b	(-.f64 (/.f64 (*.f64 m m) v) m)
	0.7b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (.f64 m m))))) 1) m)
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 m (+.f64 -1 (/.f64 (-.f64 m (.f64 m m)) v)))) (cbrt.f64 (.f64 m (+.f64 -1 (/.f64 (-.f64 m (.f64 m m)) v))))) (cbrt.f64 (.f64 m (+.f64 -1 (/.f64 (-.f64 m (.f64 m m)) v)))))
✓	0.2b	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
▶	0.2b	(-.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) m)
	20.7b	(.f64 (/.f64 (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3)) (+.f64 1 (.f64 (/.f64 (-.f64 m (.f64 m m)) v) (+.f64 (/.f64 (-.f64 m (*.f64 m m)) v) 1)))) m)

Compiler

Compiled 1528 to 858 computations (43.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) m)
0.0b	(-.f64 m (*.f64 m m))
0.2b	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))

rewrite99.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-l_binary64`
12×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`

Counts

3 → 74

Calls

3 calls:

9.0ms	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))
6.0ms	(-.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) m)
2.0ms	(-.f64 m (*.f64 m m))

Compiler

Compiled 1416 to 307 computations (78.3% saved)

series76.0ms (1.6%)

Error

Counts

3 → 30

Calls

3 calls:

31.0ms	(-.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) m)
25.0ms	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))
7.0ms	(-.f64 m (*.f64 m m))

Compiler

Compiled 713 to 471 computations (33.9% saved)

simplify107.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

300×	`associate-/l*_binary64`
282×	`distribute-rgt-in_binary64`
272×	`distribute-lft-in_binary64`
238×	`associate-*l/_binary64`
216×	`cancel-sign-sub-inv_binary64`

Counts

104 → 86

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	146	1586
1	344	1499
2	1027	1484
3	3276	1469
4	4809	1463
5	4910	1463

prune56.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	6	1	7
Picked	0	1	1
Done	1	0	1
Total	89	6	95

Error

Counts

95 → 6

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (.f64 (.f64 (/.f64 m v) (+.f64 m (sqrt.f64 m))) (-.f64 (sqrt.f64 m) m)) m)
	3.3b	(-.f64 (*.f64 (/.f64 (sqrt.f64 m) 1) (/.f64 (-.f64 (pow.f64 m 3/2) (pow.f64 m 5/2)) v)) m)
	8.6b	(-.f64 (/.f64 (-.f64 (*.f64 m m) (pow.f64 m 3)) v) m)
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v))) (cbrt.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)))) (cbrt.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)))) m)
✓	0.2b	(-.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) m)
	20.7b	(.f64 (/.f64 (+.f64 -1 (pow.f64 (/.f64 (-.f64 m (.f64 m m)) v) 3)) (+.f64 1 (.f64 (/.f64 (-.f64 m (.f64 m m)) v) (+.f64 (/.f64 (-.f64 m (*.f64 m m)) v) 1)))) m)

Compiler

Compiled 1130 to 400 computations (64.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 m (sqrt.f64 m))
0.0b	(-.f64 (sqrt.f64 m) m)
0.3b	(.f64 (.f64 (/.f64 m v) (+.f64 m (sqrt.f64 m))) (-.f64 (sqrt.f64 m) m))
0.3b	(*.f64 (/.f64 m v) (+.f64 m (sqrt.f64 m)))

rewrite139.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

39×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
18×	`frac-times_binary64`
18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`

Counts

4 → 126

Calls

4 calls:

14.0ms	(.f64 (.f64 (/.f64 m v) (+.f64 m (sqrt.f64 m))) (-.f64 (sqrt.f64 m) m))
10.0ms	(*.f64 (/.f64 m v) (+.f64 m (sqrt.f64 m)))
4.0ms	(-.f64 (sqrt.f64 m) m)
3.0ms	(+.f64 m (sqrt.f64 m))

Compiler

Compiled 2929 to 626 computations (78.6% saved)

series56.0ms (1.2%)

Error

Counts

4 → 18

Calls

4 calls:

22.0ms	(.f64 (.f64 (/.f64 m v) (+.f64 m (sqrt.f64 m))) (-.f64 (sqrt.f64 m) m))
16.0ms	(*.f64 (/.f64 m v) (+.f64 m (sqrt.f64 m)))
5.0ms	(-.f64 (sqrt.f64 m) m)
4.0ms	(+.f64 m (sqrt.f64 m))

Compiler

Compiled 752 to 475 computations (36.8% saved)

simplify147.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/l*_binary64`
362×	`associate-l_binary64`
285×	`associate-r_binary64`
240×	`distribute-rgt-in_binary64`
231×	`distribute-lft-in_binary64`

Counts

144 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	2598
1	652	2358
2	2461	2336
3	4611	2244
4	4924	2244
5	4976	2244

prune79.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	114	6	120

Error

Counts

120 → 6

Alt Table

Status	Error	Program
	3.3b	(-.f64 (.f64 (pow.f64 (/.f64 (.f64 m (+.f64 m (sqrt.f64 m))) v) 1) (-.f64 (sqrt.f64 m) m)) m)
	0.2b	(-.f64 (.f64 (/.f64 m v) (-.f64 m (.f64 m m))) m)
	0.3b	(-.f64 (.f64 (.f64 (/.f64 m v) (+.f64 m (sqrt.f64 m))) (-.f64 (sqrt.f64 m) m)) m)
	3.3b	(-.f64 (*.f64 (/.f64 (sqrt.f64 m) 1) (/.f64 (-.f64 (pow.f64 m 3/2) (pow.f64 m 5/2)) v)) m)
	8.6b	(-.f64 (/.f64 (-.f64 (*.f64 m m) (pow.f64 m 3)) v) m)
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v))) (cbrt.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)))) (cbrt.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)))) m)

Compiler

Compiled 1782 to 609 computations (65.8% saved)

regimes1.5s (32.2%)

Accuracy

Total 0.1b remaining (82.4%)

Threshold costs 0.1b (82.4%)

Compiler

Compiled 13847 to 8739 computations (36.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	21	21
2	30	19
3	40	19
4	44	19
5	45	19
6	45	19

end1.0ms (0%)

Compiler: Compiled 15 to 9 computations (40% saved)

sample869.0ms (18.6%)

Algorithm

1×

intervals

Results

327.0ms	8000×	body	128	valid
173.0ms	8064×	pre	128	true
3.0ms	64×	body	128	invalid

Compiler

Compiled 156 to 85 computations (45.5% saved)

Details

analyze358.0ms (7.6%)

sample27.0ms (0.6%)

simplify123.0ms (2.6%)

prune2.0ms (0%)

localize7.0ms (0.2%)

rewrite184.0ms (3.9%)

series103.0ms (2.2%)

simplify103.0ms (2.2%)

prune80.0ms (1.7%)

localize8.0ms (0.2%)

rewrite202.0ms (4.3%)

series105.0ms (2.3%)

simplify135.0ms (2.9%)

prune82.0ms (1.8%)

localize7.0ms (0.1%)

rewrite99.0ms (2.1%)

series76.0ms (1.6%)

simplify107.0ms (2.3%)

prune56.0ms (1.2%)

localize11.0ms (0.2%)

rewrite139.0ms (3%)

series56.0ms (1.2%)

simplify147.0ms (3.1%)

prune79.0ms (1.7%)

regimes1.5s (32.2%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample869.0ms (18.6%)

Profiling