Details

analyze332.0ms (6.1%)

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 25 to 18 computations (28% saved)

sample35.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	257×	pre	128	true
8.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 42 to 31 computations (26.2% saved)

simplify95.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1334×	`unsub-neg_binary64`
587×	`sub-neg_binary64`
522×	`div-sub_binary64`
483×	`distribute-neg-out_binary64`
441×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	46	19
3	108	19
4	319	19
5	1081	19
6	2911	19
7	3254	19
8	3891	19
9	4728	19
10	4924	19

prune5.0ms (0.1%)

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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

Compiler

Compiled 45 to 33 computations (26.7% saved)

localize8.0ms (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)
0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

rewrite223.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

33×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`

Counts

4 → 113

Calls

4 calls:

17.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
7.0ms	(*.f64 m (-.f64 1 m))

Compiler

Compiled 2420 to 1672 computations (30.9% saved)

series143.0ms (2.6%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

46.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
32.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
23.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
13.0ms	(*.f64 m (-.f64 1 m))

Compiler

Compiled 1304 to 918 computations (29.6% saved)

simplify121.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

772×	`distribute-rgt-in_binary64`
723×	`distribute-lft-in_binary64`
205×	`associate-/l/_binary64`
159×	`associate-l_binary64`
149×	`associate-/r/_binary64`

Counts

161 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	193	2768
1	476	2632
2	1612	2597
3	4724	2592
4	4972	2592

prune125.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	133	5	138

Error

Counts

138 → 5

Alt Table

Status	Error	Program
	25.3b	(/.f64 (.f64 (-.f64 m (.f64 m m)) (-.f64 1 m)) v)
▶	0.3b	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v)) 1) (-.f64 1 m))
	1.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (.f64 m m))))) 1) (-.f64 1 m))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	25.2b	(.f64 (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))) (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))))))

Compiler

Compiled 1805 to 1113 computations (38.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m))
0.1b	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v)) 1) (-.f64 1 m))
0.2b	(/.f64 m (sqrt.f64 v))
0.3b	(/.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v))

rewrite251.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

63×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
44×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
29×	`associate-l_binary64`

Counts

4 → 171

Calls

4 calls:

21.0ms	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v)) 1) (-.f64 1 m))
12.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m))
12.0ms	(/.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v))
4.0ms	(/.f64 m (sqrt.f64 v))

Compiler

Compiled 4273 to 2200 computations (48.5% saved)

series128.0ms (2.3%)

Error

Counts

4 → 41

Calls

4 calls:

35.0ms	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v)) 1) (-.f64 1 m))
30.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m))
26.0ms	(/.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v))
19.0ms	(/.f64 m (sqrt.f64 v))

Compiler

Compiled 1538 to 1117 computations (27.4% saved)

simplify123.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

875×	`distribute-rgt-in_binary64`
834×	`distribute-lft-in_binary64`
187×	`associate-l_binary64`
175×	`associate-/l*_binary64`
152×	`associate-r_binary64`

Counts

212 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	4373
1	687	3639
2	2434	3552
3	5543	3552

prune134.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	159	5	164

Error

Counts

164 → 5

Alt Table

Status	Error	Program
	25.3b	(/.f64 (.f64 (-.f64 m (.f64 m m)) (-.f64 1 m)) v)
✓	0.3b	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v)) 1) (-.f64 1 m))
▶	1.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (.f64 m m))))) 1) (-.f64 1 m))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	25.2b	(.f64 (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))) (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))))))

Compiler

Compiled 2442 to 1367 computations (44% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3)))
0.0b	(.f64 v (+.f64 1 (+.f64 m (.f64 m m))))
0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (.f64 m m))))) 1) (-.f64 1 m))
1.0b	(/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (*.f64 m m)))))

rewrite324.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

61×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
44×	`associate-r_binary64`
30×	`cancel-sign-sub-inv_binary64`
28×	`difference-of-squares_binary64`

Counts

4 → 166

Calls

4 calls:

29.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (.f64 m m))))) 1) (-.f64 1 m))
25.0ms	(*.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3)))
23.0ms	(/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (*.f64 m m)))))
7.0ms	(.f64 v (+.f64 1 (+.f64 m (.f64 m m))))

Compiler

Compiled 5454 to 3534 computations (35.2% saved)

series201.0ms (3.7%)

Error

Counts

4 → 45

Calls

4 calls:

69.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (.f64 m m))))) 1) (-.f64 1 m))
46.0ms	(/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (*.f64 m m)))))
30.0ms	(.f64 v (+.f64 1 (+.f64 m (.f64 m m))))
18.0ms	(*.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3)))

Compiler

Compiled 2109 to 1510 computations (28.4% saved)

simplify176.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

428×	`associate-l_binary64`
361×	`associate-r_binary64`
337×	`exp-prod_binary64`
298×	`times-frac_binary64`
257×	`distribute-rgt-in_binary64`

Counts

211 → 190

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	299	4884
1	771	4320
2	3968	4302
3	4566	4182
4	4976	4182

prune168.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	190	5	195

Error

Counts

195 → 5

Alt Table

Status	Error	Program
	25.3b	(/.f64 (.f64 (-.f64 m (.f64 m m)) (-.f64 1 m)) v)
✓	0.3b	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v)) 1) (-.f64 1 m))
✓	1.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (.f64 m m))))) 1) (-.f64 1 m))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
▶	25.2b	(.f64 (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))) (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))))))

Compiler

Compiled 3465 to 2186 computations (36.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (/.f64 m v) (-.f64 1 m))
0.1b	(sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m)))))
0.1b	(sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m)))))
0.3b	(.f64 (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))) (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))))))

rewrite379.0ms (6.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

160×	`sqrt-div_binary64`
146×	`frac-times_binary64`
62×	`flip3--_binary64` `flip--_binary64`
61×	`pow1_binary64`
60×	`flip3-+_binary64` `flip-+_binary64`

Counts

4 → 214

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))) (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))))))
11.0ms	(*.f64 (/.f64 m v) (-.f64 1 m))
7.0ms	(sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m)))))
7.0ms	(sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m)))))

Compiler

Compiled 11347 to 7493 computations (34% saved)

series130.0ms (2.4%)

Error

Counts

4 → 36

Calls

4 calls:

32.0ms	(.f64 (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))) (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))))))
29.0ms	(*.f64 (/.f64 m v) (-.f64 1 m))
27.0ms	(sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m)))))
25.0ms	(sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m)))))

Compiler

Compiled 2149 to 1559 computations (27.5% saved)

simplify238.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

899×	`distribute-rgt-in_binary64`
737×	`times-frac_binary64`
241×	`associate-l_binary64`
224×	`associate-r_binary64`
181×	`*-commutative_binary64`

Counts

250 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	365	10916
1	705	10653
2	2232	10481
3	5482	10481

prune152.0ms (2.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	213	5	218

Error

Counts

218 → 5

Alt Table

Status	Error	Program
	25.3b	(/.f64 (.f64 (-.f64 m (.f64 m m)) (-.f64 1 m)) v)
	0.3b	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v)) 1) (-.f64 1 m))
	1.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (.f64 v (+.f64 1 (+.f64 m (.f64 m m))))) 1) (-.f64 1 m))
	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	25.2b	(.f64 (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))) (sqrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))))))

Compiler

Compiled 5341 to 3279 computations (38.6% saved)

regimes1.1s (19.9%)

Accuracy

Total 0.0b remaining (77.5%)

Threshold costs 0.0b (77.5%)

Compiler

Compiled 17492 to 12447 computations (28.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
7×	`*-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-mul-1_binary64` `neg-sub0_binary64`
4×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	24	31
2	32	31
3	44	31
4	55	31
5	63	31
6	68	31
7	70	31
8	67	31

end1.0ms (0%)

Compiler: Compiled 23 to 14 computations (39.1% saved)

sample863.0ms (15.7%)

Algorithm

1×

intervals

Results

276.0ms	8000×	body	128	valid
159.0ms	8056×	pre	128	true
2.0ms	56×	body	128	invalid

Compiler

Compiled 155 to 108 computations (30.3% saved)

Details

analyze332.0ms (6.1%)

sample35.0ms (0.6%)

simplify95.0ms (1.7%)

prune5.0ms (0.1%)

localize8.0ms (0.2%)

rewrite223.0ms (4.1%)

series143.0ms (2.6%)

simplify121.0ms (2.2%)

prune125.0ms (2.3%)

localize11.0ms (0.2%)

rewrite251.0ms (4.6%)

series128.0ms (2.3%)

simplify123.0ms (2.2%)

prune134.0ms (2.4%)

localize18.0ms (0.3%)

rewrite324.0ms (5.9%)

series201.0ms (3.7%)

simplify176.0ms (3.2%)

prune168.0ms (3.1%)

localize12.0ms (0.2%)

rewrite379.0ms (6.9%)

series130.0ms (2.4%)

simplify238.0ms (4.3%)

prune152.0ms (2.8%)

regimes1.1s (19.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample863.0ms (15.7%)

Profiling