Details

analyze142.0ms (2.8%)

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)

sample27.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
5.0ms	260×	pre	128	true
0.0ms	4×	body	128	invalid

Compiler

Compiled 42 to 31 computations (26.2% saved)

simplify94.0ms (1.9%)

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

rewrite231.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 113

Calls

4 calls:

17.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
13.0ms	(*.f64 m (-.f64 1 m))
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

Compiler

Compiled 2420 to 1672 computations (30.9% saved)

series131.0ms (2.6%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

43.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
32.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
22.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
9.0ms	(*.f64 m (-.f64 1 m))

Compiler

Compiled 1304 to 918 computations (29.6% saved)

simplify141.0ms (2.8%)

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

prune117.0ms (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

0.0b

Counts

138 → 5

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) (-.f64 1 m))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	0.7b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))) (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m)))))) (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))))
	0.2b	(.f64 (.f64 (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))) (.f64 (cbrt.f64 (-.f64 1 m)) (cbrt.f64 (-.f64 1 m)))) (cbrt.f64 (-.f64 1 m)))
	0.1b	(.f64 (.f64 (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))

Compiler

Compiled 1841 to 1143 computations (37.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite195.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

33×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
21×	`cancel-sign-sub-inv_binary64`
20×	`add-cube-cbrt_binary64`
16×	`associate-l_binary64`

Counts

3 → 106

Calls

3 calls:

16.0ms	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) (-.f64 1 m))
11.0ms	(*.f64 (/.f64 m v) (-.f64 1 m))
10.0ms	(-.f64 (*.f64 (/.f64 m v) (-.f64 1 m)) 1)

Compiler

Compiled 2421 to 1457 computations (39.8% saved)

series104.0ms (2.1%)

Error

0.0b

Counts

3 → 42

Calls

3 calls:

33.0ms	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) (-.f64 1 m))
31.0ms	(-.f64 (*.f64 (/.f64 m v) (-.f64 1 m)) 1)
22.0ms	(*.f64 (/.f64 m v) (-.f64 1 m))

Compiler

Compiled 1160 to 810 computations (30.2% saved)

simplify115.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

810×	`distribute-rgt-in_binary64`
773×	`distribute-lft-in_binary64`
417×	`times-frac_binary64`
173×	`associate-l_binary64`
128×	`associate-r_binary64`

Counts

148 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	2682
1	510	2572
2	1614	2521
3	4917	2521
4	4993	2521

prune101.0ms (2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	126	5	131

Error

0.0b

Counts

131 → 5

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) (-.f64 1 m))
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	0.7b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))) (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m)))))) (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))))
	0.2b	(.f64 (.f64 (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))) (.f64 (cbrt.f64 (-.f64 1 m)) (cbrt.f64 (-.f64 1 m)))) (cbrt.f64 (-.f64 1 m)))
▶	0.1b	(.f64 (.f64 (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))

Compiler

Compiled 1723 to 1036 computations (39.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite333.0ms (6.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

48×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
34×	`frac-times_binary64`
24×	`cancel-sign-sub-inv_binary64`
24×	`flip-+_binary64`

Counts

4 → 164

Calls

4 calls:

16.0ms	(.f64 (.f64 (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
11.0ms	(*.f64 (/.f64 m v) (-.f64 1 m))
10.0ms	(.f64 (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m)))
5.0ms	(-.f64 1 (sqrt.f64 m))

Compiler

Compiled 5255 to 3095 computations (41.1% saved)

series126.0ms (2.5%)

Error

0.0b

Counts

4 → 31

Calls

4 calls:

42.0ms	(.f64 (.f64 (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
31.0ms	(.f64 (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m)))
23.0ms	(*.f64 (/.f64 m v) (-.f64 1 m))
8.0ms	(-.f64 1 (sqrt.f64 m))

Compiler

Compiled 1479 to 1046 computations (29.3% saved)

simplify181.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

651×	`times-frac_binary64`
447×	`associate-l_binary64`
421×	`distribute-rgt-in_binary64`
404×	`distribute-lft-in_binary64`
366×	`associate-r_binary64`

Counts

195 → 166

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	5319
1	974	4951
2	3510	4923
3	4839	4923
4	4958	4923

prune227.0ms (4.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	165	6	171

Error

Counts

171 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) (-.f64 1 m))
	0.3b	(.f64 (.f64 (.f64 (+.f64 -1 (/.f64 (-.f64 m (.f64 m m)) v)) (*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 m))) (cbrt.f64 (+.f64 1 (sqrt.f64 m))))) (cbrt.f64 (+.f64 1 (sqrt.f64 m)))) (-.f64 1 (sqrt.f64 m)))
	0.7b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))) (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m)))))) (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))))
▶	0.1b	(.f64 (.f64 (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m))) (/.f64 (-.f64 1 m) (+.f64 1 (sqrt.f64 m))))
	0.1b	(.f64 (+.f64 (/.f64 (pow.f64 m 3/2) v) (-.f64 (/.f64 (-.f64 m (.f64 m m)) v) (+.f64 (sqrt.f64 m) (+.f64 1 (/.f64 (pow.f64 m 5/2) v))))) (-.f64 1 (sqrt.f64 m)))
✓	0.1b	(.f64 (.f64 (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))

Compiler

Compiled 3675 to 1819 computations (50.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite447.0ms (8.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

119×	`*-un-lft-identity_binary64`
98×	`add-sqr-sqrt_binary64`
70×	`times-frac_binary64`
47×	`associate-r_binary64`
41×	`add-cube-cbrt_binary64`

Counts

4 → 207

Calls

4 calls:

23.0ms	(.f64 (.f64 (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m))) (/.f64 (-.f64 1 m) (+.f64 1 (sqrt.f64 m))))
11.0ms	(*.f64 (/.f64 m v) (-.f64 1 m))
10.0ms	(/.f64 (-.f64 1 m) (+.f64 1 (sqrt.f64 m)))
9.0ms	(.f64 (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m)))

Compiler

Compiled 6522 to 4086 computations (37.4% saved)

series128.0ms (2.5%)

Error

Counts

4 → 39

Calls

4 calls:

33.0ms	(.f64 (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m)))
33.0ms	(.f64 (.f64 (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m))) (/.f64 (-.f64 1 m) (+.f64 1 (sqrt.f64 m))))
24.0ms	(*.f64 (/.f64 m v) (-.f64 1 m))
8.0ms	(/.f64 (-.f64 1 m) (+.f64 1 (sqrt.f64 m)))

Compiler

Compiled 1763 to 1246 computations (29.3% saved)

simplify247.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

414×	`associate-l_binary64`
317×	`distribute-rgt-in_binary64`
310×	`associate-r_binary64`
303×	`distribute-lft-in_binary64`
243×	`*-commutative_binary64`

Counts

246 → 197

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	322	6554
1	1000	6019
2	3643	6003
3	4653	5975
4	4979	5975
5	4984	5975

prune258.0ms (5.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	197	6	203

Error

Counts

203 → 6

Alt Table

Status	Error	Program
	0.1b	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) (-.f64 1 m))
	0.3b	(.f64 (.f64 (.f64 (+.f64 -1 (/.f64 (-.f64 m (.f64 m m)) v)) (*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 m))) (cbrt.f64 (+.f64 1 (sqrt.f64 m))))) (cbrt.f64 (+.f64 1 (sqrt.f64 m)))) (-.f64 1 (sqrt.f64 m)))
	0.7b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))) (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m)))))) (cbrt.f64 (.f64 (-.f64 1 m) (+.f64 -1 (.f64 (/.f64 m v) (-.f64 1 m))))))
	0.1b	(.f64 (.f64 (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m))) (/.f64 (-.f64 1 m) (+.f64 1 (sqrt.f64 m))))
	0.1b	(.f64 (+.f64 (/.f64 (pow.f64 m 3/2) v) (-.f64 (/.f64 (-.f64 m (.f64 m m)) v) (+.f64 (sqrt.f64 m) (+.f64 1 (/.f64 (pow.f64 m 5/2) v))))) (-.f64 1 (sqrt.f64 m)))
	0.1b	(.f64 (.f64 (+.f64 -1 (*.f64 (/.f64 m v) (-.f64 1 m))) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))

Compiler

Compiled 4216 to 2578 computations (38.9% saved)

regimes753.0ms (15%)

Accuracy

Total 0.1b remaining (74.9%)

Threshold costs 0.1b (74.9%)

Compiler

Compiled 13606 to 9449 computations (30.6% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

28×	`distribute-rgt-neg-in_binary64`
20×	`distribute-lft-neg-in_binary64`
19×	`distribute-neg-in_binary64`
19×	`cancel-sign-sub-inv_binary64`
19×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	26	31
2	36	31
3	49	31
4	56	31
5	66	31
6	74	31
7	86	31
8	99	31
9	120	31
10	136	31
11	145	31
12	149	31
13	154	31
14	159	31
15	161	31
16	157	31

end1.0ms (0%)

Compiler: Compiled 23 to 16 computations (30.4% saved)

sample872.0ms (17.4%)

Algorithm

1×

intervals

Results

257.0ms	8000×	body	128	valid
158.0ms	8066×	pre	128	true
2.0ms	66×	body	128	invalid

Compiler

Compiled 222 to 155 computations (30.2% saved)

Iter	Nodes	Cost
0	12	33
1	26	31
2	36	31
3	49	31
4	56	31
5	66	31
6	74	31
7	86	31
8	99	31
9	120	31
10	136	31
11	145	31
12	149	31
13	154	31
14	159	31
15	161	31
16	157	31

Iter	Nodes	Cost
0	12	33
1	26	31
2	36	31
3	49	31
4	56	31
5	66	31
6	74	31
7	86	31
8	99	31
9	120	31
10	136	31
11	145	31
12	149	31
13	154	31
14	159	31
15	161	31
16	157	31

Details

analyze142.0ms (2.8%)

sample27.0ms (0.5%)

simplify94.0ms (1.9%)

prune5.0ms (0.1%)

localize8.0ms (0.2%)

rewrite231.0ms (4.6%)

series131.0ms (2.6%)

simplify141.0ms (2.8%)

prune117.0ms (2.3%)

localize6.0ms (0.1%)

rewrite195.0ms (3.9%)

series104.0ms (2.1%)

simplify115.0ms (2.3%)

prune101.0ms (2%)

localize11.0ms (0.2%)

rewrite333.0ms (6.6%)

series126.0ms (2.5%)

simplify181.0ms (3.6%)

prune227.0ms (4.5%)

localize11.0ms (0.2%)

rewrite447.0ms (8.9%)

series128.0ms (2.5%)

simplify247.0ms (4.9%)

prune258.0ms (5.1%)

regimes753.0ms (15%)

simplify9.0ms (0.2%)

end1.0ms (0%)

sample872.0ms (17.4%)

Profiling

Iter	Nodes	Cost
0	12	33
1	26	31
2	36	31
3	49	31
4	56	31
5	66	31
6	74	31
7	86	31
8	99	31
9	120	31
10	136	31
11	145	31
12	149	31
13	154	31
14	159	31
15	161	31
16	157	31