Details

analyze554.0ms (10.9%)

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
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample47.0ms (0.9%)

Algorithm

1×

intervals

Results

37.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 34 to 20 computations (41.2% saved)

simplify143.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

754×	`unsub-neg_binary64`
536×	`sub-neg_binary64`
532×	`neg-mul-1_binary64`
517×	`neg-sub0_binary64`
512×	`div-sub_binary64`

Counts

1 → 1

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	81	18
3	183	18
4	302	18
5	348	18
6	463	18
7	695	18
8	1110	16
9	3301	16
10	3694	16
11	4088	16
12	4978	16
13	4978	16
14	4954	16
15	4942	16

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	1.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	20.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 72 to 43 computations (40.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 -1 (/.f64 u t1))
0.0b	(/.f64 v (+.f64 t1 u))
1.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

rewrite174.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

233×	`times-frac_binary64`
194×	`add-sqr-sqrt_binary64`
184×	`*-un-lft-identity_binary64`
94×	`add-cube-cbrt_binary64`
40×	`difference-of-squares_binary64`

Counts

3 → 209

Calls

3 calls:

12.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
5.0ms	(-.f64 -1 (/.f64 u t1))
4.0ms	(/.f64 v (+.f64 t1 u))

Compiler

Compiled 4053 to 1420 computations (65% saved)

series76.0ms (1.5%)

Error

0.3b

Counts

3 → 39

Calls

3 calls:

35.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
20.0ms	(/.f64 v (+.f64 t1 u))
13.0ms	(-.f64 -1 (/.f64 u t1))

Compiler

Compiled 1221 to 799 computations (34.6% saved)

simplify211.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

585×	`times-frac_binary64`
485×	`div-sub_binary64`
347×	`distribute-rgt-in_binary64`
306×	`associate-/l/_binary64`
163×	`associate-/r*_binary64`

Counts

248 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	339	6380
1	875	6234
2	2589	6177
3	4460	6171
4	5299	6171

prune56.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	131	7	138
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	131	9	140

Error

0.2b

Counts

140 → 9

Alt Table

Status	Error	Program
✓	1.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	20.5b	(/.f64 (/.f64 v (+.f64 t1 u)) (/.f64 (-.f64 -1 (pow.f64 (/.f64 u t1) 3)) (+.f64 1 (*.f64 (/.f64 u t1) (+.f64 -1 (/.f64 u t1))))))
	3.0b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
	3.1b	(/.f64 (neg.f64 v) (+.f64 t1 (*.f64 u (+.f64 (/.f64 u t1) 2))))
	20.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	33.0b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 t1 u))) (/.f64 (/.f64 v (sqrt.f64 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
▶	1.0b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 -1 (+.f64 1 (/.f64 u t1))))
	24.1b	(cbrt.f64 (pow.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))) 3))
	30.6b	(.f64 (/.f64 (sqrt.f64 v) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 (sqrt.f64 v) (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 1655 to 713 computations (56.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (/.f64 u t1))
0.0b	(/.f64 v (+.f64 t1 u))
0.2b	(/.f64 -1 (+.f64 1 (/.f64 u t1)))
1.0b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 -1 (+.f64 1 (/.f64 u t1))))

rewrite149.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

68×	`*-un-lft-identity_binary64`
52×	`times-frac_binary64`
50×	`add-sqr-sqrt_binary64`
38×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 138

Calls

4 calls:

17.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 -1 (+.f64 1 (/.f64 u t1))))
8.0ms	(/.f64 -1 (+.f64 1 (/.f64 u t1)))
4.0ms	(+.f64 1 (/.f64 u t1))
4.0ms	(/.f64 v (+.f64 t1 u))

Compiler

Compiled 2733 to 1236 computations (54.8% saved)

series91.0ms (1.8%)

Error

0.2b

Counts

4 → 51

Calls

4 calls:

31.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 -1 (+.f64 1 (/.f64 u t1))))
21.0ms	(/.f64 v (+.f64 t1 u))
15.0ms	(/.f64 -1 (+.f64 1 (/.f64 u t1)))
12.0ms	(+.f64 1 (/.f64 u t1))

Compiler

Compiled 1657 to 1105 computations (33.3% saved)

simplify220.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

699×	`associate-/l*_binary64`
698×	`times-frac_binary64`
575×	`associate-*r/_binary64`
334×	`associate-/r*_binary64`
288×	`associate-/l/_binary64`

Counts

189 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	3159
1	558	2882
2	1567	2855
3	4839	2855
4	4998	2855
5	4961	2855

prune51.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	109	7	116

Error

0.2b

Counts

116 → 7

Alt Table

Status	Error	Program
	33.0b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 t1 u))) (/.f64 (/.f64 v (sqrt.f64 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))))
▶	1.5b	(/.f64 (/.f64 (neg.f64 v) (+.f64 1 (/.f64 u t1))) (+.f64 t1 u))
	3.0b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
	3.1b	(/.f64 (neg.f64 v) (+.f64 t1 (*.f64 u (+.f64 (/.f64 u t1) 2))))
	20.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	27.8b	(*.f64 (/.f64 v (+.f64 t1 u)) (neg.f64 (/.f64 t1 u)))
	20.5b	(/.f64 (/.f64 v (+.f64 t1 u)) (/.f64 (-.f64 -1 (pow.f64 (/.f64 u t1) 3)) (+.f64 1 (*.f64 (/.f64 u t1) (+.f64 -1 (/.f64 u t1))))))

Compiler

Compiled 1467 to 656 computations (55.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (/.f64 u t1))
0.8b	(/.f64 (/.f64 (neg.f64 v) (+.f64 1 (/.f64 u t1))) (+.f64 t1 u))
1.9b	(/.f64 (neg.f64 v) (+.f64 1 (/.f64 u t1)))

rewrite246.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

424×	`times-frac_binary64`
409×	`*-un-lft-identity_binary64`
191×	`add-sqr-sqrt_binary64`
191×	`add-cube-cbrt_binary64`
109×	`distribute-lft-out_binary64`

Counts

3 → 335

Calls

3 calls:

22.0ms	(/.f64 (neg.f64 v) (+.f64 1 (/.f64 u t1)))
15.0ms	(/.f64 (/.f64 (neg.f64 v) (+.f64 1 (/.f64 u t1))) (+.f64 t1 u))
6.0ms	(+.f64 1 (/.f64 u t1))

Compiler

Compiled 5737 to 2332 computations (59.4% saved)

series80.0ms (1.6%)

Error

0.0b

Counts

3 → 39

Calls

3 calls:

31.0ms	(/.f64 (/.f64 (neg.f64 v) (+.f64 1 (/.f64 u t1))) (+.f64 t1 u))
28.0ms	(/.f64 (neg.f64 v) (+.f64 1 (/.f64 u t1)))
12.0ms	(+.f64 1 (/.f64 u t1))

Compiler

Compiled 1207 to 787 computations (34.8% saved)

simplify317.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

791×	`div-sub_binary64`
371×	`associate-/l/_binary64`
285×	`distribute-frac-neg_binary64`
261×	`distribute-rgt-in_binary64`
249×	`associate-/l*_binary64`

Counts

374 → 316

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	372	10720
1	879	10542
2	2862	10527
3	4261	10527
4	4993	10527

prune133.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	315	1	316
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	316	7	323

Error

0.2b

Counts

323 → 7

Alt Table

Status	Error	Program
▶	3.0b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
	3.1b	(/.f64 (neg.f64 v) (+.f64 t1 (*.f64 u (+.f64 (/.f64 u t1) 2))))
	20.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	1.5b	(/.f64 (/.f64 (neg.f64 v) (+.f64 1 (/.f64 u t1))) (+.f64 t1 u))
	27.8b	(*.f64 (/.f64 v (+.f64 t1 u)) (neg.f64 (/.f64 t1 u)))
	20.5b	(/.f64 (/.f64 v (+.f64 t1 u)) (/.f64 (-.f64 -1 (pow.f64 (/.f64 u t1) 3)) (+.f64 1 (*.f64 (/.f64 u t1) (+.f64 -1 (/.f64 u t1))))))
	21.3b	(/.f64 (cbrt.f64 (pow.f64 (neg.f64 (/.f64 v (+.f64 1 (/.f64 u t1)))) 3)) (+.f64 t1 u))

Compiler

Compiled 4504 to 1820 computations (59.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 t1 u))
0.0b	(-.f64 -1 (/.f64 u t1))
0.1b	(/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
3.0b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

rewrite285.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

436×	`times-frac_binary64`
365×	`add-sqr-sqrt_binary64`
326×	`*-un-lft-identity_binary64`
163×	`add-cube-cbrt_binary64`
114×	`associate-r_binary64`

Counts

4 → 354

Calls

4 calls:

34.0ms	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
15.0ms	(/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
6.0ms	(-.f64 -1 (/.f64 u t1))
4.0ms	(/.f64 1 (+.f64 t1 u))

Compiler

Compiled 7348 to 3685 computations (49.9% saved)

series85.0ms (1.7%)

Error

0.2b

Counts

4 → 45

Calls

4 calls:

32.0ms	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
14.0ms	(-.f64 -1 (/.f64 u t1))
14.0ms	(/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
13.0ms	(/.f64 1 (+.f64 t1 u))

Compiler

Compiled 1445 to 1019 computations (29.5% saved)

simplify260.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

349×	`associate-/r/_binary64`
322×	`distribute-rgt-in_binary64`
304×	`div-sub_binary64`
302×	`distribute-lft-in_binary64`
180×	`*-commutative_binary64`

Counts

399 → 313

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	317	9080
1	850	8599
2	2765	8494
3	4553	8488
4	5107	8488

prune99.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	313	0	313
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	313	7	320

Error

0.2b

Counts

320 → 7

Alt Table

Status	Error	Program
	3.0b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
	3.1b	(/.f64 (neg.f64 v) (+.f64 t1 (*.f64 u (+.f64 (/.f64 u t1) 2))))
	20.4b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	1.5b	(/.f64 (/.f64 (neg.f64 v) (+.f64 1 (/.f64 u t1))) (+.f64 t1 u))
	27.8b	(*.f64 (/.f64 v (+.f64 t1 u)) (neg.f64 (/.f64 t1 u)))
	20.5b	(/.f64 (/.f64 v (+.f64 t1 u)) (/.f64 (-.f64 -1 (pow.f64 (/.f64 u t1) 3)) (+.f64 1 (*.f64 (/.f64 u t1) (+.f64 -1 (/.f64 u t1))))))
	21.3b	(/.f64 (cbrt.f64 (pow.f64 (neg.f64 (/.f64 v (+.f64 1 (/.f64 u t1)))) 3)) (+.f64 t1 u))

Compiler

Compiled 3583 to 1592 computations (55.6% saved)

regimes618.0ms (12.2%)

Accuracy

Total 1.1b remaining (87.7%)

Threshold costs 0b (0%)

Compiler

Compiled 12430 to 7414 computations (40.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	17	19
2	16	19

end1.0ms (0%)

Compiler: Compiled 16 to 11 computations (31.3% saved)

sample1.1s (22.3%)

Algorithm

1×

intervals

Results

551.0ms	8000×	body	128	valid
9.0ms	245×	body	128	invalid

Compiler

Compiled 155 to 100 computations (35.5% saved)

Details

analyze554.0ms (10.9%)

sample47.0ms (0.9%)

simplify143.0ms (2.8%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

rewrite174.0ms (3.4%)

series76.0ms (1.5%)

simplify211.0ms (4.2%)

prune56.0ms (1.1%)

localize8.0ms (0.2%)

rewrite149.0ms (2.9%)

series91.0ms (1.8%)

simplify220.0ms (4.3%)

prune51.0ms (1%)

localize8.0ms (0.1%)

rewrite246.0ms (4.9%)

series80.0ms (1.6%)

simplify317.0ms (6.3%)

prune133.0ms (2.6%)

localize10.0ms (0.2%)

rewrite285.0ms (5.6%)

series85.0ms (1.7%)

simplify260.0ms (5.1%)

prune99.0ms (2%)

regimes618.0ms (12.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.1s (22.3%)

Profiling