Details

analyze1.6s (17.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.2%	98.5%	0.3%	13
1.8%	97.9%	0.3%	14

Compiler

Compiled 18 to 18 computations (0% saved)

sample48.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
6.0ms	108×	body	128	invalid

Compiler

Compiled 35 to 42 computations (-20% saved)

simplify222.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	868	25
1	868	25

prune8.0ms (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

Merged error: 0.3b

Counts

2 → 1

Compiler

Compiled 34 to 34 computations (0% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
0.0b	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))
0.2b	(/.f64 (*.f64 z t) 16)

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-log-exp_binary64_5505`
12×	`*-un-lft-identity_binary64_5469`
8×	`add-exp-log_binary64_5504` `add-cbrt-cube_binary64_5502`
7×	`add-sqr-sqrt_binary64_5490`
5×	`sum-log_binary64_5557` `add-cube-cbrt_binary64_5501`
4×	`diff-log_binary64_5558`
3×	`associate-/r*_binary64_5415` `pow1_binary64_5527` `times-frac_binary64_5475`
2×	`associate--l+_binary64_5408` `frac-sub_binary64_5478` `sub-neg_binary64_5462` `distribute-lft-out_binary64_5422` `flip-+_binary64_5443` `associate-+l+_binary64_5404` `cbrt-undiv_binary64_5500` `div-exp_binary64_5517` `distribute-lft-out--_binary64_5423` `flip3-+_binary64_5472`
1×	`+-commutative_binary64_5401` `clear-num_binary64_5468` `flip3--_binary64_5473` `cbrt-unprod_binary64_5499` `associate-/l*_binary64_5416` `difference-of-squares_binary64_5438` `flip--_binary64_5444` `div-inv_binary64_5466` `frac-2neg_binary64_5480` `associate-+l-_binary64_5406` `prod-exp_binary64_5515`

Counts

3 → 56

Calls

3 calls:

15.0ms	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
12.0ms	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))
6.0ms	(/.f64 (*.f64 z t) 16)

series542.0ms (5.9%)

Counts

3 → 9

Calls

3 calls:

319.0ms	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
192.0ms	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))
30.0ms	(/.f64 (*.f64 z t) 16)

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4968	1491
1	4968	1491

prune82.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	3	66

Merged error: 0.0b

Counts

66 → 3

Compiler

Compiled 1623 to 791 computations (51.3% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (-.f64 (+.f64 (.f64 x y) (.f64 z (/.f64 t 16))) (/.f64 (*.f64 a b) 4)) c)
0.0b	(-.f64 (+.f64 (.f64 x y) (.f64 z (/.f64 t 16))) (/.f64 (*.f64 a b) 4))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-log-exp_binary64_5505`
9×	`*-un-lft-identity_binary64_5469`
5×	`sum-log_binary64_5557`
4×	`diff-log_binary64_5558` `add-sqr-sqrt_binary64_5490`
2×	`associate--l+_binary64_5408` `frac-sub_binary64_5478` `sub-neg_binary64_5462` `distribute-lft-out_binary64_5422` `flip-+_binary64_5443` `associate-+l+_binary64_5404` `add-exp-log_binary64_5504` `add-cbrt-cube_binary64_5502` `add-cube-cbrt_binary64_5501` `pow1_binary64_5527` `distribute-lft-out--_binary64_5423` `flip3-+_binary64_5472`
1×	`+-commutative_binary64_5401` `flip3--_binary64_5473` `difference-of-squares_binary64_5438` `flip--_binary64_5444` `associate-+l-_binary64_5406`

Counts

2 → 35

Calls

2 calls:

13.0ms	(+.f64 (-.f64 (+.f64 (.f64 x y) (.f64 z (/.f64 t 16))) (/.f64 (*.f64 a b) 4)) c)
10.0ms	(-.f64 (+.f64 (.f64 x y) (.f64 z (/.f64 t 16))) (/.f64 (*.f64 a b) 4))

series499.0ms (5.5%)

Counts

2 → 6

Calls

2 calls:

310.0ms	(+.f64 (-.f64 (+.f64 (.f64 x y) (.f64 z (/.f64 t 16))) (/.f64 (*.f64 a b) 4)) c)
189.0ms	(-.f64 (+.f64 (.f64 x y) (.f64 z (/.f64 t 16))) (/.f64 (*.f64 a b) 4))

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4948	1283
1	4948	1283

prune48.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	41	3	44

Merged error: 0.0b

Counts

44 → 3

Compiler

Compiled 1132 to 599 computations (47.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 (-.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)) (/.f64 (*.f64 a b) 4)) c))
0.2b	(/.f64 (*.f64 z t) 16)
0.2b	(/.f64 (*.f64 z t) 16)
0.3b	(.f64 (sqrt.f64 (+.f64 (-.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)) (/.f64 (.f64 a b) 4)) c)) (sqrt.f64 (+.f64 (-.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)) (/.f64 (*.f64 a b) 4)) c)))

rewrite85.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64_5469`
43×	`sqrt-prod_binary64_5484`
30×	`add-sqr-sqrt_binary64_5490`
20×	`pow1_binary64_5527`
18×	`distribute-lft-out_binary64_5422`
17×	`add-cube-cbrt_binary64_5501`
16×	`swap-sqr_binary64_5436` `add-exp-log_binary64_5504` `add-cbrt-cube_binary64_5502`
14×	`sqrt-div_binary64_5485`
9×	`pow1/2_binary64_5546` `distribute-lft-out--_binary64_5423` `sqrt-pow1_binary64_5486`
8×	`associate-r_binary64_5411` `associate-l_binary64_5412`
7×	`flip-+_binary64_5443` `flip3-+_binary64_5472`
6×	`associate-/r*_binary64_5415` `times-frac_binary64_5475`
5×	`pow-prod-up_binary64_5536`
4×	`cbrt-undiv_binary64_5500` `frac-times_binary64_5479` `div-exp_binary64_5517` `unswap-sqr_binary64_5437` `add-log-exp_binary64_5505`
3×	`pow-prod-down_binary64_5537` `cbrt-unprod_binary64_5499` `pow-sqr_binary64_5442` `prod-exp_binary64_5515`
2×	`clear-num_binary64_5468` `associate-l/_binary64_5414` `associate-/l_binary64_5416` `div-inv_binary64_5466` `associate-*r/_binary64_5413` `frac-2neg_binary64_5480`
1×	`rem-sqrt-square_binary64_5482` `pow2_binary64_5547` `sqrt-unprod_binary64_5488` `pow-plus_binary64_5529` `rem-square-sqrt_binary64_5481` `*-commutative_binary64_5402`

Counts

4 → 128

Calls

4 calls:

37.0ms	(.f64 (sqrt.f64 (+.f64 (-.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)) (/.f64 (.f64 a b) 4)) c)) (sqrt.f64 (+.f64 (-.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)) (/.f64 (*.f64 a b) 4)) c)))
16.0ms	(sqrt.f64 (+.f64 (-.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)) (/.f64 (*.f64 a b) 4)) c))
5.0ms	(/.f64 (*.f64 z t) 16)
5.0ms	(/.f64 (*.f64 z t) 16)

series3.2s (34.6%)

Counts

4 → 12

Calls

4 calls:

2.8s	(sqrt.f64 (+.f64 (-.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)) (/.f64 (*.f64 a b) 4)) c))
328.0ms	(.f64 (sqrt.f64 (+.f64 (-.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)) (/.f64 (.f64 a b) 4)) c)) (sqrt.f64 (+.f64 (-.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)) (/.f64 (*.f64 a b) 4)) c)))
30.0ms	(/.f64 (*.f64 z t) 16)
29.0ms	(/.f64 (*.f64 z t) 16)

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5164	3842

prune238.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	140	3	143

Merged error: 0.0b

Counts

143 → 3

Compiler

Compiled 5508 to 2685 computations (51.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(sqrt.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)))
1.8b	(sqrt.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)))
7.0b	(sqrt.f64 (/.f64 (*.f64 a b) 4))
7.0b	(sqrt.f64 (/.f64 (*.f64 a b) 4))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`sqrt-prod_binary64_5484`
14×	`add-sqr-sqrt_binary64_5490`
10×	`add-cube-cbrt_binary64_5501` `*-un-lft-identity_binary64_5469`
8×	`pow1_binary64_5527`
6×	`sqrt-div_binary64_5485` `times-frac_binary64_5475`
4×	`rem-sqrt-square_binary64_5482` `add-exp-log_binary64_5504` `pow1/2_binary64_5546` `add-cbrt-cube_binary64_5502` `add-log-exp_binary64_5505` `sqrt-pow1_binary64_5486`
2×	`flip-+_binary64_5443` `div-inv_binary64_5466` `flip3-+_binary64_5472`

Counts

4 → 66

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)))
7.0ms	(sqrt.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)))
4.0ms	(sqrt.f64 (/.f64 (*.f64 a b) 4))
4.0ms	(sqrt.f64 (/.f64 (*.f64 a b) 4))

series506.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(sqrt.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)))
154.0ms	(sqrt.f64 (+.f64 (/.f64 (.f64 z t) 16) (.f64 x y)))
100.0ms	(sqrt.f64 (/.f64 (*.f64 a b) 4))
97.0ms	(sqrt.f64 (/.f64 (*.f64 a b) 4))

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5048	1326

prune131.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	78	3	81

Merged error: 0.0b

Counts

81 → 3

Compiler

Compiled 3366 to 1709 computations (49.2% saved)

regimes194.0ms (2.1%)

Compiler: Compiled 1308 to 1196 computations (8.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	25
1	56	25

end0.0ms (0%)

sample1.3s (14.7%)

Algorithm

1×

intervals

Results

446.0ms	8000×	body	128	valid
228.0ms	3963×	body	128	invalid

Compiler

Compiled 126 to 114 computations (9.5% saved)

Details

analyze1.6s (17.1%)

sample48.0ms (0.5%)

simplify222.0ms (2.4%)

prune8.0ms (0.1%)

localize14.0ms (0.2%)

rewrite38.0ms (0.4%)

series542.0ms (5.9%)

simplify91.0ms (1%)

prune82.0ms (0.9%)

localize14.0ms (0.2%)

rewrite27.0ms (0.3%)

series499.0ms (5.5%)

simplify83.0ms (0.9%)

prune48.0ms (0.5%)

localize20.0ms (0.2%)

rewrite85.0ms (0.9%)

series3.2s (34.6%)

simplify71.0ms (0.8%)

prune238.0ms (2.6%)

localize19.0ms (0.2%)

rewrite34.0ms (0.4%)

series506.0ms (5.5%)

simplify57.0ms (0.6%)

prune131.0ms (1.4%)

regimes194.0ms (2.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.3s (14.7%)

Profiling