Details

analyze1.1s (19.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample40.0ms (0.7%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
4.0ms	76×	body	128	nan
2.0ms	35×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify173.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	175	21
1	175	21

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

Merged error: 24.6b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
4.0b	(.f64 (.f64 x y) z)
9.7b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
23.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_12843` `add-exp-log_binary64_12845`
11×	`add-sqr-sqrt_binary64_12829`
10×	`*-un-lft-identity_binary64_12807` `pow1_binary64_12868` `add-cube-cbrt_binary64_12842`
9×	`sqrt-prod_binary64_12823`
6×	`prod-exp_binary64_12856` `cbrt-unprod_binary64_12840` `times-frac_binary64_12813` `associate-/r*_binary64_12751` `add-log-exp_binary64_12846`
4×	`sqrt-div_binary64_12824`
3×	`div-exp_binary64_12858` `pow-prod-down_binary64_12878` `flip--_binary64_12782` `flip3--_binary64_12811` `cbrt-undiv_binary64_12841` `associate-r_binary64_12747`
2×	`associate-/r/_binary64_12753`
1×	`sqrt-pow1_binary64_12825` `-commutative_binary64_12738` `div-inv_binary64_12804` `clear-num_binary64_12806` `associate-/l_binary64_12752` `associate-l_binary64_12748` `rem-sqrt-square_binary64_12820` `diff-log_binary64_12899` `cancel-sign-sub-inv_binary64_12773` `sub-neg_binary64_12800` `pow1/2_binary64_12887` `frac-2neg_binary64_12818`

Counts

4 → 76

Calls

4 calls:

11.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(.f64 (.f64 x y) z)
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series464.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

254.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
108.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
52.0ms	(-.f64 (.f64 z z) (.f64 t a))
50.0ms	(.f64 (.f64 x y) z)

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5240	1472

prune278.0ms (4.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 2.8b

Counts

89 → 9

Compiler

Compiled 5453 to 2813 computations (48.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
1.0b	(-.f64 (.f64 z z) (.f64 t a))
2.1b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
23.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_12813`
34×	`add-sqr-sqrt_binary64_12829`
33×	`*-un-lft-identity_binary64_12807` `add-cube-cbrt_binary64_12842`
24×	`sqrt-prod_binary64_12823` `associate-r_binary64_12747`
18×	`add-cbrt-cube_binary64_12843` `add-exp-log_binary64_12845`
10×	`pow1_binary64_12868`
6×	`prod-exp_binary64_12856` `cbrt-unprod_binary64_12840` `associate-/r*_binary64_12751` `sqrt-div_binary64_12824` `add-log-exp_binary64_12846`
4×	`associate-/r/_binary64_12753` `flip--_binary64_12782` `flip3--_binary64_12811`
3×	`div-exp_binary64_12858` `pow-prod-down_binary64_12878` `associate-/l*_binary64_12752` `cbrt-undiv_binary64_12841`
2×	`div-inv_binary64_12804`
1×	`sqrt-pow1_binary64_12825` `-commutative_binary64_12738` `clear-num_binary64_12806` `associate-l_binary64_12748` `associate-r/_binary64_12749` `rem-sqrt-square_binary64_12820` `diff-log_binary64_12899` `cancel-sign-sub-inv_binary64_12773` `sub-neg_binary64_12800` `pow1/2_binary64_12887` `frac-2neg_binary64_12818`

Counts

4 → 112

Calls

4 calls:

14.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
7.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
7.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(-.f64 (.f64 z z) (.f64 t a))

series509.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
102.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
90.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
55.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5279	2521

prune114.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	124	9	133

Merged error: 2.8b

Counts

133 → 9

Compiler

Compiled 3020 to 706 computations (76.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
1.0b	(-.f64 (.f64 z z) (.f64 t a))
2.1b	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
23.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite82.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`times-frac_binary64_12813`
143×	`add-sqr-sqrt_binary64_12829`
142×	`*-un-lft-identity_binary64_12807` `add-cube-cbrt_binary64_12842`
71×	`associate-r_binary64_12747`
66×	`sqrt-prod_binary64_12823`
60×	`add-exp-log_binary64_12845`
30×	`add-cbrt-cube_binary64_12843`
22×	`associate-/r*_binary64_12751`
21×	`div-exp_binary64_12858` `prod-exp_binary64_12856`
11×	`pow1_binary64_12868`
9×	`cbrt-unprod_binary64_12840` `div-inv_binary64_12804` `cbrt-undiv_binary64_12841`
6×	`rec-exp_binary64_12857` `add-log-exp_binary64_12846` `1-exp_binary64_12851`
3×	`pow-prod-down_binary64_12878` `associate-/l*_binary64_12752`
2×	`associate-/r/_binary64_12753` `flip--_binary64_12782` `flip3--_binary64_12811` `sqrt-div_binary64_12824`
1×	`sqrt-pow1_binary64_12825` `-commutative_binary64_12738` `inv-pow_binary64_12892` `clear-num_binary64_12806` `associate-l_binary64_12748` `associate-r/_binary64_12749` `pow-flip_binary64_12881` `rem-sqrt-square_binary64_12820` `diff-log_binary64_12899` `cancel-sign-sub-inv_binary64_12773` `sub-neg_binary64_12800` `pow1/2_binary64_12887` `frac-2neg_binary64_12818` `un-div-inv_binary64_12805`

Counts

4 → 243

Calls

4 calls:

26.0ms	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
14.0ms	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
5.0ms	(-.f64 (.f64 z z) (.f64 t a))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series489.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(.f64 (.f64 x y) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)))
109.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
81.0ms	(/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
54.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify102.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4970	6375
1	4970	6375

prune221.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	255	9	264

Merged error: 2.8b

Counts

264 → 9

Compiler

Compiled 6662 to 1414 computations (78.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
4.0b	(.f64 z (.f64 x y))
9.7b	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (.f64 z (.f64 x y)))
23.9b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_12843` `add-exp-log_binary64_12845`
11×	`add-sqr-sqrt_binary64_12829`
10×	`*-un-lft-identity_binary64_12807` `pow1_binary64_12868` `add-cube-cbrt_binary64_12842`
9×	`sqrt-prod_binary64_12823`
6×	`prod-exp_binary64_12856` `cbrt-unprod_binary64_12840` `associate-/l*_binary64_12752` `times-frac_binary64_12813` `add-log-exp_binary64_12846`
4×	`sqrt-div_binary64_12824`
3×	`div-exp_binary64_12858` `pow-prod-down_binary64_12878` `flip--_binary64_12782` `associate-l_binary64_12748` `flip3--_binary64_12811` `cbrt-undiv_binary64_12841`
2×	`associate-/l/_binary64_12754`
1×	`sqrt-pow1_binary64_12825` `-commutative_binary64_12738` `div-inv_binary64_12804` `clear-num_binary64_12806` `associate-/r_binary64_12751` `rem-sqrt-square_binary64_12820` `diff-log_binary64_12899` `cancel-sign-sub-inv_binary64_12773` `sub-neg_binary64_12800` `pow1/2_binary64_12887` `associate-r_binary64_12747` `frac-2neg_binary64_12818`

Counts

4 → 76

Calls

4 calls:

11.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (.f64 z (.f64 x y)))
5.0ms	(.f64 z (.f64 x y))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series453.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

245.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) (.f64 z (.f64 x y)))
106.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
53.0ms	(.f64 z (.f64 x y))
49.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4978	1532
1	4978	1532

prune78.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	88	9	97

Merged error: 2.8b

Counts

97 → 9

Compiler

Compiled 2010 to 582 computations (71% saved)

regimes203.0ms (3.4%)

Compiler: Compiled 771 to 760 computations (1.4% saved)

bsearch57.0ms (1%)

Steps

Iters	Range		Point
5	6.563063877230831e+30	1.626117443720512e+31	1.2734670136616398e+31
9	-157060.7005523723	-0.7807718225393175	-154803.1985485592

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	46
1	75	46

end0.0ms (0%)

sample1.2s (19.5%)

Algorithm

1×

intervals

Results

434.0ms	8000×	body	128	valid
107.0ms	2249×	body	128	nan
47.0ms	833×	body	128	invalid

Compiler

Compiled 182 to 158 computations (13.2% saved)

Details

analyze1.1s (19.3%)

sample40.0ms (0.7%)

simplify173.0ms (2.9%)

prune3.0ms (0.1%)

localize16.0ms (0.3%)

rewrite31.0ms (0.5%)

series464.0ms (7.8%)

simplify53.0ms (0.9%)

prune278.0ms (4.7%)

localize10.0ms (0.2%)

rewrite44.0ms (0.7%)

series509.0ms (8.6%)

simplify78.0ms (1.3%)

prune114.0ms (1.9%)

localize12.0ms (0.2%)

rewrite82.0ms (1.4%)

series489.0ms (8.3%)

simplify102.0ms (1.7%)

prune221.0ms (3.7%)

localize13.0ms (0.2%)

rewrite32.0ms (0.5%)

series453.0ms (7.7%)

simplify65.0ms (1.1%)

prune78.0ms (1.3%)

regimes203.0ms (3.4%)

bsearch57.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.2s (19.5%)

Profiling