Details

analyze33.0ms (0.6%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
56.2%	43.7%	0.1%	5
65.6%	34.3%	0.1%	6
79.6%	20.3%	0.1%	7
83.5%	16.4%	0.1%	8
90.1%	9.8%	0.1%	9
91.9%	8%	0.1%	10
95.1%	4.8%	0.1%	11
96%	4%	0.1%	12
97.5%	2.4%	0.1%	13
97.9%	2%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample18.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify308.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (212.0ms)

Iter	Nodes	Cost
0	2142	13
1	2142	13

prune2.0ms (0%)

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

0.0b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
0.0b	(-.f64 2 (+.f64 x y))
0.0b	(-.f64 2 (+.f64 x y))
0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_23266`
44×	`add-sqr-sqrt_binary64_23288`
30×	`times-frac_binary64_23272`
21×	`distribute-lft-out--_binary64_23218`
16×	`add-cube-cbrt_binary64_23301`
14×	`difference-of-squares_binary64_23235`
8×	`distribute-lft-out_binary64_23217`
7×	`add-log-exp_binary64_23305`
6×	`associate-/r*_binary64_23210`
5×	`associate-/l*_binary64_23211`
4×	`add-exp-log_binary64_23304` `add-cbrt-cube_binary64_23302` `cancel-sign-sub-inv_binary64_23232`
3×	`flip--_binary64_23241` `flip3--_binary64_23270`
2×	`pow1_binary64_23327` `associate-/r/_binary64_23212` `associate-/l/_binary64_23213` `diff-log_binary64_23358`
1×	`sum-log_binary64_23357` `sub-neg_binary64_23259` `div-sub_binary64_23271` `div-exp_binary64_23317` `cbrt-undiv_binary64_23300` `frac-2neg_binary64_23277` `clear-num_binary64_23265` `div-inv_binary64_23263` `associate--r+_binary64_23202`

Counts

2 → 78

Calls

4 calls:

11.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
6.0ms	(-.f64 2 (+.f64 x y))
0.0ms	(-.f64 2 (+.f64 x y))
0.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

series216.0ms (3.8%)

Counts

2 → 36

Calls

2 calls:

170.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
46.0ms	(-.f64 2 (+.f64 x y))

Compiler

Compiled 932 to 770 computations (17.4% saved)

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4953	2535
1	4953	2535

prune122.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	4	115

Error

Counts

115 → 4

Compiler

Compiled 2119 to 1001 computations (52.8% saved)

localize8.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 y (-.f64 2 (+.f64 x y)))
0.0b	(/.f64 x (-.f64 2 (+.f64 x y)))
0.0b	(-.f64 2 (+.f64 x y))
0.0b	(-.f64 2 (+.f64 x y))
0.0b	(-.f64 2 (+.f64 x y))
0.0b	(/.f64 x (-.f64 2 (+.f64 x y)))
0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
0.0b	(/.f64 y (-.f64 2 (+.f64 x y)))

rewrite83.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

161×	`*-un-lft-identity_binary64_23266`
82×	`times-frac_binary64_23272`
79×	`add-sqr-sqrt_binary64_23288`
49×	`distribute-lft-out--_binary64_23218`
39×	`add-cube-cbrt_binary64_23301`
28×	`cancel-sign-sub-inv_binary64_23232`
19×	`distribute-lft-out_binary64_23217`
18×	`difference-of-squares_binary64_23235`
12×	`associate-/r*_binary64_23210`
11×	`add-log-exp_binary64_23305`
10×	`associate-/r/_binary64_23212`
8×	`add-exp-log_binary64_23304` `add-cbrt-cube_binary64_23302`
7×	`flip--_binary64_23241` `flip3--_binary64_23270`
6×	`associate-/l*_binary64_23211`
5×	`div-inv_binary64_23263`
4×	`pow1_binary64_23327`
3×	`distribute-rgt-out--_binary64_23220` `diff-log_binary64_23358`
2×	`sub-neg_binary64_23259` `div-exp_binary64_23317` `cbrt-undiv_binary64_23300` `frac-2neg_binary64_23277` `clear-num_binary64_23265`
1×	`sum-log_binary64_23357` `frac-sub_binary64_23275` `sub-div_binary64_23273` `associate--r+_binary64_23202`

Counts

4 → 159

Calls

8 calls:

46.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
8.0ms	(/.f64 y (-.f64 2 (+.f64 x y)))
7.0ms	(/.f64 x (-.f64 2 (+.f64 x y)))
6.0ms	(-.f64 2 (+.f64 x y))
0.0ms	(-.f64 2 (+.f64 x y))

series535.0ms (9.3%)

Counts

4 → 84

Calls

4 calls:

200.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
143.0ms	(/.f64 y (-.f64 2 (+.f64 x y)))
140.0ms	(/.f64 x (-.f64 2 (+.f64 x y)))
52.0ms	(-.f64 2 (+.f64 x y))

Compiler

Compiled 2820 to 2206 computations (21.8% saved)

simplify103.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4959	6140
1	4959	6140

prune465.0ms (8.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	243	4	247

Error

Counts

247 → 4

Compiler

Compiled 6178 to 3152 computations (49% saved)

localize20.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (*.f64 (cbrt.f64 (-.f64 2 (+.f64 x y))) (cbrt.f64 (-.f64 2 (+.f64 x y))))) (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 2 (+.f64 x y)))))
0.0b	(-.f64 2 (+.f64 x y))
0.0b	(-.f64 2 (+.f64 x y))
0.0b	(-.f64 2 (+.f64 x y))
0.5b	(cbrt.f64 (-.f64 x y))
0.6b	(cbrt.f64 (-.f64 2 (+.f64 x y)))
0.6b	(cbrt.f64 (-.f64 2 (+.f64 x y)))
0.6b	(cbrt.f64 (-.f64 2 (+.f64 x y)))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64_23266`
23×	`cbrt-prod_binary64_23297`
16×	`add-sqr-sqrt_binary64_23288`
8×	`cbrt-div_binary64_23298` `add-cube-cbrt_binary64_23301`
7×	`distribute-lft-out--_binary64_23218`
4×	`difference-of-squares_binary64_23235` `flip--_binary64_23241` `pow1_binary64_23327` `flip3--_binary64_23270` `pow1/3_binary64_23348` `add-exp-log_binary64_23304` `add-cbrt-cube_binary64_23302` `add-log-exp_binary64_23305`
3×	`distribute-lft-out_binary64_23217`

Counts

4 → 63

Calls

8 calls:

5.0ms	(cbrt.f64 (-.f64 2 (+.f64 x y)))
5.0ms	(cbrt.f64 (-.f64 2 (+.f64 x y)))
5.0ms	(cbrt.f64 (-.f64 2 (+.f64 x y)))
3.0ms	(cbrt.f64 (-.f64 x y))
0.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (*.f64 (cbrt.f64 (-.f64 2 (+.f64 x y))) (cbrt.f64 (-.f64 2 (+.f64 x y))))) (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 2 (+.f64 x y)))))

series531.0ms (9.3%)

Counts

4 → 44

Calls

4 calls:

150.0ms	(cbrt.f64 (-.f64 2 (+.f64 x y)))
150.0ms	(cbrt.f64 (-.f64 2 (+.f64 x y)))
147.0ms	(cbrt.f64 (-.f64 2 (+.f64 x y)))
84.0ms	(cbrt.f64 (-.f64 x y))

Compiler

Compiled 3196 to 2201 computations (31.1% saved)

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5007	1987

prune176.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	107	4	111

Error

Counts

111 → 4

Compiler

Compiled 4607 to 2069 computations (55.1% saved)

localize11.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 2 (+.f64 x y))
0.0b	(-.f64 2 (+.f64 x y))
0.0b	(sqrt.f64 (-.f64 2 (+.f64 x y)))
0.0b	(sqrt.f64 (-.f64 2 (+.f64 x y)))
0.0b	(sqrt.f64 (-.f64 2 (+.f64 x y)))
0.2b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y)))))
0.3b	(/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y))))
0.4b	(/.f64 1 (sqrt.f64 (-.f64 2 (+.f64 x y))))

rewrite122.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

220×	`*-un-lft-identity_binary64_23266`
204×	`add-sqr-sqrt_binary64_23288`
166×	`times-frac_binary64_23272`
125×	`sqrt-prod_binary64_23282`
81×	`add-cube-cbrt_binary64_23301`
57×	`distribute-lft-out--_binary64_23218`
51×	`associate-r_binary64_23206`
38×	`difference-of-squares_binary64_23235`
33×	`associate-l_binary64_23207`
32×	`add-exp-log_binary64_23304`
20×	`add-cbrt-cube_binary64_23302`
19×	`distribute-lft-out_binary64_23217`
18×	`associate-/r*_binary64_23210`
15×	`unswap-sqr_binary64_23234`
11×	`div-exp_binary64_23317`
10×	`sqrt-div_binary64_23283`
9×	`pow1_binary64_23327`
8×	`associate-/r/_binary64_23212` `prod-exp_binary64_23315` `associate-/l*_binary64_23211`
6×	`cbrt-undiv_binary64_23300` `flip--_binary64_23241` `flip3--_binary64_23270`
4×	`cbrt-unprod_binary64_23299` `div-inv_binary64_23263` `add-log-exp_binary64_23305`
3×	`1-exp_binary64_23310` `rec-exp_binary64_23316` `pow-flip_binary64_23340`
2×	`frac-2neg_binary64_23277` `clear-num_binary64_23265` `associate-/l/_binary64_23213` `sqrt-pow1_binary64_23284` `pow1/2_binary64_23346`
1×	`rem-sqrt-square_binary64_23279` `div-sub_binary64_23271` `inv-pow_binary64_23351` `-commutative_binary64_23197` `associate-r/_binary64_23208` `pow-prod-down_binary64_23337` `frac-times_binary64_23276` `associate-*l/_binary64_23209`

Counts

4 → 276

Calls

8 calls:

53.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y)))))
15.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y))))
9.0ms	(/.f64 1 (sqrt.f64 (-.f64 2 (+.f64 x y))))
6.0ms	(sqrt.f64 (-.f64 2 (+.f64 x y)))
0.0ms	(sqrt.f64 (-.f64 2 (+.f64 x y)))

series635.0ms (11.1%)

Counts

4 → 60

Calls

4 calls:

243.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y)))))
180.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y))))
110.0ms	(sqrt.f64 (-.f64 2 (+.f64 x y)))
102.0ms	(/.f64 1 (sqrt.f64 (-.f64 2 (+.f64 x y))))

Compiler

Compiled 2396 to 1974 computations (17.6% saved)

simplify142.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5534	9101

prune530.0ms (9.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	336	4	340

Error

Counts

340 → 4

Compiler

Compiled 9417 to 5246 computations (44.3% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	199	519
1	199	519

regimes122.0ms (2.1%)

Compiler: Compiled 1114 to 795 computations (28.6% saved)

bsearch0.0ms (0%)

regimes46.0ms (0.8%)

Compiler: Compiled 211 to 205 computations (2.8% saved)

bsearch0.0ms (0%)

regimes81.0ms (1.4%)

Compiler: Compiled 46 to 60 computations (-30.4% saved)

bsearch52.0ms (0.9%)

Steps

Iters	Range		Point
9	5.996663553806771e+111	6.895816104389786e+118	6.106868182373121e+111
7	3.718690693193203e+36	1.139813992951078e+38	1.0248782980155822e+38
10	4.088275092156049e-09	2827.388582405466	23.91208970233615
9	-2.9390170618960914e+24	-5.39461787143076e+18	-1.865170802071591e+19

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes76.0ms (1.3%)

Compiler: Compiled 32 to 48 computations (-50% saved)

bsearch42.0ms (0.7%)

Steps

Iters	Range		Point
9	5.996663553806771e+111	6.895816104389786e+118	6.106868182373121e+111
7	3.718690693193203e+36	1.139813992951078e+38	2.7929760088083384e+37
1	1.5043914238054803e-60	1.6437691757542662e-60	1.6089247377670696e-60
9	-2.9390170618960914e+24	-5.39461787143076e+18	-6.097443044253342e+20

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes74.0ms (1.3%)

Compiler: Compiled 20 to 36 computations (-80% saved)

bsearch24.0ms (0.4%)

Steps

Iters	Range		Point
9	19324063239578.91	2.140085187479381e+20	5.4721065798649715e+17
9	-1.370884269312206e+18	-12917940695.295689	-6761793997916965.0

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes46.0ms (0.8%)

Compiler: Compiled 10 to 26 computations (-160% saved)

bsearch23.0ms (0.4%)

Steps

Iters	Range		Point
9	5.996663553806771e+111	6.895816104389786e+118	6.547686696638525e+111
9	-2.9390170618960914e+24	-5.39461787143076e+18	-2.905893372197331e+22

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes17.0ms (0.3%)

Accuracy

Total 0.0b remaining (89.4%)

Threshold costs 0.0b (89.4%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 122 to 98 computations (19.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	106	175
1	106	175

end0.0ms (0%)

sample841.0ms (14.7%)

Algorithm

1×

intervals

Results

204.0ms	7996×	body	128	valid
0.0ms	2×	body	1024	valid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 490 to 358 computations (26.9% saved)

Pareto

0.24150377365790357

Details

analyze33.0ms (0.6%)

sample18.0ms (0.3%)

simplify308.0ms (5.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite24.0ms (0.4%)

series216.0ms (3.8%)

simplify76.0ms (1.3%)

prune122.0ms (2.1%)

localize8.0ms (0.1%)

rewrite83.0ms (1.4%)

series535.0ms (9.3%)

simplify103.0ms (1.8%)

prune465.0ms (8.1%)

localize20.0ms (0.4%)

rewrite27.0ms (0.5%)

series531.0ms (9.3%)

simplify61.0ms (1.1%)

prune176.0ms (3.1%)

localize11.0ms (0.2%)

rewrite122.0ms (2.1%)

series635.0ms (11.1%)

simplify142.0ms (2.5%)

prune530.0ms (9.3%)

simplify10.0ms (0.2%)

regimes122.0ms (2.1%)

bsearch0.0ms (0%)

regimes46.0ms (0.8%)

bsearch0.0ms (0%)

regimes81.0ms (1.4%)

bsearch52.0ms (0.9%)

regimes76.0ms (1.3%)

bsearch42.0ms (0.7%)

regimes74.0ms (1.3%)

bsearch24.0ms (0.4%)

regimes46.0ms (0.8%)

bsearch23.0ms (0.4%)

regimes17.0ms (0.3%)

bsearch6.0ms (0.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample841.0ms (14.7%)

Profiling