Details

analyze57.0ms (1.7%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
50%	50%	0.1%	5
62.4%	37.5%	0.1%	6
74.9%	25%	0.1%	7
81.2%	18.7%	0.1%	8
87.4%	12.5%	0.1%	9
90.5%	9.4%	0.1%	10
93.7%	6.2%	0.1%	11
95.2%	4.7%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample15.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify350.0ms (10.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (256.0ms)

Iter	Nodes	Cost
0	3112	16
1	3112	16

prune2.0ms (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

0.0b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.0b	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))
0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
9.0b	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))

rewrite26.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64_6898`
25×	`times-frac_binary64_6904`
24×	`add-sqr-sqrt_binary64_6920`
19×	`add-cube-cbrt_binary64_6933`
18×	`cancel-sign-sub-inv_binary64_6864`
7×	`distribute-lft-out_binary64_6849`
4×	`add-exp-log_binary64_6936` `add-log-exp_binary64_6937` `add-cbrt-cube_binary64_6934` `associate-/r/_binary64_6844` `associate-/r*_binary64_6842`
3×	`associate-/l*_binary64_6843`
2×	`flip-+_binary64_6872` `pow1_binary64_6959` `flip3-+_binary64_6901` `div-inv_binary64_6895` `difference-of-squares_binary64_6867`
1×	`sub-neg_binary64_6891` `div-exp_binary64_6949` `distribute-lft-out--_binary64_6850` `flip--_binary64_6873` `cbrt-undiv_binary64_6932` `clear-num_binary64_6897` `flip3--_binary64_6902` `frac-2neg_binary64_6909` `diff-log_binary64_6990`

Counts

2 → 65

Calls

4 calls:

13.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
7.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))
0.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
0.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))

series145.0ms (4.4%)

Counts

2 → 27

Calls

2 calls:

80.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
65.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))

Compiler

Compiled 559 to 491 computations (12.2% saved)

simplify79.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4899	1619
1	4899	1619

prune95.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	3	93

Error

Counts

93 → 3

Compiler

Compiled 1412 to 793 computations (43.8% saved)

localize11.0ms (0.3%)

Local error

Found 6 expressions with local error:

9.0b	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)
0.1b	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))
0.0b	(-.f64 x (/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)))
0.0b	(-.f64 x (/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)))
0.1b	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))
9.0b	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)

rewrite64.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`times-frac_binary64_6904`
157×	`*-un-lft-identity_binary64_6898`
116×	`add-sqr-sqrt_binary64_6920`
102×	`add-cube-cbrt_binary64_6933`
53×	`cancel-sign-sub-inv_binary64_6864`
25×	`distribute-lft-out_binary64_6849`
19×	`associate-/r*_binary64_6842`
16×	`add-exp-log_binary64_6936`
11×	`div-inv_binary64_6895`
10×	`add-cbrt-cube_binary64_6934`
8×	`div-exp_binary64_6949`
7×	`associate-/l*_binary64_6843`
5×	`add-log-exp_binary64_6937` `difference-of-squares_binary64_6867`
4×	`pow1_binary64_6959` `cbrt-undiv_binary64_6932`
2×	`1-exp_binary64_6942` `distribute-lft-out--_binary64_6850` `rec-exp_binary64_6948` `associate-/r/_binary64_6844` `clear-num_binary64_6897` `frac-2neg_binary64_6909` `associate-/l/_binary64_6845`
1×	`sub-neg_binary64_6891` `flip-+_binary64_6872` `pow-flip_binary64_6972` `flip3-+_binary64_6901` `flip--_binary64_6873` `flip3--_binary64_6902` `diff-log_binary64_6990` `inv-pow_binary64_6983`

Counts

3 → 192

Calls

6 calls:

26.0ms	(-.f64 x (/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)))
10.0ms	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))
7.0ms	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)
0.0ms	(-.f64 x (/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)))
0.0ms	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))

series264.0ms (8.1%)

Counts

3 → 39

Calls

3 calls:

116.0ms	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)
80.0ms	(-.f64 x (/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)))
68.0ms	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))

Compiler

Compiled 733 to 653 computations (10.9% saved)

simplify98.0ms (3%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5088	5066

prune214.0ms (6.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	231	3	234

Error

Counts

234 → 3

Compiler

Compiled 4315 to 2579 computations (40.2% saved)

localize14.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (/.f64 (.f64 y x) 2)))) (/.f64 y (sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)))))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2))))
0.1b	(/.f64 y (sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2))))
0.0b	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (/.f64 (.f64 y x) 2)))) (/.f64 y (sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2))))))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2))))
0.1b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (/.f64 (.f64 y x) 2)))) (/.f64 y (sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)))))
4.8b	(sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)))
4.8b	(sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)))

rewrite78.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`add-sqr-sqrt_binary64_6920`
85×	`times-frac_binary64_6904`
80×	`*-un-lft-identity_binary64_6898`
59×	`sqrt-prod_binary64_6914`
50×	`add-cube-cbrt_binary64_6933`
30×	`add-exp-log_binary64_6936`
27×	`associate-r_binary64_6838` `associate-l_binary64_6839`
18×	`add-cbrt-cube_binary64_6934`
15×	`unswap-sqr_binary64_6866`
12×	`distribute-lft-out_binary64_6849`
10×	`div-exp_binary64_6949` `pow1_binary64_6959` `sqrt-div_binary64_6915`
8×	`prod-exp_binary64_6947`
7×	`associate-/r*_binary64_6842`
6×	`associate-/r/_binary64_6844`
5×	`flip-+_binary64_6872` `flip3-+_binary64_6901` `cbrt-undiv_binary64_6932`
4×	`add-log-exp_binary64_6937` `cbrt-unprod_binary64_6931`
3×	`pow-flip_binary64_6972` `1-exp_binary64_6942` `sqrt-pow1_binary64_6916` `rec-exp_binary64_6948` `div-inv_binary64_6895` `associate-/l*_binary64_6843` `pow1/2_binary64_6978`
2×	`rem-sqrt-square_binary64_6911`
1×	`associate-l/_binary64_6841` `frac-times_binary64_6908` `associate-r/_binary64_6840` `*-commutative_binary64_6829` `clear-num_binary64_6897` `pow-prod-down_binary64_6969` `frac-2neg_binary64_6909` `inv-pow_binary64_6983`

Counts

4 → 176

Calls

8 calls:

32.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (/.f64 (.f64 y x) 2)))) (/.f64 y (sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)))))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2))))
5.0ms	(sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)))
5.0ms	(sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)))
0.0ms	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (/.f64 (.f64 y x) 2)))) (/.f64 y (sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2))))))

series221.0ms (6.8%)

Counts

4 → 36

Calls

4 calls:

72.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (/.f64 (.f64 y x) 2)))) (/.f64 y (sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)))))
57.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2))))
49.0ms	(sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)))
43.0ms	(sqrt.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)))

Compiler

Compiled 1326 to 1074 computations (19% saved)

simplify95.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5041	4336

prune277.0ms (8.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	212	3	215

Error

Counts

215 → 3

Compiler

Compiled 5652 to 3705 computations (34.4% saved)

simplify18.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	660	371
1	660	371

regimes91.0ms (2.8%)

Compiler: Compiled 767 to 608 computations (20.7% saved)

bsearch0.0ms (0%)

regimes66.0ms (2%)

Compiler: Compiled 54 to 68 computations (-25.9% saved)

bsearch30.0ms (0.9%)

Steps

Iters	Range		Point
10	5.245977391550362e+53	6.16800420098598e+63	2.9796951571665817e+63
9	-2.6352034982196117e+107	-1.0939295647390656e+101	-3.545134243483185e+104

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes49.0ms (1.5%)

Compiler: Compiled 22 to 42 computations (-90.9% saved)

bsearch25.0ms (0.8%)

Steps

Iters	Range		Point
9	0.015142169522585408	3613469.350260401	1.3146011246479754
7	-4.6333404398521304e-08	-7.666138463630564e-10	-4.564557606821874e-08

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes34.0ms (1%)

Compiler: Compiled 16 to 36 computations (-125% saved)

bsearch28.0ms (0.9%)

Steps

Iters	Range		Point
8	3.1899025933482202e-83	4.410715218126272e-79	2.0183392620009757e-82
10	-6.447746917770433e-137	-8.53659491953579e-151	-8.576064509687241e-138

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes19.0ms (0.6%)

Compiler: Compiled 12 to 30 computations (-150% saved)

bsearch0.0ms (0%)

regimes16.0ms (0.5%)

Accuracy

Total 0.0b remaining (96.2%)

Threshold costs 0.0b (96.2%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch6.0ms (0.2%)

Compiler: Compiled 59 to 47 computations (20.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	78
1	72	78

end0.0ms (0%)

sample765.0ms (23.4%)

Algorithm

1×

intervals

Results

249.0ms	7998×	body	128	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 314 to 251 computations (20.1% saved)

Pareto

0.11814883017991144

Details

analyze57.0ms (1.7%)

sample15.0ms (0.5%)

simplify350.0ms (10.7%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite26.0ms (0.8%)

series145.0ms (4.4%)

simplify79.0ms (2.4%)

prune95.0ms (2.9%)

localize11.0ms (0.3%)

rewrite64.0ms (2%)

series264.0ms (8.1%)

simplify98.0ms (3%)

prune214.0ms (6.5%)

localize14.0ms (0.4%)

rewrite78.0ms (2.4%)

series221.0ms (6.8%)

simplify95.0ms (2.9%)

prune277.0ms (8.5%)

simplify18.0ms (0.6%)

regimes91.0ms (2.8%)

bsearch0.0ms (0%)

regimes66.0ms (2%)

bsearch30.0ms (0.9%)

regimes49.0ms (1.5%)

bsearch25.0ms (0.8%)

regimes34.0ms (1%)

bsearch28.0ms (0.9%)

regimes19.0ms (0.6%)

bsearch0.0ms (0%)

regimes16.0ms (0.5%)

bsearch6.0ms (0.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample765.0ms (23.4%)

Profiling