Details

analyze11.0ms (0.4%)

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
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample18.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 39 to 27 computations (30.8% saved)

simplify198.0ms (6.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4787	28
1	4787	28

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

32.1b

Counts

2 → 1

Compiler

Compiled 38 to 24 computations (36.8% saved)

localize10.0ms (0.3%)

Local error

Found 6 expressions with local error:

31.4b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
2.7b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
2.7b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
31.4b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_18514` `add-cube-cbrt_binary64_18527` `*-un-lft-identity_binary64_18492`
9×	`times-frac_binary64_18498`
7×	`add-log-exp_binary64_18531`
5×	`add-exp-log_binary64_18530` `add-cbrt-cube_binary64_18528`
3×	`pow1_binary64_18553` `associate-/l_binary64_18437` `associate-/r_binary64_18436`
2×	`associate-/l/_binary64_18439` `flip-+_binary64_18466` `flip--_binary64_18467` `flip3--_binary64_18496` `associate-/r/_binary64_18438` `flip3-+_binary64_18495`
1×	`div-exp_binary64_18543` `+-commutative_binary64_18422` `diff-log_binary64_18584` `frac-2neg_binary64_18503` `sub-neg_binary64_18485` `sum-log_binary64_18583` `clear-num_binary64_18491` `cancel-sign-sub-inv_binary64_18458` `cbrt-undiv_binary64_18526` `div-inv_binary64_18489` `div-sub_binary64_18497`

Counts

3 → 55

Calls

6 calls:

9.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
4.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
4.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
0.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
0.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series396.0ms (12.6%)

Counts

3 → 39

Calls

3 calls:

165.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
121.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
109.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

Compiler

Compiled 915 to 771 computations (15.7% saved)

simplify62.0ms (2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5063	2122

prune104.0ms (3.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	3	95

Error

0.4b

Counts

95 → 3

Compiler

Compiled 2222 to 1155 computations (48% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune2.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	0	0
Total	3	3

Error

0.4b

Counts

3 → 3

Compiler

Compiled 30 to 20 computations (33.3% saved)

localize10.0ms (0.3%)

Local error

Found 8 expressions with local error:

20.7b	(/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
0.0b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4)))) (/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))))
0.0b	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
0.0b	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
0.0b	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
0.0b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4)))) (/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))))
20.7b	(/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
25.3b	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))

rewrite53.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_18530` `add-cbrt-cube_binary64_18528`
14×	`add-sqr-sqrt_binary64_18514`
12×	`*-un-lft-identity_binary64_18492`
10×	`times-frac_binary64_18498` `add-cube-cbrt_binary64_18527` `associate-/r/_binary64_18438`
9×	`cancel-sign-sub-inv_binary64_18458`
8×	`add-log-exp_binary64_18531`
6×	`flip-+_binary64_18466` `flip3-+_binary64_18495` `associate-/r*_binary64_18436`
5×	`div-exp_binary64_18543` `cbrt-undiv_binary64_18526` `div-inv_binary64_18489`
4×	`pow1_binary64_18553` `prod-exp_binary64_18541` `cbrt-unprod_binary64_18525`
3×	`distribute-rgt-out--_binary64_18446`
2×	`frac-2neg_binary64_18503` `associate-/l*_binary64_18437` `clear-num_binary64_18491` `difference-of-squares_binary64_18461`
1×	`+-commutative_binary64_18422` `diff-log_binary64_18584` `flip--_binary64_18467` `distribute-lft-out--_binary64_18444` `sub-neg_binary64_18485` `sum-log_binary64_18583` `flip3--_binary64_18496` `sub-div_binary64_18499` `frac-sub_binary64_18501`

Counts

4 → 87

Calls

8 calls:

18.0ms	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4)))) (/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))))
9.0ms	(/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
7.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))
5.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
0.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

series575.0ms (18.4%)

Counts

4 → 51

Calls

4 calls:

210.0ms	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4)))) (/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))))
124.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))
123.0ms	(/.f64 (.f64 y (.f64 y 4)) (+.f64 (.f64 x x) (.f64 y (*.f64 y 4))))
118.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

Compiler

Compiled 1869 to 1431 computations (23.4% saved)

simplify76.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5053	3371

prune163.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	138	3	141

Error

0.4b

Counts

141 → 3

Compiler

Compiled 4387 to 2261 computations (48.5% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Error

0.4b

Counts

3 → 3

Compiler

Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	101	168
1	101	168

regimes124.0ms (4%)

Compiler: Compiled 355 to 266 computations (25.1% saved)

bsearch48.0ms (1.5%)

Steps

Iters	Range		Point
4	5.001370242576063e+187	9.770499792614024e+187	9.560203192398091e+187
8	1.4077435868477773e-128	4.5634043574256304e-125	3.938995416799686e-128
6	6.546871147194143e-226	8.269715064530922e-225	1.622883590444815e-225
6	4.318107323633723e-290	2.4787394071453353e-289	1.55715602789528e-289

Compiler

Compiled 3 to 3 computations (0% saved)

regimes110.0ms (3.5%)

Compiler: Compiled 205 to 173 computations (15.6% saved)

bsearch48.0ms (1.5%)

Steps

Iters	Range		Point
4	5.001370242576063e+187	9.770499792614024e+187	6.158001543763689e+187
8	1.4077435868477773e-128	4.5634043574256304e-125	1.4341416860597047e-128
6	6.546871147194143e-226	8.269715064530922e-225	1.8503167553059872e-225
6	4.318107323633723e-290	2.4787394071453353e-289	1.314293898980315e-289

Compiler

Compiled 3 to 3 computations (0% saved)

regimes101.0ms (3.2%)

Compiler: Compiled 142 to 131 computations (7.7% saved)

bsearch46.0ms (1.5%)

Steps

Iters	Range		Point
4	5.001370242576063e+187	9.770499792614024e+187	9.560203192398091e+187
8	1.4077435868477773e-128	4.5634043574256304e-125	2.3419485415457023e-127
6	6.546871147194143e-226	8.269715064530922e-225	2.9701073345171666e-225
6	4.318107323633723e-290	2.4787394071453353e-289	1.476201984923625e-289

Compiler

Compiled 3 to 3 computations (0% saved)

regimes74.0ms (2.4%)

Compiler: Compiled 85 to 95 computations (-11.8% saved)

bsearch23.0ms (0.7%)

Steps

Iters	Range		Point
5	824774.8097494192	2010627.0788228896	1459981.196274432
7	-1.2666199391921107e-45	-5.110620672074071e-47	-1.1465352812211946e-46

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes15.0ms (0.5%)

Accuracy

Total 12.7b remaining (97.2%)

Threshold costs 0b (0%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch8.0ms (0.3%)

Compiler: Compiled 249 to 144 computations (42.2% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	110	364
1	110	364

end0.0ms (0%)

sample795.0ms (25.4%)

Algorithm

1×

intervals

Results

327.0ms

8000×

body

128

valid

Compiler

Compiled 465 to 284 computations (38.9% saved)

Pareto

0.6830754758924105

Details

analyze11.0ms (0.4%)

sample18.0ms (0.6%)

simplify198.0ms (6.3%)

prune7.0ms (0.2%)

localize10.0ms (0.3%)

rewrite23.0ms (0.7%)

series396.0ms (12.6%)

simplify62.0ms (2%)

prune104.0ms (3.3%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.2%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

rewrite53.0ms (1.7%)

series575.0ms (18.4%)

simplify76.0ms (2.4%)

prune163.0ms (5.2%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.2%)

prune0.0ms (0%)

simplify6.0ms (0.2%)

regimes124.0ms (4%)

bsearch48.0ms (1.5%)

regimes110.0ms (3.5%)

bsearch48.0ms (1.5%)

regimes101.0ms (3.2%)

bsearch46.0ms (1.5%)

regimes74.0ms (2.4%)

bsearch23.0ms (0.7%)

regimes15.0ms (0.5%)

bsearch8.0ms (0.3%)

simplify8.0ms (0.2%)

end0.0ms (0%)

sample795.0ms (25.4%)

Profiling