Details

analyze40.0ms (1.2%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
59.3%	40.6%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample17.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify153.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	782	10
1	782	10

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 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64_26378`
22×	`add-sqr-sqrt_binary64_26400`
20×	`times-frac_binary64_26384`
12×	`add-cube-cbrt_binary64_26413`
6×	`distribute-lft-out_binary64_26329`
5×	`difference-of-squares_binary64_26347` `distribute-lft-out--_binary64_26330` `associate-/l*_binary64_26323`
4×	`associate-/r*_binary64_26322`
3×	`add-cbrt-cube_binary64_26414` `add-exp-log_binary64_26416`
2×	`associate-/l/_binary64_26325` `associate-/r/_binary64_26324`
1×	`div-sub_binary64_26383` `frac-2neg_binary64_26389` `flip3-+_binary64_26381` `add-log-exp_binary64_26417` `div-exp_binary64_26429` `flip3--_binary64_26382` `flip-+_binary64_26352` `cbrt-undiv_binary64_26412` `flip--_binary64_26353` `div-inv_binary64_26375` `pow1_binary64_26439` `clear-num_binary64_26377`

Counts

1 → 46

Calls

2 calls:

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

series89.0ms (2.8%)

Counts

1 → 21

Calls

1 calls:

89.0ms

(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 312 to 288 computations (7.7% saved)

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5390	1071

prune62.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	5	68

Error

Counts

68 → 5

Compiler

Compiled 919 to 267 computations (70.9% saved)

localize6.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

rewrite47.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_26378`
52×	`times-frac_binary64_26384`
43×	`add-sqr-sqrt_binary64_26400`
31×	`add-cube-cbrt_binary64_26413`
18×	`cancel-sign-sub-inv_binary64_26344`
15×	`distribute-lft-out_binary64_26329`
10×	`associate-/r/_binary64_26324`
8×	`associate-/r*_binary64_26322`
7×	`distribute-lft-out--_binary64_26330` `add-cbrt-cube_binary64_26414` `add-exp-log_binary64_26416`
6×	`associate-/l*_binary64_26323`
5×	`flip3-+_binary64_26381` `add-log-exp_binary64_26417` `flip-+_binary64_26352` `div-inv_binary64_26375`
4×	`difference-of-squares_binary64_26347`
3×	`distribute-rgt-out--_binary64_26332` `pow1_binary64_26439`
2×	`frac-2neg_binary64_26389` `div-exp_binary64_26429` `cbrt-undiv_binary64_26412` `clear-num_binary64_26377`
1×	`diff-log_binary64_26470` `flip3--_binary64_26382` `sub-neg_binary64_26371` `flip--_binary64_26353` `frac-sub_binary64_26387` `sub-div_binary64_26385`

Counts

3 → 111

Calls

6 calls:

28.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
5.0ms	(/.f64 x (+.f64 x y))
5.0ms	(/.f64 y (+.f64 x y))
0.0ms	(/.f64 x (+.f64 x y))
0.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))

series248.0ms (7.8%)

Counts

3 → 57

Calls

3 calls:

106.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
79.0ms	(/.f64 y (+.f64 x y))
63.0ms	(/.f64 x (+.f64 x y))

Compiler

Compiled 1101 to 864 computations (21.5% saved)

simplify73.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5267	2288

prune100.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	168	5	173

Error

Counts

173 → 5

Compiler

Compiled 2597 to 591 computations (77.2% saved)

localize9.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (+.f64 x y))
0.0b	(/.f64 (-.f64 x y) (+.f64 x y))
0.0b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
0.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))) (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
0.0b	(/.f64 (-.f64 x y) (+.f64 x y))
0.0b	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
0.0b	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
0.0b	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))

rewrite52.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`*-un-lft-identity_binary64_26378`
80×	`times-frac_binary64_26384`
79×	`add-sqr-sqrt_binary64_26400`
78×	`cbrt-prod_binary64_26409`
45×	`add-cube-cbrt_binary64_26413`
21×	`distribute-lft-out_binary64_26329`
17×	`difference-of-squares_binary64_26347` `distribute-lft-out--_binary64_26330`
8×	`associate-/r/_binary64_26324`
6×	`add-cbrt-cube_binary64_26414` `add-exp-log_binary64_26416`
5×	`associate-/l*_binary64_26323`
4×	`flip3-+_binary64_26381` `add-log-exp_binary64_26417` `flip-+_binary64_26352` `associate-/r*_binary64_26322` `div-inv_binary64_26375` `pow1_binary64_26439`
3×	`cbrt-div_binary64_26410` `pow1/3_binary64_26460`
2×	`associate-/l/_binary64_26325`
1×	`div-sub_binary64_26383` `frac-2neg_binary64_26389` `div-exp_binary64_26429` `flip3--_binary64_26382` `cbrt-undiv_binary64_26412` `flip--_binary64_26353` `clear-num_binary64_26377`

Counts

4 → 151

Calls

8 calls:

8.0ms	(/.f64 (-.f64 x y) (+.f64 x y))
7.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
7.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
7.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
0.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))) (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))))

series325.0ms (10.3%)

Counts

4 → 57

Calls

4 calls:

92.0ms	(/.f64 (-.f64 x y) (+.f64 x y))
81.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
79.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
73.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))

Compiler

Compiled 2163 to 1275 computations (41.1% saved)

simplify92.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5853	3967

prune191.0ms (6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	208	5	213

Error

Counts

213 → 5

Compiler

Compiled 6744 to 995 computations (85.2% saved)

localize16.0ms (0.5%)

Local error

Found 8 expressions with local error:

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

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`cbrt-prod_binary64_26409`
16×	`*-un-lft-identity_binary64_26378`
14×	`add-sqr-sqrt_binary64_26400`
8×	`add-cube-cbrt_binary64_26413` `cbrt-div_binary64_26410`
4×	`add-log-exp_binary64_26417` `pow1_binary64_26439` `add-cbrt-cube_binary64_26414` `add-exp-log_binary64_26416` `pow1/3_binary64_26460`
3×	`difference-of-squares_binary64_26347` `flip3--_binary64_26382` `distribute-lft-out--_binary64_26330` `flip--_binary64_26353`
1×	`flip3-+_binary64_26381` `flip-+_binary64_26352` `distribute-lft-out_binary64_26329`

Counts

4 → 59

Calls

8 calls:

3.0ms	(cbrt.f64 (-.f64 x y))
3.0ms	(cbrt.f64 (-.f64 x y))
3.0ms	(cbrt.f64 (-.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 x y)) (cbrt.f64 (+.f64 x y)))) (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (+.f64 x y))))

series326.0ms (10.3%)

Counts

4 → 34

Calls

4 calls:

90.0ms	(cbrt.f64 (+.f64 x y))
82.0ms	(cbrt.f64 (-.f64 x y))
78.0ms	(cbrt.f64 (-.f64 x y))
75.0ms	(cbrt.f64 (-.f64 x y))

Compiler

Compiled 2330 to 1367 computations (41.3% saved)

simplify52.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5116	1010

prune87.0ms (2.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	93	5	98

Error

Counts

98 → 5

Compiler

Compiled 3087 to 391 computations (87.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	250
1	130	250

regimes67.0ms (2.1%)

Accuracy

Total 0.0b remaining (94.4%)

Threshold costs 0.0b (94.4%)

Compiler

Compiled 522 to 333 computations (36.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	10
1	17	10

end0.0ms (0%)

sample1.0s (32%)

Algorithm

1×

intervals

Results

196.0ms

8000×

body

128

valid

Compiler

Compiled 523 to 329 computations (37.1% saved)

Pareto

0.8550103391042787

Details

analyze40.0ms (1.2%)

sample17.0ms (0.5%)

simplify153.0ms (4.8%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite13.0ms (0.4%)

series89.0ms (2.8%)

simplify61.0ms (1.9%)

prune62.0ms (2%)

localize6.0ms (0.2%)

rewrite47.0ms (1.5%)

series248.0ms (7.8%)

simplify73.0ms (2.3%)

prune100.0ms (3.1%)

localize9.0ms (0.3%)

rewrite52.0ms (1.6%)

series325.0ms (10.3%)

simplify92.0ms (2.9%)

prune191.0ms (6%)

localize16.0ms (0.5%)

rewrite19.0ms (0.6%)

series326.0ms (10.3%)

simplify52.0ms (1.7%)

prune87.0ms (2.7%)

simplify6.0ms (0.2%)

regimes67.0ms (2.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (32%)

Profiling