Details

analyze35.0ms (0.1%)

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
43.7%	56.2%	0.1%	5
65.6%	34.3%	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 6 to 5 computations (16.7% saved)

sample11.0ms (0%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 11 to 11 computations (0% saved)

simplify101.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	6	7
1	6	7

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 5 to 4 computations (20% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_11672`
12×	`times-frac_binary64_11678`
10×	`add-cube-cbrt_binary64_11707` `add-sqr-sqrt_binary64_11694`
4×	`associate-/r*_binary64_11616` `distribute-lft-out_binary64_11623`
3×	`add-exp-log_binary64_11710` `associate-/l*_binary64_11617` `add-cbrt-cube_binary64_11708`
2×	`associate-/r/_binary64_11618`
1×	`cbrt-undiv_binary64_11706` `pow1_binary64_11733` `div-exp_binary64_11723` `clear-num_binary64_11671` `add-log-exp_binary64_11711` `flip-+_binary64_11646` `flip3-+_binary64_11675` `frac-2neg_binary64_11683` `div-inv_binary64_11669`

Counts

1 → 33

Calls

2 calls:

6.0ms	(/.f64 x (+.f64 x y))
0.0ms	(/.f64 x (+.f64 x y))

series76.0ms (0.2%)

Counts

1 → 21

Calls

1 calls:

76.0ms

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

Compiler

Compiled 300 to 252 computations (16% saved)

simplify66.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5434	719

prune145.0ms (0.3%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	25	29	54
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	25	30	55

Error

Counts

55 → 30

Compiler

Compiled 722 to 318 computations (56% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_11672`
12×	`times-frac_binary64_11678`
10×	`add-cube-cbrt_binary64_11707` `add-sqr-sqrt_binary64_11694`
4×	`associate-/r*_binary64_11616` `distribute-lft-out_binary64_11623`
3×	`add-exp-log_binary64_11710` `associate-/l*_binary64_11617` `add-cbrt-cube_binary64_11708`
2×	`associate-/r/_binary64_11618`
1×	`cbrt-undiv_binary64_11706` `pow1_binary64_11733` `div-exp_binary64_11723` `clear-num_binary64_11671` `add-log-exp_binary64_11711` `flip-+_binary64_11646` `flip3-+_binary64_11675` `frac-2neg_binary64_11683` `div-inv_binary64_11669`

Counts

1 → 33

Calls

2 calls:

6.0ms	(/.f64 x (+.f64 x y))
0.0ms	(/.f64 x (+.f64 x y))

series80.0ms (0.2%)

Counts

1 → 21

Calls

1 calls:

79.0ms

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

Compiler

Compiled 348 to 300 computations (13.8% saved)

simplify61.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5434	719

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

20.9b	(/.f64 x (-.f64 (.f64 x x) (.f64 y y)))
5.7b	(.f64 (/.f64 x (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
3.5b	(-.f64 (.f64 x x) (.f64 y y))
3.5b	(-.f64 (.f64 x x) (.f64 y y))
5.7b	(.f64 (/.f64 x (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
20.9b	(/.f64 x (-.f64 (.f64 x x) (.f64 y y)))

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_11694`
25×	`*-un-lft-identity_binary64_11672` `times-frac_binary64_11678`
23×	`add-cube-cbrt_binary64_11707`
18×	`associate-l_binary64_11613`
10×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
9×	`difference-of-squares_binary64_11641`
7×	`cancel-sign-sub-inv_binary64_11638`
5×	`associate-r_binary64_11612` `pow1_binary64_11733` `add-log-exp_binary64_11711` `flip3--_binary64_11676` `flip--_binary64_11647`
4×	`associate-/r/_binary64_11618` `associate-/r*_binary64_11616` `distribute-lft-in_binary64_11621` `distribute-rgt-in_binary64_11622`
3×	`sub-neg_binary64_11665` `associate-/l*_binary64_11617`
2×	`cbrt-undiv_binary64_11706` `cbrt-unprod_binary64_11705` `div-exp_binary64_11723` `frac-times_binary64_11682` `associate-*r/_binary64_11614` `unswap-sqr_binary64_11640` `prod-exp_binary64_11721` `div-inv_binary64_11669`
1×	`distribute-lft-out--_binary64_11624` `clear-num_binary64_11671` `associate-l/_binary64_11615` `frac-2neg_binary64_11683` `-commutative_binary64_11603` `pow-prod-down_binary64_11743` `diff-log_binary64_11764`

Counts

3 → 97

Calls

6 calls:

14.0ms	(.f64 (/.f64 x (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
6.0ms	(/.f64 x (-.f64 (.f64 x x) (.f64 y y)))
4.0ms	(-.f64 (.f64 x x) (.f64 y y))
0.0ms	(-.f64 (.f64 x x) (.f64 y y))
0.0ms	(.f64 (/.f64 x (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))

series301.0ms (0.7%)

Counts

3 → 45

Calls

3 calls:

106.0ms	(.f64 (/.f64 x (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
102.0ms	(/.f64 x (-.f64 (.f64 x x) (.f64 y y)))
93.0ms	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 816 to 657 computations (19.5% saved)

simplify85.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5011	2311

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 x y) (sqrt.f64 x))
0.1b	(/.f64 (sqrt.f64 x) (/.f64 (+.f64 x y) (sqrt.f64 x)))
0.1b	(/.f64 (sqrt.f64 x) (/.f64 (+.f64 x y) (sqrt.f64 x)))
0.2b	(/.f64 (+.f64 x y) (sqrt.f64 x))

rewrite58.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

360×	`times-frac_binary64_11678`
280×	`*-un-lft-identity_binary64_11672`
186×	`sqrt-prod_binary64_11688`
182×	`add-cube-cbrt_binary64_11707` `add-sqr-sqrt_binary64_11694`
49×	`distribute-lft-out_binary64_11623`
34×	`associate-/r*_binary64_11616`
10×	`associate-/l*_binary64_11617`
9×	`add-exp-log_binary64_11710` `div-inv_binary64_11669` `add-cbrt-cube_binary64_11708`
4×	`cbrt-undiv_binary64_11706` `div-exp_binary64_11723`
2×	`pow1_binary64_11733` `clear-num_binary64_11671` `add-log-exp_binary64_11711` `frac-2neg_binary64_11683` `associate-/l/_binary64_11619`
1×	`associate-/r/_binary64_11618` `flip-+_binary64_11646` `flip3-+_binary64_11675`

Counts

2 → 265

Calls

4 calls:

14.0ms	(/.f64 (sqrt.f64 x) (/.f64 (+.f64 x y) (sqrt.f64 x)))
7.0ms	(/.f64 (+.f64 x y) (sqrt.f64 x))
0.0ms	(/.f64 (sqrt.f64 x) (/.f64 (+.f64 x y) (sqrt.f64 x)))
0.0ms	(/.f64 (+.f64 x y) (sqrt.f64 x))

series157.0ms (0.4%)

Counts

2 → 28

Calls

2 calls:

80.0ms	(/.f64 (+.f64 x y) (sqrt.f64 x))
77.0ms	(/.f64 (sqrt.f64 x) (/.f64 (+.f64 x y) (sqrt.f64 x)))

Compiler

Compiled 447 to 368 computations (17.7% saved)

simplify133.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4972	6677
1	4972	6677

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y)))
0.2b	(/.f64 (cbrt.f64 x) (+.f64 x y))
0.6b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_11703`
23×	`add-sqr-sqrt_binary64_11694`
15×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
11×	`pow1_binary64_11733`
9×	`pow1/3_binary64_11754`
6×	`associate-r_binary64_11612` `add-exp-log_binary64_11710` `swap-sqr_binary64_11639` `associate-l_binary64_11613`
4×	`add-log-exp_binary64_11711` `unswap-sqr_binary64_11640` `add-cbrt-cube_binary64_11708`
2×	`pow-sqr_binary64_11645` `pow-prod-up_binary64_11742` `pow-prod-down_binary64_11743`
1×	`cbrt-unprod_binary64_11705` `pow2_binary64_11753` `prod-exp_binary64_11721` `*-commutative_binary64_11603` `pow-plus_binary64_11735`

Counts

4 → 73

Calls

8 calls:

7.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(/.f64 (cbrt.f64 x) (+.f64 x y))

series317.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
75.0ms	(cbrt.f64 x)
73.0ms	(cbrt.f64 x)
73.0ms	(cbrt.f64 x)

Compiler

Compiled 346 to 262 computations (24.3% saved)

simplify88.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

prune4.3s (10.2%)

Pruning

218 alts after pruning (214 fresh and 4 done)

	Pruned	Kept	Total
New	382	192	574
Fresh	2	22	24
Picked	0	0	0
Done	2	4	6
Total	386	218	604

Error

Counts

604 → 218

Compiler

Compiled 8767 to 3216 computations (63.3% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_11672`
12×	`times-frac_binary64_11678`
10×	`add-cube-cbrt_binary64_11707` `add-sqr-sqrt_binary64_11694`
4×	`associate-/r*_binary64_11616` `distribute-lft-out_binary64_11623`
3×	`add-exp-log_binary64_11710` `associate-/l*_binary64_11617` `add-cbrt-cube_binary64_11708`
2×	`associate-/r/_binary64_11618`
1×	`cbrt-undiv_binary64_11706` `pow1_binary64_11733` `div-exp_binary64_11723` `clear-num_binary64_11671` `add-log-exp_binary64_11711` `flip-+_binary64_11646` `flip3-+_binary64_11675` `frac-2neg_binary64_11683` `div-inv_binary64_11669`

Counts

1 → 33

Calls

2 calls:

6.0ms	(/.f64 x (+.f64 x y))
0.0ms	(/.f64 x (+.f64 x y))

series82.0ms (0.2%)

Counts

1 → 21

Calls

1 calls:

82.0ms

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

Compiler

Compiled 396 to 348 computations (12.1% saved)

simplify59.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5434	719

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

4.6b	(/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (.f64 y y)))
4.6b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (*.f64 y y))))
3.5b	(-.f64 (.f64 x x) (.f64 y y))
2.7b	(.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (.f64 y y)))) (-.f64 x y))
2.7b	(.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (.f64 y y)))) (-.f64 x y))
3.5b	(-.f64 (.f64 x x) (.f64 y y))
4.6b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (*.f64 y y))))
4.6b	(/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (.f64 y y)))

rewrite60.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64_11694`
52×	`times-frac_binary64_11678`
43×	`*-un-lft-identity_binary64_11672`
41×	`add-cube-cbrt_binary64_11707`
35×	`associate-r_binary64_11612` `sqrt-prod_binary64_11688`
20×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
15×	`difference-of-squares_binary64_11641`
11×	`pow1_binary64_11733`
7×	`cbrt-unprod_binary64_11705` `cancel-sign-sub-inv_binary64_11638` `prod-exp_binary64_11721` `associate-l_binary64_11613`
6×	`add-log-exp_binary64_11711` `associate-r/_binary64_11614` `unswap-sqr_binary64_11640` `associate-/l_binary64_11617`
5×	`flip3--_binary64_11676` `flip--_binary64_11647`
4×	`associate-/r/_binary64_11618` `associate-/r*_binary64_11616` `distribute-lft-in_binary64_11621` `distribute-rgt-in_binary64_11622` `pow-prod-down_binary64_11743`
3×	`cbrt-undiv_binary64_11706` `div-exp_binary64_11723` `sub-neg_binary64_11665`
2×	`frac-times_binary64_11682` `div-inv_binary64_11669` `*-commutative_binary64_11603`
1×	`distribute-lft-out--_binary64_11624` `clear-num_binary64_11671` `associate-*l/_binary64_11615` `frac-2neg_binary64_11683` `diff-log_binary64_11764`

Counts

4 → 152

Calls

8 calls:

17.0ms	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (*.f64 y y))))
16.0ms	(.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (.f64 y y)))) (-.f64 x y))
7.0ms	(/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (.f64 y y)))
4.0ms	(-.f64 (.f64 x x) (.f64 y y))
0.0ms	(.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (.f64 y y)))) (-.f64 x y))

series365.0ms (0.9%)

Counts

4 → 50

Calls

4 calls:

103.0ms	(.f64 (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (.f64 y y)))) (-.f64 x y))
91.0ms	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (*.f64 y y))))
88.0ms	(-.f64 (.f64 x x) (.f64 y y))
81.0ms	(/.f64 (sqrt.f64 x) (-.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 1173 to 921 computations (21.5% saved)

simplify114.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4963	3883
1	4963	3883

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.2b	(/.f64 (+.f64 x y) (cbrt.f64 x))
0.1b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (+.f64 x y) (cbrt.f64 x)))
0.6b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_11703`
23×	`add-sqr-sqrt_binary64_11694`
15×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
11×	`pow1_binary64_11733`
9×	`pow1/3_binary64_11754`
6×	`associate-r_binary64_11612` `add-exp-log_binary64_11710` `swap-sqr_binary64_11639` `associate-l_binary64_11613`
4×	`add-log-exp_binary64_11711` `unswap-sqr_binary64_11640` `add-cbrt-cube_binary64_11708`
2×	`pow-sqr_binary64_11645` `pow-prod-up_binary64_11742` `pow-prod-down_binary64_11743`
1×	`cbrt-unprod_binary64_11705` `pow2_binary64_11753` `prod-exp_binary64_11721` `*-commutative_binary64_11603` `pow-plus_binary64_11735`

Counts

4 → 73

Calls

8 calls:

6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (+.f64 x y) (cbrt.f64 x)))

series328.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
83.0ms	(cbrt.f64 x)
75.0ms	(cbrt.f64 x)
72.0ms	(cbrt.f64 x)

Compiler

Compiled 394 to 310 computations (21.3% saved)

simplify82.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(cbrt.f64 (pow.f64 x 2/3))
0.2b	(*.f64 (cbrt.f64 (pow.f64 x 2/3)) (cbrt.f64 (cbrt.f64 x)))
0.1b	(/.f64 (*.f64 (cbrt.f64 (pow.f64 x 2/3)) (cbrt.f64 (cbrt.f64 x))) (+.f64 x y))
0.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (*.f64 (cbrt.f64 (pow.f64 x 2/3)) (cbrt.f64 (cbrt.f64 x))) (+.f64 x y)))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 (cbrt.f64 x))
2.7b	(pow.f64 x 2/3)

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cbrt-prod_binary64_11703`
10×	`add-cube-cbrt_binary64_11707` `add-sqr-sqrt_binary64_11694` `*-un-lft-identity_binary64_11672`
5×	`pow1_binary64_11733` `add-exp-log_binary64_11710`
4×	`add-log-exp_binary64_11711` `add-cbrt-cube_binary64_11708`
3×	`unpow-prod-down_binary64_11751` `pow1/3_binary64_11754` `pow-unpow_binary64_11749`
1×	`pow-exp_binary64_11740` `pow-to-exp_binary64_11741` `sqr-pow_binary64_11644` `pow-pow_binary64_11744`

Counts

4 → 53

Calls

8 calls:

2.0ms	(pow.f64 x 2/3)
1.0ms	(cbrt.f64 (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (*.f64 (cbrt.f64 (pow.f64 x 2/3)) (cbrt.f64 (cbrt.f64 x))) (+.f64 x y)))

series318.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt.f64 (cbrt.f64 x))
74.0ms	(cbrt.f64 x)
73.0ms	(cbrt.f64 x)
72.0ms	(pow.f64 x 2/3)

Compiler

Compiled 500 to 374 computations (25.2% saved)

simplify84.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4945	401
1	4945	401

prune6.9s (16.4%)

Pruning

343 alts after pruning (334 fresh and 9 done)

	Pruned	Kept	Total
New	263	143	406
Fresh	18	191	209
Picked	0	0	0
Done	0	9	9
Total	281	343	624

Error

Counts

624 → 343

Compiler

Compiled 11853 to 5217 computations (56% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_11672`
12×	`times-frac_binary64_11678`
10×	`add-cube-cbrt_binary64_11707` `add-sqr-sqrt_binary64_11694`
4×	`associate-/r*_binary64_11616` `distribute-lft-out_binary64_11623`
3×	`add-exp-log_binary64_11710` `associate-/l*_binary64_11617` `add-cbrt-cube_binary64_11708`
2×	`associate-/r/_binary64_11618`
1×	`cbrt-undiv_binary64_11706` `pow1_binary64_11733` `div-exp_binary64_11723` `clear-num_binary64_11671` `add-log-exp_binary64_11711` `flip-+_binary64_11646` `flip3-+_binary64_11675` `frac-2neg_binary64_11683` `div-inv_binary64_11669`

Counts

1 → 33

Calls

2 calls:

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

series81.0ms (0.2%)

Counts

1 → 21

Calls

1 calls:

81.0ms

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

Compiler

Compiled 396 to 348 computations (12.1% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5434	719

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (/.f64 (+.f64 x y) x))
0.0b	(/.f64 (+.f64 x y) x)
0.0b	(/.f64 (+.f64 x y) x)
0.3b	(/.f64 1 (/.f64 (+.f64 x y) x))

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_11678`
92×	`*-un-lft-identity_binary64_11672`
60×	`add-cube-cbrt_binary64_11707` `add-sqr-sqrt_binary64_11694`
19×	`associate-/r*_binary64_11616`
16×	`distribute-lft-out_binary64_11623`
15×	`add-exp-log_binary64_11710`
9×	`add-cbrt-cube_binary64_11708`
8×	`div-exp_binary64_11723`
7×	`associate-/l*_binary64_11617`
6×	`div-inv_binary64_11669`
4×	`cbrt-undiv_binary64_11706`
3×	`pow1_binary64_11733`
2×	`clear-num_binary64_11671` `1-exp_binary64_11716` `add-log-exp_binary64_11711` `frac-2neg_binary64_11683` `associate-/l/_binary64_11619` `rec-exp_binary64_11722`
1×	`associate-/r/_binary64_11618` `inv-pow_binary64_11757` `pow-flip_binary64_11746` `flip-+_binary64_11646` `flip3-+_binary64_11675`

Counts

2 → 121

Calls

4 calls:

8.0ms	(/.f64 1 (/.f64 (+.f64 x y) x))
5.0ms	(/.f64 (+.f64 x y) x)
0.0ms	(/.f64 (+.f64 x y) x)
0.0ms	(/.f64 1 (/.f64 (+.f64 x y) x))

series150.0ms (0.4%)

Counts

2 → 33

Calls

2 calls:

77.0ms	(/.f64 1 (/.f64 (+.f64 x y) x))
73.0ms	(/.f64 (+.f64 x y) x)

Compiler

Compiled 408 to 366 computations (10.3% saved)

simplify94.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5130	2281

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.3b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (+.f64 x y))
0.2b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (+.f64 x y)) (cbrt.f64 x))
0.6b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_11703`
23×	`add-sqr-sqrt_binary64_11694`
15×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
11×	`pow1_binary64_11733`
9×	`pow1/3_binary64_11754`
6×	`associate-r_binary64_11612` `add-exp-log_binary64_11710` `swap-sqr_binary64_11639` `associate-l_binary64_11613`
4×	`add-log-exp_binary64_11711` `unswap-sqr_binary64_11640` `add-cbrt-cube_binary64_11708`
2×	`pow-sqr_binary64_11645` `pow-prod-up_binary64_11742` `pow-prod-down_binary64_11743`
1×	`cbrt-unprod_binary64_11705` `pow2_binary64_11753` `prod-exp_binary64_11721` `*-commutative_binary64_11603` `pow-plus_binary64_11735`

Counts

4 → 73

Calls

8 calls:

7.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
2.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (+.f64 x y)) (cbrt.f64 x))

series317.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
77.0ms	(cbrt.f64 x)
76.0ms	(cbrt.f64 x)
73.0ms	(cbrt.f64 x)

Compiler

Compiled 346 to 262 computations (24.3% saved)

simplify83.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (+.f64 x y) (sqrt.f64 (sqrt.f64 x)))
0.1b	(/.f64 (sqrt.f64 x) (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 (+.f64 x y) (sqrt.f64 (sqrt.f64 x)))))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.1b	(/.f64 (sqrt.f64 x) (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 (+.f64 x y) (sqrt.f64 (sqrt.f64 x)))))
0.1b	(/.f64 (+.f64 x y) (sqrt.f64 (sqrt.f64 x)))
0.2b	(/.f64 1 (sqrt.f64 (sqrt.f64 x)))
0.2b	(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 (+.f64 x y) (sqrt.f64 (sqrt.f64 x))))

rewrite110.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`sqrt-prod_binary64_11688`
185×	`add-sqr-sqrt_binary64_11694`
177×	`times-frac_binary64_11678`
146×	`*-un-lft-identity_binary64_11672`
96×	`add-cube-cbrt_binary64_11707`
64×	`add-exp-log_binary64_11710`
40×	`associate-r_binary64_11612`
38×	`add-cbrt-cube_binary64_11708`
31×	`associate-l_binary64_11613`
28×	`div-exp_binary64_11723` `unswap-sqr_binary64_11640`
19×	`associate-/r*_binary64_11616` `distribute-lft-out_binary64_11623`
16×	`prod-exp_binary64_11721`
15×	`cbrt-undiv_binary64_11706`
13×	`associate-/l*_binary64_11617`
9×	`pow1_binary64_11733`
8×	`cbrt-unprod_binary64_11705`
5×	`1-exp_binary64_11716` `pow-flip_binary64_11746` `div-inv_binary64_11669` `rec-exp_binary64_11722`
4×	`add-log-exp_binary64_11711` `sqrt-pow1_binary64_11690`
3×	`associate-/r/_binary64_11618` `clear-num_binary64_11671` `frac-2neg_binary64_11683`
2×	`frac-times_binary64_11682` `pow1/2_binary64_11752` `associate-l/_binary64_11615` `associate-r/_binary64_11614` `associate-/l/_binary64_11619`
1×	`inv-pow_binary64_11757` `flip-+_binary64_11646` `flip3-+_binary64_11675` `*-commutative_binary64_11603` `pow-prod-down_binary64_11743`

Counts

4 → 285

Calls

8 calls:

38.0ms	(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 (+.f64 x y) (sqrt.f64 (sqrt.f64 x))))
18.0ms	(/.f64 (sqrt.f64 x) (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 (+.f64 x y) (sqrt.f64 (sqrt.f64 x)))))
8.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (sqrt.f64 x)))
6.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 x)))
0.0ms	(sqrt.f64 (sqrt.f64 x))

series449.0ms (1.1%)

Counts

4 → 42

Calls

4 calls:

227.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (sqrt.f64 x)))
90.0ms	(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 (+.f64 x y) (sqrt.f64 (sqrt.f64 x))))
80.0ms	(/.f64 (sqrt.f64 x) (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 (+.f64 x y) (sqrt.f64 (sqrt.f64 x)))))
51.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 x)))

Compiler

Compiled 892 to 729 computations (18.3% saved)

simplify142.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

327 → 327

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4962	6038
1	4962	6038

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (cbrt.f64 (exp.f64 (.f64 2/3 (log.f64 x)))) (cbrt.f64 (cbrt.f64 x)))
0.2b	(*.f64 2/3 (log.f64 x))
0.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 2/3 (log.f64 x)))) (cbrt.f64 (cbrt.f64 x))) (+.f64 x y)))
0.1b	(/.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 2/3 (log.f64 x)))) (cbrt.f64 (cbrt.f64 x))) (+.f64 x y))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 (cbrt.f64 x))
2.3b	(exp.f64 (*.f64 2/3 (log.f64 x)))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cbrt-prod_binary64_11703`
10×	`add-cube-cbrt_binary64_11707` `add-sqr-sqrt_binary64_11694` `*-un-lft-identity_binary64_11672`
6×	`add-log-exp_binary64_11711` `exp-sum_binary64_11718` `log-prod_binary64_11758`
4×	`pow1_binary64_11733` `add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
3×	`distribute-lft-in_binary64_11621` `pow1/3_binary64_11754` `distribute-rgt-in_binary64_11622`
1×	`exp-prod_binary64_11724` `rem-exp-log_binary64_11712` `exp-to-pow_binary64_11734`

Counts

4 → 52

Calls

8 calls:

3.0ms	(exp.f64 (*.f64 2/3 (log.f64 x)))
2.0ms	(cbrt.f64 (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(/.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 2/3 (log.f64 x)))) (cbrt.f64 (cbrt.f64 x))) (+.f64 x y))

series329.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt.f64 (cbrt.f64 x))
83.0ms	(cbrt.f64 x)
76.0ms	(exp.f64 (*.f64 2/3 (log.f64 x)))
72.0ms	(cbrt.f64 x)

Compiler

Compiled 536 to 410 computations (23.5% saved)

simplify86.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4940	356
1	4940	356

prune12.7s (30.1%)

Pruning

507 alts after pruning (493 fresh and 14 done)

	Pruned	Kept	Total
New	488	196	684
Fresh	32	297	329
Picked	0	0	0
Done	0	14	14
Total	520	507	1027

Error

Counts

1027 → 507

Compiler

Compiled 6461 to 2047 computations (68.3% saved)

simplify401.0ms (0.9%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5181	22868

regimes3.4s (8%)

Compiler: Compiled 33359 to 19222 computations (42.4% saved)

bsearch0.0ms (0%)

regimes56.0ms (0.1%)

Compiler: Compiled 26 to 42 computations (-61.5% saved)

bsearch27.0ms (0.1%)

Steps

Iters	Range		Point
10	351902502.9441016	2.238936288103518e+23	15209305513240696.0
9	-1.9388901295283305e-53	-6.223747592983215e-62	-8.148757402396204e-60

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes55.0ms (0.1%)

Compiler: Compiled 16 to 32 computations (-100% saved)

bsearch23.0ms (0.1%)

Steps

Iters	Range		Point
10	351902502.9441016	2.238936288103518e+23	10019188617662314.0
9	-1.9388901295283305e-53	-6.223747592983215e-62	-1.3338772661658133e-53

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes31.0ms (0.1%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch20.0ms (0%)

Steps

Iters	Range		Point
6	2.0774735668554936e-203	1.5995483430950576e-202	9.234413159601361e-203
7	-3.9726711792157e-214	-3.805706130164023e-216	-3.874652219877624e-214

Compiler

Compiled 52 to 42 computations (19.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	55	67
1	55	67

end0.0ms (0%)

sample8.9s (20.9%)

Algorithm

1×

intervals

Results

161.0ms

8000×

body

128

valid

Compiler

Compiled 11262 to 6535 computations (42% saved)

Pareto

0.12165173459240143