Details

analyze69.0ms (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
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample16.0ms (0%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 18 to 18 computations (0% saved)

simplify102.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

3 → 3

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	12
1	9	12

prune2.0ms (0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Kept	Total
New	3	3
Fresh	3	3
Picked	0	0
Done	0	0
Total	6	6

Error

0.0b

Counts

6 → 3

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_7960`
1×	`+-commutative_binary64_7851` `add-cube-cbrt_binary64_7956` `add-cbrt-cube_binary64_7957` `pow1_binary64_7982` `flip3-+_binary64_7924` `sum-log_binary64_8012` `add-exp-log_binary64_7959` `*-un-lft-identity_binary64_7921` `flip-+_binary64_7895` `add-sqr-sqrt_binary64_7943`

Counts

1 → 11

Calls

2 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series87.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

87.0ms

(+.f64 (*.f64 x x) (*.f64 y y))

Compiler

Compiled 102 to 108 computations (-5.9% saved)

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4921	247
1	4921	247

prune49.0ms (0.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	13	10	23
Fresh	0	2	2
Picked	0	0	0
Done	0	1	1
Total	13	13	26

Error

Counts

26 → 13

Compiler

Compiled 271 to 120 computations (55.7% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_7960`
1×	`+-commutative_binary64_7851` `add-cube-cbrt_binary64_7956` `add-cbrt-cube_binary64_7957` `pow1_binary64_7982` `flip3-+_binary64_7924` `sum-log_binary64_8012` `add-exp-log_binary64_7959` `*-un-lft-identity_binary64_7921` `flip-+_binary64_7895` `add-sqr-sqrt_binary64_7943`

Counts

1 → 11

Calls

2 calls:

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

series87.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

87.0ms

(+.f64 (*.f64 x x) (*.f64 y y))

Compiler

Compiled 138 to 144 computations (-4.3% saved)

simplify84.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4921	247
1	4921	247

localize2.0ms (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

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_7960`
1×	`+-commutative_binary64_7851` `add-cube-cbrt_binary64_7956` `add-cbrt-cube_binary64_7957` `pow1_binary64_7982` `flip3-+_binary64_7924` `sum-log_binary64_8012` `add-exp-log_binary64_7959` `*-un-lft-identity_binary64_7921` `flip-+_binary64_7895` `add-sqr-sqrt_binary64_7943`

Counts

1 → 11

Calls

2 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series91.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

90.0ms

(+.f64 (*.f64 x x) (*.f64 y y))

Compiler

Compiled 138 to 144 computations (-4.3% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4921	247
1	4921	247

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

37.1b	(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3))
0.2b	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3)
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.2b	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3)
37.1b	(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3))

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_7952`
9×	`add-cube-cbrt_binary64_7956` `*-un-lft-identity_binary64_7921` `add-sqr-sqrt_binary64_7943`
6×	`cube-prod_binary64_7949` `unpow-prod-down_binary64_8000`
5×	`add-log-exp_binary64_7960`
4×	`add-cbrt-cube_binary64_7957` `pow1_binary64_7982` `add-exp-log_binary64_7959` `cube-div_binary64_7950`
3×	`flip3-+_binary64_7924` `flip-+_binary64_7895` `pow-unpow_binary64_7998`
2×	`unpow3_binary64_7987` `cube-mult_binary64_7951` `cbrt-div_binary64_7953` `sqr-pow_binary64_7893`
1×	`+-commutative_binary64_7851` `pow-exp_binary64_7989` `pow-to-exp_binary64_7990` `rem-cbrt-cube_binary64_7945` `pow-pow_binary64_7993` `pow1/3_binary64_8003` `rem-cube-cbrt_binary64_7944` `sum-log_binary64_8012`

Counts

3 → 59

Calls

6 calls:

5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3))
5.0ms	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3)
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))
0.0ms	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3)

series326.0ms (0.4%)

Counts

3 → 48

Calls

3 calls:

146.0ms	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3)
90.0ms	(+.f64 (.f64 x x) (.f64 y y))
89.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3))

Compiler

Compiled 678 to 648 computations (4.4% saved)

simplify54.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4938	1703
1	4938	1703

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

6.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
0.0b	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
6.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
6.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite35.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_7943`
24×	`sqrt-prod_binary64_7937`
21×	`pow1_binary64_7982`
16×	`sqrt-div_binary64_7938`
14×	`add-cube-cbrt_binary64_7956` `*-un-lft-identity_binary64_7921`
10×	`sqrt-pow1_binary64_7939` `pow1/2_binary64_8001`
9×	`flip3-+_binary64_7924` `flip-+_binary64_7895`
8×	`swap-sqr_binary64_7888`
6×	`associate-r_binary64_7861` `add-log-exp_binary64_7960` `add-cbrt-cube_binary64_7957` `associate-l_binary64_7862` `add-exp-log_binary64_7959`
5×	`pow-prod-up_binary64_7991`
4×	`frac-times_binary64_7931` `unswap-sqr_binary64_7889` `rem-sqrt-square_binary64_7934`
3×	`pow-sqr_binary64_7894` `pow-prod-down_binary64_7992`
2×	`associate-r/_binary64_7863` `associate-l/_binary64_7864`
1×	`+-commutative_binary64_7851` `sqrt-unprod_binary64_7941` `pow2_binary64_8002` `prod-exp_binary64_7970` `cbrt-unprod_binary64_7954` `pow-plus_binary64_7984` `*-commutative_binary64_7852` `sqr-abs_binary64_7936` `sum-log_binary64_8012` `rem-square-sqrt_binary64_7933`

Counts

4 → 99

Calls

8 calls:

13.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series441.0ms (0.5%)

Counts

4 → 64

Calls

4 calls:

129.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
126.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
95.0ms	(+.f64 (.f64 x x) (.f64 y y))
90.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))

Compiler

Compiled 1524 to 1176 computations (22.8% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5093	2397

prune1.6s (2%)

Pruning

93 alts after pruning (88 fresh and 5 done)

	Pruned	Kept	Total
New	235	81	316
Fresh	0	7	7
Picked	0	0	0
Done	1	5	6
Total	236	93	329

Error

Counts

329 → 93

Compiler

Compiled 4390 to 1788 computations (59.3% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_7960`
1×	`+-commutative_binary64_7851` `add-cube-cbrt_binary64_7956` `add-cbrt-cube_binary64_7957` `pow1_binary64_7982` `flip3-+_binary64_7924` `sum-log_binary64_8012` `add-exp-log_binary64_7959` `*-un-lft-identity_binary64_7921` `flip-+_binary64_7895` `add-sqr-sqrt_binary64_7943`

Counts

1 → 11

Calls

2 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series83.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

83.0ms

(+.f64 (*.f64 x x) (*.f64 y y))

Compiler

Compiled 174 to 180 computations (-3.4% saved)

simplify100.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4921	247
1	4921	247

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

17.7b	(sqrt.f64 (*.f64 x x))
6.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
0.0b	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (.f64 x x)))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (.f64 x x)))
6.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
17.7b	(sqrt.f64 (*.f64 x x))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64_7982`
15×	`add-sqr-sqrt_binary64_7943`
12×	`sqrt-prod_binary64_7937`
11×	`sqrt-pow1_binary64_7939`
8×	`add-cube-cbrt_binary64_7956` `*-un-lft-identity_binary64_7921`
6×	`add-log-exp_binary64_7960` `add-cbrt-cube_binary64_7957` `associate-l_binary64_7862` `add-exp-log_binary64_7959` `pow-prod-down_binary64_7992`
4×	`associate-r_binary64_7861` `sqrt-div_binary64_7938` `unswap-sqr_binary64_7889` `pow1/2_binary64_8001`
3×	`flip3-+_binary64_7924` `flip-+_binary64_7895`
2×	`rem-sqrt-square_binary64_7934` `associate-*l/_binary64_7864`
1×	`+-commutative_binary64_7851` `sqrt-unprod_binary64_7941` `pow2_binary64_8002` `prod-exp_binary64_7970` `cbrt-unprod_binary64_7954` `pow-plus_binary64_7984` `*-commutative_binary64_7852` `sum-log_binary64_8012` `pow-prod-up_binary64_7991` `pow-sqr_binary64_7894`

Counts

4 → 73

Calls

8 calls:

14.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (.f64 x x)))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(sqrt.f64 (*.f64 x x))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series379.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

135.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
130.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (.f64 x x)))
98.0ms	(+.f64 (.f64 x x) (.f64 y y))
16.0ms	(sqrt.f64 (*.f64 x x))

Compiler

Compiled 1042 to 859 computations (17.6% saved)

simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5295	1667

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2)
0.1b	(.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2) (pow.f64 (+.f64 (.f64 x x) (*.f64 y y)) 3/2))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.1b	(.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2) (pow.f64 (+.f64 (.f64 x x) (*.f64 y y)) 3/2))
0.3b	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2)
0.3b	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2)
37.1b	(cbrt.f64 (.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2) (pow.f64 (+.f64 (.f64 x x) (*.f64 y y)) 3/2)))

rewrite49.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_7943`
24×	`unpow-prod-down_binary64_8000`
18×	`add-exp-log_binary64_7959`
16×	`add-cube-cbrt_binary64_7956` `*-un-lft-identity_binary64_7921`
12×	`sqr-pow_binary64_7893`
9×	`unswap-sqr_binary64_7889` `prod-exp_binary64_7970`
8×	`pow-exp_binary64_7989` `pow-to-exp_binary64_7990`
7×	`associate-r_binary64_7861` `associate-l_binary64_7862` `swap-sqr_binary64_7888`
6×	`add-cbrt-cube_binary64_7957` `pow1_binary64_7982` `pow-unpow_binary64_7998`
4×	`add-log-exp_binary64_7960`
2×	`pow-pow_binary64_7993`
1×	`pow2_binary64_8002` `cbrt-unprod_binary64_7954` `pow1/3_binary64_8003` `*-commutative_binary64_7852` `pow-prod-up_binary64_7991` `cbrt-prod_binary64_7952` `pow-sqr_binary64_7894` `pow-prod-down_binary64_7992`

Counts

4 → 95

Calls

8 calls:

14.0ms	(.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2) (pow.f64 (+.f64 (.f64 x x) (*.f64 y y)) 3/2))
10.0ms	(cbrt.f64 (.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2) (pow.f64 (+.f64 (.f64 x x) (*.f64 y y)) 3/2)))
5.0ms	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2)
5.0ms	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2)
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series805.0ms (1%)

Counts

4 → 84

Calls

4 calls:

278.0ms	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2)
264.0ms	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2)
164.0ms	(.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2) (pow.f64 (+.f64 (.f64 x x) (*.f64 y y)) 3/2))
98.0ms	(cbrt.f64 (.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3/2) (pow.f64 (+.f64 (.f64 x x) (*.f64 y y)) 3/2)))

Compiler

Compiled 1810 to 1486 computations (17.9% saved)

simplify96.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4978	3548
1	4978	3548

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

2.3b	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
0.2b	(pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3)
0.1b	(pow.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) 3)
0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.2b	(pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3)
2.3b	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
37.1b	(cbrt.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) 3) (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3)))
47.9b	(/.f64 (pow.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) 3) (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3))

rewrite352.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

1161×	`unpow-prod-down_binary64_8000`
1012×	`add-sqr-sqrt_binary64_7943`
952×	`times-frac_binary64_7927`
686×	`cube-prod_binary64_7949`
671×	`difference-of-squares_binary64_7890`
540×	`*-un-lft-identity_binary64_7921`
482×	`cbrt-prod_binary64_7952`
454×	`sqr-pow_binary64_7893`
304×	`add-cube-cbrt_binary64_7956`
118×	`distribute-lft-out--_binary64_7873`
99×	`unpow3_binary64_7987` `cube-mult_binary64_7951`
34×	`associate-/l*_binary64_7866`
17×	`add-exp-log_binary64_7959`
14×	`associate-/r*_binary64_7865`
9×	`div-exp_binary64_7972`
8×	`cube-div_binary64_7950`
7×	`pow-exp_binary64_7989` `add-cbrt-cube_binary64_7957` `pow-to-exp_binary64_7990` `cancel-sign-sub-inv_binary64_7887`
6×	`add-log-exp_binary64_7960`
5×	`flip3--_binary64_7925` `pow1_binary64_7982` `flip--_binary64_7896`
4×	`associate-/r/_binary64_7867`
3×	`pow-unpow_binary64_7998`
2×	`associate-/l/_binary64_7868` `div-inv_binary64_7918`
1×	`diff-log_binary64_8013` `clear-num_binary64_7920` `frac-2neg_binary64_7932` `sub-neg_binary64_7914` `pow-pow_binary64_7993` `pow1/3_binary64_8003` `cbrt-div_binary64_7953` `cbrt-undiv_binary64_7955` `rem-cube-cbrt_binary64_7944`

Counts

4 → 1000

Calls

8 calls:

57.0ms	(cbrt.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) 3) (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3)))
36.0ms	(/.f64 (pow.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) 3) (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3))
9.0ms	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
5.0ms	(pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3)
0.0ms	(-.f64 (.f64 x x) (.f64 y y))

series890.0ms (1.1%)

Counts

4 → 72

Calls

4 calls:

313.0ms	(/.f64 (pow.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) 3) (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3))
237.0ms	(cbrt.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) 3) (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3)))
171.0ms	(pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3)
168.0ms	(-.f64 (pow.f64 x 4) (pow.f64 y 4))

Compiler

Compiled 1530 to 1338 computations (12.5% saved)

simplify493.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1072 → 1072

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4789	50371
1	4789	50371

prune11.2s (13.7%)

Pruning

323 alts after pruning (314 fresh and 9 done)

	Pruned	Kept	Total
New	1157	238	1395
Fresh	7	76	83
Picked	0	0	0
Done	1	9	10
Total	1165	323	1488

Error

Counts

1488 → 323

Compiler

Compiled 19113 to 10596 computations (44.6% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_7960`
1×	`+-commutative_binary64_7851` `add-cube-cbrt_binary64_7956` `add-cbrt-cube_binary64_7957` `pow1_binary64_7982` `flip3-+_binary64_7924` `sum-log_binary64_8012` `add-exp-log_binary64_7959` `*-un-lft-identity_binary64_7921` `flip-+_binary64_7895` `add-sqr-sqrt_binary64_7943`

Counts

1 → 11

Calls

2 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series88.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

88.0ms

(+.f64 (*.f64 x x) (*.f64 y y))

Compiler

Compiled 174 to 180 computations (-3.4% saved)

simplify84.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4921	247
1	4921	247

localize4.0ms (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

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.5b	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
7.1b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.1b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.1b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite37.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_7952`
23×	`add-sqr-sqrt_binary64_7943`
18×	`cbrt-div_binary64_7953`
15×	`add-cube-cbrt_binary64_7956` `*-un-lft-identity_binary64_7921`
11×	`pow1_binary64_7982`
9×	`pow1/3_binary64_8003` `flip3-+_binary64_7924` `flip-+_binary64_7895`
6×	`associate-r_binary64_7861` `associate-l_binary64_7862` `add-exp-log_binary64_7959` `swap-sqr_binary64_7888`
4×	`add-log-exp_binary64_7960` `frac-times_binary64_7931` `add-cbrt-cube_binary64_7957` `unswap-sqr_binary64_7889`
2×	`associate-r/_binary64_7863` `associate-l/_binary64_7864` `pow-prod-up_binary64_7991` `pow-sqr_binary64_7894` `pow-prod-down_binary64_7992`
1×	`pow2_binary64_8002` `prod-exp_binary64_7970` `cbrt-unprod_binary64_7954` `pow-plus_binary64_7984` `*-commutative_binary64_7852`

Counts

4 → 87

Calls

8 calls:

15.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series1.0s (1.3%)

Counts

4 → 60

Calls

4 calls:

278.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
272.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))
250.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
245.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 3423 to 2451 computations (28.4% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5043	3163

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

37.1b	(cbrt.f64 (pow.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3)))
1.8b	(pow.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
1.6b	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3)))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
1.6b	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3)))
1.8b	(pow.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
37.1b	(cbrt.f64 (pow.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3)))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`unpow-prod-down_binary64_8000`
14×	`cbrt-prod_binary64_7952`
12×	`add-cube-cbrt_binary64_7956` `*-un-lft-identity_binary64_7921` `add-sqr-sqrt_binary64_7943`
7×	`add-exp-log_binary64_7959` `pow-unpow_binary64_7998`
6×	`add-log-exp_binary64_7960`
5×	`pow-exp_binary64_7989` `pow1_binary64_7982` `sqr-pow_binary64_7893`
4×	`add-cbrt-cube_binary64_7957`
3×	`pow-to-exp_binary64_7990`
2×	`pow-pow_binary64_7993`
1×	`+-commutative_binary64_7851` `pow1/3_binary64_8003` `flip3-+_binary64_7924` `sum-log_binary64_8012` `flip-+_binary64_7895`

Counts

4 → 71

Calls

8 calls:

7.0ms	(pow.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
6.0ms	(cbrt.f64 (pow.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3)))
5.0ms	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series2.5s (3%)

Counts

4 → 62

Calls

4 calls:

928.0ms	(pow.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
839.0ms	(cbrt.f64 (pow.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3)))
626.0ms	(pow.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (cbrt.f64 3) (cbrt.f64 3)))
90.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 5070 to 4760 computations (6.1% saved)

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5550	5822

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (cbrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))) 6)
0.1b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))) 6) (pow.f64 (+.f64 x y) 3)) (/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (pow.f64 (-.f64 x y) 3)))
0.0b	(pow.f64 (-.f64 x y) 3)
0.0b	(pow.f64 (+.f64 x y) 3)
30.5b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))) 6) (pow.f64 (+.f64 x y) 3))
35.1b	(cbrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))
36.7b	(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (pow.f64 (-.f64 x y) 3))
37.1b	(cbrt.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))) 6) (pow.f64 (+.f64 x y) 3)) (/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (pow.f64 (-.f64 x y) 3))))

rewrite270.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

682×	`unpow-prod-down_binary64_8000`
634×	`add-sqr-sqrt_binary64_7943`
518×	`times-frac_binary64_7927`
458×	`*-un-lft-identity_binary64_7921`
327×	`difference-of-squares_binary64_7890`
250×	`sqr-pow_binary64_7893`
225×	`cbrt-prod_binary64_7952`
178×	`add-cube-cbrt_binary64_7956`
163×	`cube-prod_binary64_7949`
96×	`distribute-lft-out--_binary64_7873`
44×	`distribute-lft-out_binary64_7872`
37×	`unpow3_binary64_7987` `cube-mult_binary64_7951`
35×	`associate-/l*_binary64_7866`
30×	`associate-/r*_binary64_7865`
21×	`add-exp-log_binary64_7959`
12×	`div-exp_binary64_7972`
8×	`add-cbrt-cube_binary64_7957`
7×	`pow-exp_binary64_7989` `pow-to-exp_binary64_7990`
5×	`cbrt-div_binary64_7953`
4×	`add-log-exp_binary64_7960` `associate-/r/_binary64_7867` `pow1_binary64_7982` `cube-div_binary64_7950`
3×	`flip3--_binary64_7925` `flip--_binary64_7896`
2×	`clear-num_binary64_7920` `frac-2neg_binary64_7932` `pow1/3_binary64_8003` `associate-/l/_binary64_7868` `cbrt-undiv_binary64_7955` `div-inv_binary64_7918`
1×	`div-sub_binary64_7926` `frac-times_binary64_7931` `associate-r/_binary64_7863` `associate-l/_binary64_7864` `flip3-+_binary64_7924` `flip-+_binary64_7895`

Counts

4 → 660

Calls

8 calls:

64.0ms	(cbrt.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))) 6) (pow.f64 (+.f64 x y) 3)) (/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (pow.f64 (-.f64 x y) 3))))
32.0ms	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))) 6) (pow.f64 (+.f64 x y) 3))
22.0ms	(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (pow.f64 (-.f64 x y) 3))
8.0ms	(cbrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))
0.0ms	(pow.f64 (+.f64 x y) 3)

series761.0ms (0.9%)

Counts

4 → 54

Calls

4 calls:

285.0ms	(cbrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))
243.0ms	(cbrt.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))) 6) (pow.f64 (+.f64 x y) 3)) (/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (pow.f64 (-.f64 x y) 3))))
155.0ms	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))) 6) (pow.f64 (+.f64 x y) 3))
78.0ms	(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (pow.f64 (-.f64 x y) 3))

Compiler

Compiled 1974 to 1653 computations (16.3% saved)

simplify290.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

714 → 714

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5031	25299

prune24.3s (29.8%)

Pruning

628 alts after pruning (614 fresh and 14 done)

	Pruned	Kept	Total
New	709	308	1017
Fresh	3	306	309
Picked	0	0	0
Done	0	14	14
Total	712	628	1340

Error

Counts

1340 → 628

Compiler

Compiled 16541 to 9630 computations (41.8% saved)

simplify630.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4998	44477
1	4998	44477

regimes10.4s (12.8%)

Compiler: Compiled 120230 to 84070 computations (30.1% saved)

bsearch0.0ms (0%)

regimes95.0ms (0.1%)

Compiler: Compiled 76 to 96 computations (-26.3% saved)

bsearch40.0ms (0%)

Steps

Iters	Range		Point
8	2.4945894549984816e-29	3.10642201279487e-25	1.1271085824046623e-28
7	-1.7999400822701893e-140	-4.554835028155275e-142	-1.7781012792143406e-140
5	-2.1840213589811134e-115	-6.032549369806289e-116	-9.475100020882994e-116
9	-1.8947816468533454e-69	-5.956529313499214e-76	-6.118930439520561e-70

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes24.0ms (0%)

Compiler: Compiled 25 to 41 computations (-64% saved)

bsearch0.0ms (0%)

regimes13.0ms (0%)

Accuracy

Total 0.0b remaining (87.3%)

Threshold costs 0.0b (87.3%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch3.0ms (0%)

Compiler: Compiled 42 to 27 computations (35.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	51
1	40	51

end0.0ms (0%)

sample22.7s (27.8%)

Algorithm

1×

intervals

Results

191.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 24118 to 16874 computations (30% saved)

Pareto

0.4529376259441915