Details

analyze53.0ms (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)

sample12.0ms (0%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify101.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

prune1.0ms (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 7 to 5 computations (28.6% saved)

localize4.0ms (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_5914`
1×	`flip-+_binary64_5849` `add-cube-cbrt_binary64_5910` `flip3-+_binary64_5878` `add-exp-log_binary64_5913` `add-sqr-sqrt_binary64_5897` `*-un-lft-identity_binary64_5875` `add-cbrt-cube_binary64_5911` `sum-log_binary64_5966` `pow1_binary64_5936` `+-commutative_binary64_5805`

Counts

1 → 11

Calls

2 calls:

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

series89.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

89.0ms

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

Compiler

Compiled 102 to 108 computations (-5.9% saved)

simplify82.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4921	247
1	4921	247

prune43.0ms (0.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	12	11	23
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	12	12	24

Error

0.0b

Counts

24 → 12

Compiler

Compiled 280 to 127 computations (54.6% saved)

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_5914`
1×	`flip-+_binary64_5849` `add-cube-cbrt_binary64_5910` `flip3-+_binary64_5878` `add-exp-log_binary64_5913` `add-sqr-sqrt_binary64_5897` `*-un-lft-identity_binary64_5875` `add-cbrt-cube_binary64_5911` `sum-log_binary64_5966` `pow1_binary64_5936` `+-commutative_binary64_5805`

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 (0.2%)

Counts

1 → 12

Calls

1 calls:

87.0ms

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

Compiler

Compiled 138 to 144 computations (-4.3% saved)

simplify82.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (74.0ms)

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

simplify9.0ms (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_5914`
1×	`flip-+_binary64_5849` `add-cube-cbrt_binary64_5910` `flip3-+_binary64_5878` `add-exp-log_binary64_5913` `add-sqr-sqrt_binary64_5897` `*-un-lft-identity_binary64_5875` `add-cbrt-cube_binary64_5911` `sum-log_binary64_5966` `pow1_binary64_5936` `+-commutative_binary64_5805`

Counts

1 → 11

Calls

2 calls:

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

series89.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

89.0ms

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

Compiler

Compiled 138 to 144 computations (-4.3% saved)

simplify82.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4921	247
1	4921	247

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

2.8b	(log.f64 (exp.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(exp.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	(exp.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.8b	(log.f64 (exp.f64 (+.f64 (.f64 x x) (.f64 y y))))

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_5914`
6×	`add-cube-cbrt_binary64_5910` `add-sqr-sqrt_binary64_5897` `*-un-lft-identity_binary64_5875` `exp-prod_binary64_5927`
4×	`pow1_binary64_5936` `log-prod_binary64_5961` `log-pow_binary64_5964`
3×	`add-exp-log_binary64_5913` `add-cbrt-cube_binary64_5911`
2×	`rem-exp-log_binary64_5915` `exp-sum_binary64_5921` `sum-log_binary64_5966`
1×	`flip-+_binary64_5849` `rem-log-exp_binary64_5916` `flip3-+_binary64_5878` `+-commutative_binary64_5805`

Counts

3 → 40

Calls

6 calls:

7.0ms	(exp.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(log.f64 (exp.f64 (+.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	(log.f64 (exp.f64 (+.f64 (.f64 x x) (.f64 y y))))

series390.0ms (0.7%)

Counts

3 → 29

Calls

3 calls:

249.0ms	(log.f64 (exp.f64 (+.f64 (.f64 x x) (.f64 y y))))
92.0ms	(+.f64 (.f64 x x) (.f64 y y))
49.0ms	(exp.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 452 to 449 computations (0.7% saved)

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4926	832
1	4926	832

localize10.0ms (0%)

Local error

Found 6 expressions with local error:

31.9b	(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (-.f64 (.f64 x x) (.f64 y y)))
0.9b	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.9b	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
31.9b	(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (-.f64 (.f64 x x) (.f64 y y)))

rewrite45.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-sqr-sqrt_binary64_5897`
70×	`difference-of-squares_binary64_5844`
56×	`times-frac_binary64_5881`
51×	`unpow-prod-down_binary64_5954`
49×	`*-un-lft-identity_binary64_5875`
37×	`sqr-pow_binary64_5847`
25×	`add-cube-cbrt_binary64_5910`
14×	`associate-/l*_binary64_5820`
12×	`distribute-lft-out--_binary64_5827`
8×	`cancel-sign-sub-inv_binary64_5841`
7×	`add-log-exp_binary64_5914`
5×	`add-exp-log_binary64_5913` `add-cbrt-cube_binary64_5911`
4×	`associate-/r*_binary64_5819` `flip3--_binary64_5879` `flip--_binary64_5850`
3×	`pow1_binary64_5936`
2×	`associate-/r/_binary64_5821` `diff-log_binary64_5967` `sub-neg_binary64_5868` `associate-/l/_binary64_5822`
1×	`cbrt-undiv_binary64_5909` `div-sub_binary64_5880` `div-inv_binary64_5872` `frac-2neg_binary64_5886` `div-exp_binary64_5926` `clear-num_binary64_5874`

Counts

3 → 133

Calls

6 calls:

15.0ms	(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (-.f64 (.f64 x x) (.f64 y y)))
8.0ms	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
6.0ms	(-.f64 (.f64 x x) (.f64 y y))
0.0ms	(-.f64 (.f64 x x) (.f64 y y))
0.0ms	(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (-.f64 (.f64 x x) (.f64 y y)))

series509.0ms (1%)

Counts

3 → 36

Calls

3 calls:

244.0ms	(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (-.f64 (.f64 x x) (.f64 y y)))
168.0ms	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
96.0ms	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 606 to 516 computations (14.9% saved)

simplify84.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4940	3865
1	4940	3865

prune1.5s (2.7%)

Pruning

97 alts after pruning (91 fresh and 6 done)

	Pruned	Kept	Total
New	197	87	284
Fresh	2	4	6
Picked	0	0	0
Done	0	6	6
Total	199	97	296

Error

0.0b

Counts

296 → 97

Compiler

Compiled 4955 to 2390 computations (51.8% 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_5914`
1×	`flip-+_binary64_5849` `add-cube-cbrt_binary64_5910` `flip3-+_binary64_5878` `add-exp-log_binary64_5913` `add-sqr-sqrt_binary64_5897` `*-un-lft-identity_binary64_5875` `add-cbrt-cube_binary64_5911` `sum-log_binary64_5966` `pow1_binary64_5936` `+-commutative_binary64_5805`

Counts

1 → 11

Calls

2 calls:

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

series84.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

84.0ms

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

Compiler

Compiled 174 to 180 computations (-3.4% saved)

simplify82.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (74.0ms)

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

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

20.1b	(/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) (.f64 y y)))
19.6b	(/.f64 (pow.f64 y 4) (-.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 (.f64 x x) (.f64 y y))
19.6b	(/.f64 (pow.f64 y 4) (-.f64 (.f64 x x) (.f64 y y)))
20.1b	(/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) (.f64 y y)))

rewrite40.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`times-frac_binary64_5881`
40×	`add-cube-cbrt_binary64_5910` `add-sqr-sqrt_binary64_5897` `*-un-lft-identity_binary64_5875`
30×	`unpow-prod-down_binary64_5954`
18×	`difference-of-squares_binary64_5844`
14×	`add-exp-log_binary64_5913` `associate-/l*_binary64_5820`
10×	`sqr-pow_binary64_5847`
8×	`associate-/r*_binary64_5819` `add-cbrt-cube_binary64_5911` `add-log-exp_binary64_5914`
6×	`div-exp_binary64_5926`
4×	`associate-/r/_binary64_5821` `pow1_binary64_5936` `flip3--_binary64_5879` `flip--_binary64_5850`
2×	`cbrt-undiv_binary64_5909` `div-inv_binary64_5872` `diff-log_binary64_5967` `sub-neg_binary64_5868` `cancel-sign-sub-inv_binary64_5841` `frac-2neg_binary64_5886` `pow-exp_binary64_5943` `clear-num_binary64_5874` `pow-to-exp_binary64_5944`

Counts

4 → 136

Calls

8 calls:

10.0ms	(/.f64 (pow.f64 y 4) (-.f64 (.f64 x x) (.f64 y y)))
7.0ms	(/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) (.f64 y y)))
4.0ms	(-.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))

series475.0ms (0.9%)

Counts

4 → 54

Calls

4 calls:

155.0ms	(/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) (.f64 y y)))
119.0ms	(/.f64 (pow.f64 y 4) (-.f64 (.f64 x x) (.f64 y y)))
106.0ms	(-.f64 (.f64 x x) (.f64 y y))
94.0ms	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 1803 to 1344 computations (25.5% saved)

simplify98.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4941	3894
1	4941	3894

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(exp.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (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	(exp.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
2.8b	(log.f64 (exp.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))))
5.9b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
5.9b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite19.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_5897`
7×	`add-cube-cbrt_binary64_5910` `*-un-lft-identity_binary64_5875` `pow1_binary64_5936` `add-log-exp_binary64_5914`
6×	`sqrt-prod_binary64_5891`
4×	`add-exp-log_binary64_5913` `sqrt-div_binary64_5892` `add-cbrt-cube_binary64_5911`
3×	`log-prod_binary64_5961` `log-pow_binary64_5964`
2×	`flip-+_binary64_5849` `flip3-+_binary64_5878` `exp-to-pow_binary64_5937` `pow1/2_binary64_5955` `sqrt-pow1_binary64_5893` `rem-sqrt-square_binary64_5888` `exp-prod_binary64_5927`
1×	`rem-exp-log_binary64_5915` `rem-log-exp_binary64_5916`

Counts

4 → 54

Calls

8 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(exp.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
2.0ms	(log.f64 (exp.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))))
0.0ms	(+.f64 (.f64 x x) (.f64 y y))

series390.0ms (0.7%)

Counts

4 → 31

Calls

4 calls:

251.0ms	(log.f64 (exp.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))))
54.0ms	(exp.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
44.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
41.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 770 to 651 computations (15.5% saved)

simplify90.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4919	1056
1	4919	1056

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

2.4b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))))
0.9b	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
0.9b	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.9b	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
2.4b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))))
21.5b	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))
21.5b	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))

rewrite69.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

134×	`add-sqr-sqrt_binary64_5897`
98×	`sqrt-prod_binary64_5891`
90×	`difference-of-squares_binary64_5844`
68×	`times-frac_binary64_5881` `*-un-lft-identity_binary64_5875`
67×	`unpow-prod-down_binary64_5954`
49×	`sqr-pow_binary64_5847`
36×	`add-cube-cbrt_binary64_5910`
17×	`associate-/r*_binary64_5819`
16×	`distribute-lft-out--_binary64_5827`
7×	`cancel-sign-sub-inv_binary64_5841`
6×	`add-exp-log_binary64_5913` `sqrt-div_binary64_5892` `add-cbrt-cube_binary64_5911` `pow1_binary64_5936` `add-log-exp_binary64_5914`
5×	`flip3--_binary64_5879` `flip--_binary64_5850`
4×	`associate-/l*_binary64_5820`
2×	`associate-/r/_binary64_5821` `associate-/l/_binary64_5822` `pow1/2_binary64_5955` `sqrt-pow1_binary64_5893` `rem-sqrt-square_binary64_5888`
1×	`cbrt-undiv_binary64_5909` `div-sub_binary64_5880` `div-inv_binary64_5872` `diff-log_binary64_5967` `sub-neg_binary64_5868` `frac-2neg_binary64_5886` `div-exp_binary64_5926` `clear-num_binary64_5874`

Counts

4 → 187

Calls

8 calls:

18.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))))
8.0ms	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
8.0ms	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))
8.0ms	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))
0.0ms	(-.f64 (.f64 x x) (.f64 y y))

series328.0ms (0.6%)

Counts

4 → 27

Calls

4 calls:

110.0ms	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
78.0ms	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))
70.0ms	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))
69.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4))))

Compiler

Compiled 1210 to 966 computations (20.2% saved)

simplify114.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4959	5757
1	4959	5757

prune9.0s (16.8%)

Pruning

251 alts after pruning (241 fresh and 10 done)

	Pruned	Kept	Total
New	355	157	512
Fresh	2	84	86
Picked	0	0	0
Done	1	10	11
Total	358	251	609

Error

0.0b

Counts

609 → 251

Compiler

Compiled 16386 to 8255 computations (49.6% saved)

localize8.0ms (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_5914`
1×	`flip-+_binary64_5849` `add-cube-cbrt_binary64_5910` `flip3-+_binary64_5878` `add-exp-log_binary64_5913` `add-sqr-sqrt_binary64_5897` `*-un-lft-identity_binary64_5875` `add-cbrt-cube_binary64_5911` `sum-log_binary64_5966` `pow1_binary64_5936` `+-commutative_binary64_5805`

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 (0.2%)

Counts

1 → 12

Calls

1 calls:

87.0ms

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

Compiler

Compiled 210 to 216 computations (-2.9% saved)

simplify84.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (76.0ms)

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

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

20.1b	(/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) (.f64 y y)))
19.6b	(/.f64 (pow.f64 y 4) (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 1))
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 (.f64 x x) (.f64 y y))
19.6b	(/.f64 (pow.f64 y 4) (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 1))
20.1b	(/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) (.f64 y y)))

rewrite45.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_5881`
74×	`unpow-prod-down_binary64_5954`
56×	`add-cube-cbrt_binary64_5910` `add-sqr-sqrt_binary64_5897` `*-un-lft-identity_binary64_5875`
22×	`sqr-pow_binary64_5847`
21×	`add-exp-log_binary64_5913`
18×	`difference-of-squares_binary64_5844`
14×	`associate-/l*_binary64_5820`
12×	`associate-/r*_binary64_5819` `div-exp_binary64_5926`
8×	`add-cbrt-cube_binary64_5911` `add-log-exp_binary64_5914`
7×	`pow-exp_binary64_5943` `pow-to-exp_binary64_5944`
4×	`pow1_binary64_5936`
3×	`flip3--_binary64_5879` `flip--_binary64_5850`
2×	`cbrt-undiv_binary64_5909` `associate-/r/_binary64_5821` `div-inv_binary64_5872` `diff-log_binary64_5967` `sub-neg_binary64_5868` `cancel-sign-sub-inv_binary64_5841` `frac-2neg_binary64_5886` `clear-num_binary64_5874`

Counts

4 → 172

Calls

8 calls:

9.0ms	(/.f64 (pow.f64 y 4) (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 1))
7.0ms	(/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) (.f64 y y)))
4.0ms	(-.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))

series497.0ms (0.9%)

Counts

4 → 54

Calls

4 calls:

162.0ms	(/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) (.f64 y y)))
124.0ms	(/.f64 (pow.f64 y 4) (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 1))
107.0ms	(-.f64 (.f64 x x) (.f64 y y))
104.0ms	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 1917 to 1458 computations (23.9% saved)

simplify97.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5049	4806

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

8.4b	(/.f64 (sqrt.f64 (pow.f64 x 4)) (-.f64 (.f64 x x) (.f64 y y)))
0.1b	(.f64 (sqrt.f64 (pow.f64 x 4)) (/.f64 (sqrt.f64 (pow.f64 x 4)) (-.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))
8.4b	(/.f64 (sqrt.f64 (pow.f64 x 4)) (-.f64 (.f64 x x) (.f64 y y)))
17.7b	(sqrt.f64 (pow.f64 x 4))
17.7b	(sqrt.f64 (pow.f64 x 4))
19.6b	(/.f64 (pow.f64 y 4) (-.f64 (.f64 x x) (.f64 y y)))

rewrite44.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`times-frac_binary64_5881`
56×	`add-sqr-sqrt_binary64_5897`
52×	`add-cube-cbrt_binary64_5910` `*-un-lft-identity_binary64_5875`
49×	`sqrt-prod_binary64_5891`
38×	`unpow-prod-down_binary64_5954`
19×	`difference-of-squares_binary64_5844`
17×	`associate-/l*_binary64_5820`
14×	`sqr-pow_binary64_5847`
11×	`add-exp-log_binary64_5913`
8×	`associate-/r*_binary64_5819` `add-cbrt-cube_binary64_5911`
6×	`rem-sqrt-square_binary64_5888`
4×	`associate-/r/_binary64_5821` `div-exp_binary64_5926` `pow1_binary64_5936` `add-log-exp_binary64_5914`
2×	`cbrt-undiv_binary64_5909` `div-inv_binary64_5872` `pow1/2_binary64_5955` `frac-2neg_binary64_5886` `sqrt-pow1_binary64_5893` `flip3--_binary64_5879` `clear-num_binary64_5874` `flip--_binary64_5850`
1×	`pow-exp_binary64_5943` `pow-to-exp_binary64_5944`

Counts

4 → 161

Calls

8 calls:

8.0ms	(/.f64 (sqrt.f64 (pow.f64 x 4)) (-.f64 (.f64 x x) (.f64 y y)))
7.0ms	(/.f64 (pow.f64 y 4) (-.f64 (.f64 x x) (.f64 y y)))
2.0ms	(sqrt.f64 (pow.f64 x 4))
2.0ms	(sqrt.f64 (pow.f64 x 4))
0.0ms	(-.f64 (.f64 x x) (.f64 y y))

series300.0ms (0.6%)

Counts

4 → 33

Calls

4 calls:

131.0ms	(/.f64 (pow.f64 y 4) (-.f64 (.f64 x x) (.f64 y y)))
120.0ms	(/.f64 (sqrt.f64 (pow.f64 x 4)) (-.f64 (.f64 x x) (.f64 y y)))
24.0ms	(sqrt.f64 (pow.f64 x 4))
24.0ms	(sqrt.f64 (pow.f64 x 4))

Compiler

Compiled 1464 to 1053 computations (28.1% saved)

simplify86.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5291	4183

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (+.f64 (.f64 x x) (sqrt.f64 (pow.f64 y 4))) (-.f64 (*.f64 x x) (sqrt.f64 (pow.f64 y 4))))
0.0b	(+.f64 (*.f64 x x) (sqrt.f64 (pow.f64 y 4)))
0.0b	(-.f64 (*.f64 x x) (sqrt.f64 (pow.f64 y 4)))
0.0b	(-.f64 (.f64 x x) (.f64 y y))
19.6b	(sqrt.f64 (pow.f64 y 4))
19.6b	(sqrt.f64 (pow.f64 y 4))
21.5b	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))
21.5b	(sqrt.f64 (.f64 (+.f64 (.f64 x x) (sqrt.f64 (pow.f64 y 4))) (-.f64 (*.f64 x x) (sqrt.f64 (pow.f64 y 4)))))

rewrite37.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`sqrt-prod_binary64_5891`
26×	`add-sqr-sqrt_binary64_5897`
16×	`unpow-prod-down_binary64_5954`
13×	`*-un-lft-identity_binary64_5875`
10×	`sqrt-div_binary64_5892` `sqr-pow_binary64_5847`
9×	`add-cube-cbrt_binary64_5910` `difference-of-squares_binary64_5844`
8×	`pow1_binary64_5936`
7×	`rem-sqrt-square_binary64_5888`
5×	`sqrt-pow1_binary64_5893`
4×	`add-exp-log_binary64_5913` `pow1/2_binary64_5955` `frac-times_binary64_5885` `add-cbrt-cube_binary64_5911` `flip3--_binary64_5879` `add-log-exp_binary64_5914` `flip--_binary64_5850`
3×	`flip-+_binary64_5849` `flip3-+_binary64_5878`
2×	`distribute-lft-out--_binary64_5827` `associate-l/_binary64_5818` `associate-r/_binary64_5817`
1×	`pow-prod-down_binary64_5946`

Counts

4 → 83

Calls

8 calls:

14.0ms	(sqrt.f64 (.f64 (+.f64 (.f64 x x) (sqrt.f64 (pow.f64 y 4))) (-.f64 (*.f64 x x) (sqrt.f64 (pow.f64 y 4)))))
8.0ms	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))
2.0ms	(sqrt.f64 (pow.f64 y 4))
2.0ms	(sqrt.f64 (pow.f64 y 4))
0.0ms	(-.f64 (.f64 x x) (.f64 y y))

series233.0ms (0.4%)

Counts

4 → 18

Calls

4 calls:

106.0ms	(sqrt.f64 (.f64 (+.f64 (.f64 x x) (sqrt.f64 (pow.f64 y 4))) (-.f64 (*.f64 x x) (sqrt.f64 (pow.f64 y 4)))))
78.0ms	(sqrt.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)))
25.0ms	(sqrt.f64 (pow.f64 y 4))
23.0ms	(sqrt.f64 (pow.f64 y 4))

Compiler

Compiled 1179 to 819 computations (30.5% saved)

simplify82.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5074	1459

prune16.9s (31.8%)

Pruning

371 alts after pruning (358 fresh and 13 done)

	Pruned	Kept	Total
New	395	149	544
Fresh	27	209	236
Picked	0	0	0
Done	2	13	15
Total	424	371	795

Error

0.0b

Counts

795 → 371

Compiler

Compiled 11503 to 5076 computations (55.9% saved)

simplify438.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5017	32723

regimes6.3s (11.8%)

Compiler: Compiled 84275 to 51405 computations (39% saved)

bsearch0.0ms (0%)

regimes116.0ms (0.2%)

Compiler: Compiled 52 to 80 computations (-53.8% saved)

bsearch57.0ms (0.1%)

Steps

Iters	Range		Point
5	5.11254154434744e-74	1.1526948571501244e-73	6.486829903925052e-74
7	1.0032141931006373e-89	4.1401836524300407e-88	3.24388670869413e-88
7	3.430522550046695e-120	2.010535086696515e-118	3.787932310089533e-120
6	2.0130258833352778e-163	1.211854441126889e-162	2.910329577898235e-163
9	1.004553520507413e-217	9.475371125872406e-213	1.774386743510888e-214
8	1.247538675445245e-249	2.0890077320457285e-246	1.2709100034154791e-249
6	9.776436296215694e-272	5.503459884629919e-271	3.5865650814659467e-271

Compiler

Compiled 3 to 3 computations (0% saved)

regimes24.0ms (0%)

Compiler: Compiled 28 to 50 computations (-78.6% saved)

bsearch0.0ms (0%)

regimes17.0ms (0%)

Accuracy

Total 0.0b remaining (84.3%)

Threshold costs 0.0b (84.3%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch4.0ms (0%)

Compiler: Compiled 78 to 39 computations (50% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	77	93
1	77	93

end0.0ms (0%)

sample13.6s (25.5%)

Algorithm

1×

intervals

Results

169.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 17046 to 10409 computations (38.9% saved)

Pareto

0.6730899101027639