Details

analyze235.0ms (6%)

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
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample16.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify239.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	756	10
1	756	10

prune6.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (+.f64 f n) (-.f64 n f))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out_binary64`
5×	`associate-/r*_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
4×	`associate-/l*_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`

Counts

1 → 45

Calls

1 calls:

10.0ms

(/.f64 (+.f64 f n) (-.f64 n f))

series103.0ms (2.6%)

Counts

1 → 3

Calls

1 calls:

102.0ms

(/.f64 (+.f64 f n) (-.f64 n f))

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4962	802
1	4962	802

prune40.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Merged error: 0.0b

Counts

49 → 4

Compiler

Compiled 719 to 169 computations (76.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
0.0b	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)
0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))

rewrite56.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

150×	`*-un-lft-identity_binary64`
100×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
58×	`cbrt-prod_binary64`
56×	`add-cube-cbrt_binary64`
52×	`unpow-prod-down_binary64` `cube-prod_binary64`
26×	`distribute-lft-out_binary64`
21×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`associate-/r/_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r*_binary64` `flip3--_binary64` `div-inv_binary64` `flip--_binary64`
4×	`pow1_binary64` `associate-/l*_binary64`
3×	`pow-unpow_binary64` `add-log-exp_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `flip3-+_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

3 → 185

Calls

3 calls:

13.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
12.0ms	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)
11.0ms	(/.f64 (+.f64 f n) (-.f64 n f))

series292.0ms (7.5%)

Counts

3 → 9

Calls

3 calls:

122.0ms	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)
93.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
77.0ms	(/.f64 (+.f64 f n) (-.f64 n f))

simplify70.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5450	3740

prune140.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	194	4	198

Merged error: 0.0b

Counts

198 → 4

Compiler

Compiled 3160 to 1011 computations (68% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))
0.6b	(cbrt.f64 (-.f64 n f))
0.6b	(cbrt.f64 (-.f64 n f))
0.6b	(cbrt.f64 (-.f64 n f))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`cbrt-prod_binary64`
37×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
18×	`cbrt-div_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`
10×	`swap-sqr_binary64`
9×	`flip3--_binary64` `pow1/3_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
8×	`associate-r_binary64` `associate-l_binary64`
7×	`difference-of-squares_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 101

Calls

4 calls:

12.0ms	(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))
4.0ms	(cbrt.f64 (-.f64 n f))
3.0ms	(cbrt.f64 (-.f64 n f))
3.0ms	(cbrt.f64 (-.f64 n f))

series880.0ms (22.6%)

Counts

4 → 12

Calls

4 calls:

237.0ms	(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))
219.0ms	(cbrt.f64 (-.f64 n f))
215.0ms	(cbrt.f64 (-.f64 n f))
209.0ms	(cbrt.f64 (-.f64 n f))

simplify56.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4966	1654
1	4966	1654

prune105.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	112	5	117

Merged error: 0b

Counts

117 → 5

Compiler

Compiled 2938 to 836 computations (71.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f)))
0.0b	(*.f64 (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
0.0b	(/.f64 (+.f64 f n) (-.f64 n f))

rewrite107.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

316×	`*-un-lft-identity_binary64`
191×	`times-frac_binary64`
188×	`sqrt-prod_binary64`
187×	`add-sqr-sqrt_binary64`
88×	`add-cube-cbrt_binary64`
55×	`distribute-lft-out_binary64`
53×	`swap-sqr_binary64`
46×	`distribute-lft-out--_binary64`
34×	`difference-of-squares_binary64`
29×	`associate-r_binary64` `associate-l_binary64`
20×	`pow1_binary64`
14×	`associate-/r/_binary64`
10×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1/2_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64`
8×	`associate-/l*_binary64`
7×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64`
5×	`pow-prod-up_binary64` `sqrt-div_binary64`
4×	`associate-/l/_binary64` `add-log-exp_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `associate-r/_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 276

Calls

4 calls:

37.0ms	(*.f64 (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
9.0ms	(sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f)))
9.0ms	(/.f64 (+.f64 f n) (-.f64 n f))
9.0ms	(/.f64 (+.f64 f n) (-.f64 n f))

series605.0ms (15.6%)

Counts

4 → 12

Calls

4 calls:

308.0ms	(sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f)))
137.0ms	(*.f64 (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
87.0ms	(/.f64 (+.f64 f n) (-.f64 n f))
73.0ms	(/.f64 (+.f64 f n) (-.f64 n f))

simplify121.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4914	5414
1	4914	5414

prune192.0ms (4.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	288	5	293

Merged error: 0b

Counts

293 → 5

Compiler

Compiled 6052 to 857 computations (85.8% saved)

regimes29.0ms (0.8%)

Compiler: Compiled 178 to 98 computations (44.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	15
1	20	15

end0.0ms (0%)

sample448.0ms (11.5%)

Algorithm

1×

intervals

Results

205.0ms

8000×

body

128

valid

Compiler

Compiled 106 to 62 computations (41.5% saved)

Details

analyze235.0ms (6%)

sample16.0ms (0.4%)

simplify239.0ms (6.2%)

prune6.0ms (0.2%)

localize6.0ms (0.2%)

rewrite15.0ms (0.4%)

series103.0ms (2.6%)

simplify62.0ms (1.6%)

prune40.0ms (1%)

localize7.0ms (0.2%)

rewrite56.0ms (1.4%)

series292.0ms (7.5%)

simplify70.0ms (1.8%)

prune140.0ms (3.6%)

localize11.0ms (0.3%)

rewrite33.0ms (0.8%)

series880.0ms (22.6%)

simplify56.0ms (1.4%)

prune105.0ms (2.7%)

localize10.0ms (0.2%)

rewrite107.0ms (2.8%)

series605.0ms (15.6%)

simplify121.0ms (3.1%)

prune192.0ms (4.9%)

regimes29.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample448.0ms (11.5%)

Profiling