Details

analyze78.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

Compiler

Compiled 21 to 20 computations (4.8% saved)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	80	valid
1.0ms	12×	body	80	nan
0.0ms	7×	body	80	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify112.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	1031	21
1	1031	21

prune4.0ms (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

Merged error: 0.1b

Counts

2 → 2

Compiler

Compiled 48 to 45 computations (6.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

rewrite44.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
8×	`associate-*l/_binary64`
7×	`associate-r_binary64`
6×	`flip3--_binary64` `flip--_binary64`
5×	`sqrt-prod_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `insert-posit16` `frac-times_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 103

Calls

4 calls:

17.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series298.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
78.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
45.0ms	(*.f64 (-.f64 a 1/3) 9)
37.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify79.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5378	2293

prune175.0ms (3.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	107	8	115
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Merged error: 0.0b

Counts

117 → 8

Compiler

Compiled 2656 to 2073 computations (22% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
4.8b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite48.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
10×	`associate-l_binary64` `associate-*l/_binary64`
8×	`sqrt-prod_binary64`
6×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
2×	`cbrt-undiv_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 115

Calls

4 calls:

19.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series330.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
118.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
43.0ms	(*.f64 (-.f64 a 1/3) 9)
37.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify121.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4939	2458
1	4939	2458

prune177.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	129	6	135

Merged error: 0b

Counts

135 → 6

Compiler

Compiled 3124 to 2323 computations (25.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9)))
0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
0.2b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.3b	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))

rewrite164.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

372×	`times-frac_binary64`
246×	`*-un-lft-identity_binary64`
244×	`add-sqr-sqrt_binary64`
218×	`sqrt-prod_binary64`
190×	`add-cube-cbrt_binary64`
33×	`associate-/l*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
16×	`associate-/r/_binary64` `sqrt-div_binary64`
14×	`associate-/r*_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`flip3--_binary64` `flip--_binary64`
9×	`div-inv_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
5×	`associate-l_binary64`
4×	`flip3-+_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `insert-posit16` `flip-+_binary64` `frac-times_binary64`
2×	`distribute-lft-out_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 327

Calls

4 calls:

61.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
53.0ms	(+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9)))
17.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
8.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

series430.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
111.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
91.0ms	(+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9)))
90.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))

simplify187.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4984	9123
1	4984	9123

prune644.0ms (14.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	338	1	339
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	339	6	345

Merged error: 0b

Counts

345 → 6

Compiler

Compiled 8690 to 6544 computations (24.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b

(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))

0.4b

(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))

0.5b

(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

rewrite72.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`add-sqr-sqrt_binary64`
112×	`*-un-lft-identity_binary64`
110×	`times-frac_binary64`
70×	`sqrt-prod_binary64`
56×	`add-cube-cbrt_binary64`
46×	`associate-l_binary64`
28×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
22×	`associate-r_binary64`
17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`unswap-sqr_binary64`
8×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64`
6×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
5×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-/r/_binary64` `prod-exp_binary64` `sqrt-div_binary64`
3×	`associate-r/_binary64` `div-inv_binary64` `insert-posit16` `frac-times_binary64` `associate-l/_binary64`
2×	`associate-/l/_binary64` `pow-div_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

3 → 192

Calls

3 calls:

39.0ms

(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))

11.0ms

(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

9.0ms

(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))

series239.0ms (5.3%)

Counts

3 → 9

Calls

3 calls:

112.0ms

(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))

85.0ms

(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))

41.0ms

(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

simplify110.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5708	4276

prune307.0ms (6.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	2	1	3
Picked	0	1	1
Done	1	1	2
Total	202	5	207

Merged error: 0b

Counts

207 → 5

Compiler

Compiled 4808 to 3683 computations (23.4% saved)

regimes27.0ms (0.6%)

Compiler: Compiled 158 to 148 computations (6.3% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	24
1	24	24

end0.0ms (0%)

sample768.0ms (17.1%)

Algorithm

1×

intervals

Results

461.0ms	8000×	body	80	valid
15.0ms	253×	body	80	nan
14.0ms	242×	body	80	invalid

Compiler

Compiled 114 to 106 computations (7% saved)

Details

analyze78.0ms (1.7%)

sample23.0ms (0.5%)

simplify112.0ms (2.5%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite44.0ms (1%)

series298.0ms (6.7%)

simplify79.0ms (1.8%)

prune175.0ms (3.9%)

localize11.0ms (0.3%)

rewrite48.0ms (1.1%)

series330.0ms (7.4%)

simplify121.0ms (2.7%)

prune177.0ms (3.9%)

localize9.0ms (0.2%)

rewrite164.0ms (3.7%)

series430.0ms (9.6%)

simplify187.0ms (4.2%)

prune644.0ms (14.4%)

localize9.0ms (0.2%)

rewrite72.0ms (1.6%)

series239.0ms (5.3%)

simplify110.0ms (2.5%)

prune307.0ms (6.8%)

regimes27.0ms (0.6%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample768.0ms (17.1%)

Profiling