Details

analyze77.0ms (2.1%)

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)

sample22.0ms (0.6%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid
0.0ms	3×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify68.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	1030	21
1	1030	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)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite70.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
26×	`associate-l_binary64`
24×	`add-cube-cbrt_binary64`
19×	`add-exp-log_binary64`
15×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
8×	`associate-*r/_binary64` `sqrt-prod_binary64`
6×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64` `sqrt-div_binary64`
5×	`prod-exp_binary64`
4×	`pow-prod-down_binary64` `associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `div-exp_binary64` `pow-flip_binary64` `frac-times_binary64`
3×	`flip3-+_binary64` `cbrt-unprod_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `associate-l/_binary64`
2×	`pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64`

Counts

4 → 126

Calls

4 calls:

20.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
14.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
12.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
9.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

series311.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
90.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
49.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
34.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

simplify60.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4986	2820
1	4986	2820

prune240.0ms (6.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	131	7	138
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	133	7	140

Merged error: 0.0b

Counts

140 → 7

Compiler

Compiled 3734 to 3062 computations (18% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 9 (-.f64 a (/.f64 1 3)))
0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
0.1b	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)
0.2b	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)

rewrite55.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64` `add-exp-log_binary64`
16×	`associate-l_binary64`
14×	`associate-r_binary64`
11×	`pow1_binary64` `add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`prod-exp_binary64`
6×	`difference-of-squares_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `flip--_binary64` `frac-times_binary64` `pow-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unpow-prod-down_binary64` `div-inv_binary64` `associate-*l/_binary64`

Counts

4 → 100

Calls

4 calls:

16.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
11.0ms	(*.f64 9 (-.f64 a (/.f64 1 3)))
10.0ms	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)
6.0ms	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)

series302.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)
77.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
53.0ms	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)
40.0ms	(*.f64 9 (-.f64 a (/.f64 1 3)))

simplify52.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5032	2166

prune163.0ms (4.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	112	7	119

Merged error: 0.0b

Counts

119 → 7

Compiler

Compiled 2905 to 2378 computations (18.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite80.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`add-sqr-sqrt_binary64`
90×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64`
60×	`sqrt-prod_binary64`
52×	`add-cube-cbrt_binary64`
33×	`associate-r_binary64`
30×	`add-exp-log_binary64` `associate-l_binary64`
20×	`add-cbrt-cube_binary64`
16×	`unswap-sqr_binary64`
11×	`difference-of-squares_binary64`
10×	`distribute-lft-out--_binary64`
9×	`pow1_binary64` `prod-exp_binary64` `div-exp_binary64`
8×	`associate-/r*_binary64`
6×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
5×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `frac-times_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `div-inv_binary64`
3×	`flip3-+_binary64` `associate-r/_binary64` `associate-/l_binary64` `flip-+_binary64` `associate-*l/_binary64`
2×	`pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 190

Calls

4 calls:

30.0ms	(*.f64 (/.f64 1 (sqrt.f64 9)) (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))
14.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 9)) (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))
8.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(sqrt.f64 (-.f64 a 1/3))

series364.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(*.f64 (/.f64 1 (sqrt.f64 9)) (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))
104.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
89.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 9)) (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))
27.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify75.0ms (2%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5526	4045

prune322.0ms (8.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	202	7	209

Merged error: 0.0b

Counts

209 → 7

Compiler

Compiled 5357 to 4260 computations (20.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 9 (-.f64 a 1/3))
0.2b	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))
0.3b	(/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))
6.8b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3)))))

rewrite52.0ms (1.4%)

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`
23×	`associate-r_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
9×	`associate-*r/_binary64`
8×	`associate-l_binary64` `sqrt-prod_binary64`
6×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 113

Calls

4 calls:

20.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3)))))
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))
7.0ms	(*.f64 9 (-.f64 a 1/3))
5.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))

series327.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))
114.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3)))))
41.0ms	(*.f64 9 (-.f64 a 1/3))
34.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))

simplify53.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4992	2385
1	4992	2385

prune165.0ms (4.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	3	1	4
Picked	0	1	1
Done	1	1	2
Total	126	6	132

Merged error: 0.0b

Counts

132 → 6

Compiler

Compiled 2975 to 2193 computations (26.3% saved)

regimes33.0ms (0.9%)

Compiler: Compiled 254 to 230 computations (9.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	24
1	23	24

end0.0ms (0%)

sample795.0ms (21.3%)

Algorithm

1×

intervals

Results

454.0ms	8000×	body	128	valid
15.0ms	261×	body	128	invalid
14.0ms	267×	body	128	nan

Compiler

Compiled 162 to 147 computations (9.3% saved)

Details

analyze77.0ms (2.1%)

sample22.0ms (0.6%)

simplify68.0ms (1.8%)

prune4.0ms (0.1%)

localize11.0ms (0.3%)

rewrite70.0ms (1.9%)

series311.0ms (8.3%)

simplify60.0ms (1.6%)

prune240.0ms (6.4%)

localize14.0ms (0.4%)

rewrite55.0ms (1.5%)

series302.0ms (8.1%)

simplify52.0ms (1.4%)

prune163.0ms (4.4%)

localize13.0ms (0.3%)

rewrite80.0ms (2.1%)

series364.0ms (9.7%)

simplify75.0ms (2%)

prune322.0ms (8.6%)

localize9.0ms (0.2%)

rewrite52.0ms (1.4%)

series327.0ms (8.7%)

simplify53.0ms (1.4%)

prune165.0ms (4.4%)

regimes33.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample795.0ms (21.3%)

Profiling