Details

analyze9.0ms (0.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample11.0ms (0.9%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify12.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	15	16
1	15	16

prune3.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize6.0ms (0.5%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(/.f64 1 (-.f64 x 1))

rewrite40.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
8×	`distribute-lft-out_binary64` `difference-of-squares_binary64`
7×	`associate-/r*_binary64`
6×	`add-exp-log_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `difference-of-sqr-1_binary64` `add-cbrt-cube_binary64`
3×	`pow1_binary64` `associate-/l*_binary64`
2×	`associate-/r/_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

2 → 67

Calls

2 calls:

28.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
6.0ms	(/.f64 1 (-.f64 x 1))

series8.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

6.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
2.0ms	(/.f64 1 (-.f64 x 1))

simplify114.0ms (8.9%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4866	1117
1	4866	1117

prune56.0ms (4.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	2	74

Merged error: 0b

Counts

74 → 2

Compiler

Compiled 1277 to 961 computations (24.7% saved)

localize8.0ms (0.6%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.4b	(/.f64 1 (+.f64 -1 (*.f64 x x)))
16.0b	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))

rewrite38.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
15×	`associate-l_binary64`
10×	`add-cbrt-cube_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`pow1_binary64`
5×	`add-log-exp_binary64` `frac-add_binary64`
4×	`associate-r_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`associate-/r_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rec-exp_binary64` `div-inv_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 95

Calls

3 calls:

16.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
13.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
5.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))

series16.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

9.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
4.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))
4.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))

simplify82.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4991	1770
1	4991	1770

prune78.0ms (6.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	104	2	106

Merged error: 0b

Counts

106 → 2

Compiler

Compiled 2300 to 1566 computations (31.9% saved)

localize9.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
0.0b	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
0.0b	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
0.0b	(/.f64 1 (+.f64 -1 x))

rewrite87.0ms (6.7%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`*-un-lft-identity_binary64`
54×	`distribute-lft-out_binary64`
52×	`times-frac_binary64`
24×	`cbrt-prod_binary64`
19×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`unpow-prod-down_binary64` `cube-prod_binary64`
9×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cube-div_binary64` `div-inv_binary64`
4×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
3×	`cbrt-div_binary64` `pow-unpow_binary64` `frac-add_binary64` `associate-/l*_binary64`
2×	`sqr-pow_binary64` `associate-/r/_binary64` `div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `pow-pow_binary64` `clear-num_binary64` `inv-pow_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `rec-exp_binary64` `+-commutative_binary64` `pow-flip_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 129

Calls

4 calls:

26.0ms	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
24.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
23.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
6.0ms	(/.f64 1 (+.f64 -1 x))

series23.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
7.0ms	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
6.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
2.0ms	(/.f64 1 (+.f64 -1 x))

simplify107.0ms (8.3%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4936	2805
1	4936	2805

prune119.0ms (9.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	141	2	143

Merged error: 0b

Counts

143 → 2

Compiler

Compiled 2754 to 2166 computations (21.4% saved)

regimes14.0ms (1.1%)

Compiler: Compiled 33 to 27 computations (18.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	25
1	17	25

end0.0ms (0%)

sample441.0ms (34.4%)

Algorithm

1×

intervals

Results

222.0ms

8000×

body

valid

Compiler

Compiled 60 to 49 computations (18.3% saved)

Details

analyze9.0ms (0.7%)

sample11.0ms (0.9%)

simplify12.0ms (1%)

prune3.0ms (0.2%)

localize6.0ms (0.5%)

rewrite40.0ms (3.1%)

series8.0ms (0.6%)

simplify114.0ms (8.9%)

prune56.0ms (4.4%)

localize8.0ms (0.6%)

rewrite38.0ms (2.9%)

series16.0ms (1.3%)

simplify82.0ms (6.4%)

prune78.0ms (6.1%)

localize9.0ms (0.7%)

rewrite87.0ms (6.7%)

series23.0ms (1.8%)

simplify107.0ms (8.3%)

prune119.0ms (9.3%)

regimes14.0ms (1.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.3%)

end0.0ms (0%)

sample441.0ms (34.4%)

Profiling