Details

analyze59.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 23 to 18 computations (21.7% saved)

sample35.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
6.0ms	259×	pre	80	true
0.0ms	3×	body	80	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify234.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5014	19

prune4.0ms (0.1%)

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: 0.1b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)

rewrite259.0ms (7.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 76

Calls

3 calls:

224.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
20.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
12.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

series163.0ms (4.6%)

Counts

3 → 9

Calls

3 calls:

79.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
52.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
32.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify105.0ms (3%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5426	1714

prune117.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	6	86

Merged error: 0.0b

Counts

86 → 6

Compiler

Compiled 1849 to 1300 computations (29.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 m (/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m)))
0.0b	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.2b	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))

rewrite67.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`add-log-exp_binary64`
16×	`associate-/r*_binary64`
8×	`cbrt-undiv_binary64` `div-exp_binary64`
7×	`distribute-lft-out_binary64` `sum-log_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/l/_binary64` `pow1_binary64` `associate-*r/_binary64` `frac-add_binary64` `div-inv_binary64` `insert-posit16`
3×	`flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64`
1×	`sub-neg_binary64` `associate-+l+_binary64` `distribute-rgt-out_binary64` `distribute-rgt1-in_binary64` `associate-+l-_binary64` `associate-+r+_binary64`

Counts

4 → 114

Calls

4 calls:

26.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
14.0ms	(+.f64 m (/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m)))
12.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series211.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
54.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
53.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
44.0ms	(+.f64 m (/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m)))

simplify89.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4977	2945
1	4977	2945

prune164.0ms (4.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	127	5	132

Merged error: 0.0b

Counts

132 → 5

Compiler

Compiled 3613 to 2026 computations (43.9% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 v m))
0.1b	(sqrt.f64 (/.f64 v m))
0.2b	(/.f64 m (sqrt.f64 (/.f64 v m)))
0.3b	(/.f64 (*.f64 (/.f64 m (sqrt.f64 (/.f64 v m))) (+.f64 m -1)) (sqrt.f64 (/.f64 v m)))

rewrite51.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
104×	`sqrt-prod_binary64`
89×	`add-sqr-sqrt_binary64`
83×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
32×	`associate-/r*_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`div-inv_binary64`
6×	`pow1_binary64`
5×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `rem-sqrt-square_binary64` `associate-/l*_binary64` `insert-posit16` `sqrt-div_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `flip-+_binary64` `frac-times_binary64`
1×	`associate-*l/_binary64`

Counts

4 → 189

Calls

4 calls:

21.0ms	(/.f64 (*.f64 (/.f64 m (sqrt.f64 (/.f64 v m))) (+.f64 m -1)) (sqrt.f64 (/.f64 v m)))
8.0ms	(/.f64 m (sqrt.f64 (/.f64 v m)))
4.0ms	(sqrt.f64 (/.f64 v m))
3.0ms	(sqrt.f64 (/.f64 v m))

series343.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(/.f64 m (sqrt.f64 (/.f64 v m)))
84.0ms	(sqrt.f64 (/.f64 v m))
81.0ms	(sqrt.f64 (/.f64 v m))
55.0ms	(/.f64 (*.f64 (/.f64 m (sqrt.f64 (/.f64 v m))) (+.f64 m -1)) (sqrt.f64 (/.f64 v m)))

simplify90.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5072	3734

prune273.0ms (7.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	201	5	206

Merged error: 0.0b

Counts

206 → 5

Compiler

Compiled 6734 to 2933 computations (56.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v)) 1)
0.1b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))
0.3b	(.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v))

rewrite53.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
19×	`associate-r_binary64`
17×	`add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
13×	`prod-exp_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`flip3--_binary64` `times-frac_binary64` `flip--_binary64`
7×	`cbrt-unprod_binary64` `associate-*r/_binary64`
6×	`frac-times_binary64`
5×	`add-log-exp_binary64`
4×	`pow-prod-down_binary64` `associate-l_binary64` `div-exp_binary64` `associate-*l/_binary64`
3×	`sub-neg_binary64` `insert-posit16`
2×	`1-exp_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`

Counts

3 → 87

Calls

3 calls:

21.0ms	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))
14.0ms	(-.f64 (.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v)) 1)
14.0ms	(.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v))

series148.0ms (4.2%)

Counts

3 → 9

Calls

3 calls:

63.0ms	(.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v))
52.0ms	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))
33.0ms	(-.f64 (.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v)) 1)

simplify145.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4996	1783
1	4996	1783

prune98.0ms (2.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	96	5	101

Merged error: 0.0b

Counts

101 → 5

Compiler

Compiled 1930 to 1370 computations (29% saved)

regimes45.0ms (1.3%)

Compiler: Compiled 333 to 258 computations (22.5% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	31
1	32	31

end0.0ms (0%)

sample751.0ms (21.1%)

Algorithm

1×

intervals

Results

276.0ms	8000×	body	80	valid
171.0ms	8054×	pre	80	true
2.0ms	54×	body	80	invalid

Compiler

Compiled 145 to 111 computations (23.4% saved)

Details

analyze59.0ms (1.7%)

sample35.0ms (1%)

simplify234.0ms (6.6%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite259.0ms (7.3%)

series163.0ms (4.6%)

simplify105.0ms (3%)

prune117.0ms (3.3%)

localize13.0ms (0.4%)

rewrite67.0ms (1.9%)

series211.0ms (5.9%)

simplify89.0ms (2.5%)

prune164.0ms (4.6%)

localize15.0ms (0.4%)

rewrite51.0ms (1.4%)

series343.0ms (9.6%)

simplify90.0ms (2.5%)

prune273.0ms (7.7%)

localize8.0ms (0.2%)

rewrite53.0ms (1.5%)

series148.0ms (4.2%)

simplify145.0ms (4.1%)

prune98.0ms (2.8%)

regimes45.0ms (1.3%)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

end0.0ms (0%)

sample751.0ms (21.1%)

Profiling