Details

analyze407.0ms (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)

sample39.0ms (0.7%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
9.0ms	259×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify470.0ms (8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (153.0ms)

Iter	Nodes	Cost
0	5013	19

prune7.0ms (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)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite93.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 83

Calls

3 calls:

37.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
16.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
15.0ms	(*.f64 m (-.f64 1 m))

series327.0ms (5.6%)

Counts

3 → 9

Calls

3 calls:

123.0ms	(*.f64 m (-.f64 1 m))
103.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
100.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify110.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4959	1544
1	4959	1544

prune219.0ms (3.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 0b

Counts

93 → 5

Compiler

Compiled 1881 to 1309 computations (30.4% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite163.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

171×	`times-frac_binary64`
155×	`add-sqr-sqrt_binary64`
137×	`*-un-lft-identity_binary64`
81×	`add-cube-cbrt_binary64`
40×	`difference-of-squares_binary64`
30×	`associate-/r*_binary64`
18×	`distribute-lft-out--_binary64`
13×	`associate-l_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
6×	`associate-r_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`add-log-exp_binary64` `difference-of-sqr-1_binary64`
2×	`sub-neg_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

3 → 196

Calls

3 calls:

79.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
26.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
12.0ms	(/.f64 v (-.f64 1 m))

series278.0ms (4.7%)

Counts

3 → 9

Calls

3 calls:

99.0ms	(/.f64 v (-.f64 1 m))
96.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
82.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))

simplify205.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4959	4291
1	4959	4291

prune431.0ms (7.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	205	5	210

Merged error: 0b

Counts

210 → 5

Compiler

Compiled 4624 to 2875 computations (37.8% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite122.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64` `add-log-exp_binary64`
8×	`cbrt-undiv_binary64` `div-exp_binary64`
7×	`distribute-lft-out_binary64`
6×	`pow1_binary64` `associate-*r/_binary64` `sum-log_binary64`
5×	`flip3-+_binary64` `associate-r_binary64` `flip-+_binary64`
4×	`associate-/l/_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `prod-exp_binary64` `div-inv_binary64`
3×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
2×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `associate-+l-_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-sqr--1_binary64` `+-commutative_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

4 → 120

Calls

4 calls:

45.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
19.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
18.0ms	(*.f64 m (+.f64 m -1))
14.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series390.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(*.f64 m (+.f64 m -1))
99.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
96.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
92.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))

simplify130.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4958	2717
1	4958	2717

prune284.0ms (4.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	132	5	137

Merged error: 0b

Counts

137 → 5

Compiler

Compiled 3700 to 2093 computations (43.4% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 m (-.f64 1 m))
0.0b	(.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))

rewrite92.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 98

Calls

3 calls:

36.0ms	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))
23.0ms	(.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v))
14.0ms	(*.f64 m (-.f64 1 m))

series276.0ms (4.7%)

Counts

3 → 9

Calls

3 calls:

109.0ms	(*.f64 m (-.f64 1 m))
87.0ms	(.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v))
80.0ms	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))

simplify109.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5136	1716

prune194.0ms (3.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	107	5	112

Merged error: 0b

Counts

112 → 5

Compiler

Compiled 2140 to 1522 computations (28.9% saved)

regimes58.0ms (1%)

Compiler: Compiled 176 to 148 computations (15.9% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

end0.0ms (0%)

sample1.4s (23.4%)

Algorithm

1×

intervals

Results

539.0ms	8000×	body	128	valid
299.0ms	8053×	pre	128	true
4.0ms	53×	body	128	invalid

Compiler

Compiled 122 to 101 computations (17.2% saved)

Details

analyze407.0ms (7%)

sample39.0ms (0.7%)

simplify470.0ms (8%)

prune7.0ms (0.1%)

localize17.0ms (0.3%)

rewrite93.0ms (1.6%)

series327.0ms (5.6%)

simplify110.0ms (1.9%)

prune219.0ms (3.7%)

localize14.0ms (0.2%)

rewrite163.0ms (2.8%)

series278.0ms (4.7%)

simplify205.0ms (3.5%)

prune431.0ms (7.4%)

localize26.0ms (0.5%)

rewrite122.0ms (2.1%)

series390.0ms (6.7%)

simplify130.0ms (2.2%)

prune284.0ms (4.9%)

localize15.0ms (0.3%)

rewrite92.0ms (1.6%)

series276.0ms (4.7%)

simplify109.0ms (1.9%)

prune194.0ms (3.3%)

regimes58.0ms (1%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.4s (23.4%)

Profiling