Details

analyze53.0ms (1.4%)

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 21 to 16 computations (23.8% saved)

sample23.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	80	valid
6.0ms	257×	pre	80	true
0.0ms	1×	body	80	invalid

Compiler

Compiled 32 to 27 computations (15.6% saved)

simplify321.0ms (8.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (175.0ms)

Iter	Nodes	Cost
0	4945	16
1	4945	16

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: 0.2b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite250.0ms (6.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64` `associate-l_binary64`
9×	`associate-r_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64`
4×	`flip3--_binary64` `associate-*r/_binary64` `insert-posit16` `flip--_binary64`
3×	`associate-/r*_binary64` `sub-neg_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` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 91

Calls

4 calls:

217.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
11.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
8.0ms	(*.f64 m (-.f64 1 m))

series217.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
69.0ms	(*.f64 m (-.f64 1 m))
49.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
28.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify102.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5346	1475

prune118.0ms (3.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 0.0b

Counts

104 → 9

Compiler

Compiled 1882 to 1268 computations (32.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite83.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
55×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
20×	`difference-of-squares_binary64`
18×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
12×	`distribute-rgt-out--_binary64`
10×	`associate-/r_binary64` `associate-l*_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64` `neg-mul-1_binary64`
5×	`associate-/l*_binary64`
4×	`flip3--_binary64` `difference-of-sqr-1_binary64` `insert-posit16` `flip--_binary64`
3×	`associate-r_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `distribute-lft-out--_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 143

Calls

4 calls:

34.0ms	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) m)
27.0ms	(-.f64 (/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v)) 1)
10.0ms	(/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v))
5.0ms	(-.f64 (*.f64 m m) m)

series210.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(-.f64 (*.f64 m m) m)
63.0ms	(/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v))
51.0ms	(.f64 (-.f64 (/.f64 (-.f64 (.f64 m m) m) (neg.f64 v)) 1) m)
32.0ms	(-.f64 (/.f64 (-.f64 (*.f64 m m) m) (neg.f64 v)) 1)

simplify121.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5762	3116

prune136.0ms (3.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	156	8	164

Merged error: 0.0b

Counts

164 → 8

Compiler

Compiled 3187 to 1080 computations (66.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite44.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-l_binary64`
8×	`add-log-exp_binary64` `distribute-rgt-out--_binary64` `difference-of-squares_binary64`
6×	`pow1_binary64`
5×	`associate-/l*_binary64`
4×	`insert-posit16`
3×	`associate-/r*_binary64` `flip3--_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `distribute-lft-neg-out_binary64` `neg-mul-1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 112

Calls

4 calls:

15.0ms	(.f64 (neg.f64 m) (/.f64 (-.f64 (.f64 m m) m) v))
11.0ms	(-.f64 (.f64 (neg.f64 m) (/.f64 (-.f64 (.f64 m m) m) v)) m)
8.0ms	(/.f64 (-.f64 (*.f64 m m) m) v)
5.0ms	(-.f64 (*.f64 m m) m)

series231.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 (neg.f64 m) (/.f64 (-.f64 (.f64 m m) m) v))
61.0ms	(-.f64 (*.f64 m m) m)
52.0ms	(/.f64 (-.f64 (*.f64 m m) m) v)
41.0ms	(-.f64 (.f64 (neg.f64 m) (/.f64 (-.f64 (.f64 m m) m) v)) m)

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5027	2078

prune100.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	125	7	132

Merged error: 0b

Counts

132 → 7

Compiler

Compiled 2381 to 588 computations (75.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (/.f64 (neg.f64 m) (sqrt.f64 v)) (/.f64 (-.f64 (.f64 m m) m) (sqrt.f64 v))) m)
0.2b	(/.f64 (-.f64 (*.f64 m m) m) (sqrt.f64 v))
0.2b	(/.f64 (neg.f64 m) (sqrt.f64 v))
0.3b	(.f64 (/.f64 (neg.f64 m) (sqrt.f64 v)) (/.f64 (-.f64 (.f64 m m) m) (sqrt.f64 v)))

rewrite107.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`times-frac_binary64`
165×	`add-sqr-sqrt_binary64`
135×	`*-un-lft-identity_binary64`
122×	`add-cube-cbrt_binary64`
102×	`sqrt-prod_binary64`
64×	`associate-l_binary64`
39×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
34×	`associate-r_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`associate-/l*_binary64`
13×	`distribute-rgt-out--_binary64` `neg-mul-1_binary64` `difference-of-squares_binary64`
12×	`associate-/r*_binary64`
9×	`unswap-sqr_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `div-inv_binary64` `insert-posit16`
2×	`associate-/l/_binary64` `flip3--_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-frac-neg_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `neg-sub0_binary64` `associate-r/_binary64` `distribute-lft-neg-out_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 289

Calls

4 calls:

52.0ms	(.f64 (/.f64 (neg.f64 m) (sqrt.f64 v)) (/.f64 (-.f64 (.f64 m m) m) (sqrt.f64 v)))
22.0ms	(-.f64 (.f64 (/.f64 (neg.f64 m) (sqrt.f64 v)) (/.f64 (-.f64 (.f64 m m) m) (sqrt.f64 v))) m)
9.0ms	(/.f64 (-.f64 (*.f64 m m) m) (sqrt.f64 v))
7.0ms	(/.f64 (neg.f64 m) (sqrt.f64 v))

series301.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(.f64 (/.f64 (neg.f64 m) (sqrt.f64 v)) (/.f64 (-.f64 (.f64 m m) m) (sqrt.f64 v)))
79.0ms	(/.f64 (neg.f64 m) (sqrt.f64 v))
72.0ms	(-.f64 (.f64 (/.f64 (neg.f64 m) (sqrt.f64 v)) (/.f64 (-.f64 (.f64 m m) m) (sqrt.f64 v))) m)
51.0ms	(/.f64 (-.f64 (*.f64 m m) m) (sqrt.f64 v))

simplify166.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5164	6476

prune234.0ms (6.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	301	7	308

Merged error: 0b

Counts

308 → 7

Compiler

Compiled 7127 to 1173 computations (83.5% saved)

regimes38.0ms (1%)

Compiler: Compiled 298 to 216 computations (27.5% saved)

bsearch0.0ms (0%)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	185	23
1	185	23

end0.0ms (0%)

sample737.0ms (19.9%)

Algorithm

1×

intervals

Results

252.0ms	8000×	body	80	valid
166.0ms	8065×	pre	80	true
2.0ms	65×	body	80	invalid

Compiler

Compiled 183 to 131 computations (28.4% saved)

Details

analyze53.0ms (1.4%)

sample23.0ms (0.6%)

simplify321.0ms (8.6%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

rewrite250.0ms (6.7%)

series217.0ms (5.8%)

simplify102.0ms (2.7%)

prune118.0ms (3.2%)

localize8.0ms (0.2%)

rewrite83.0ms (2.2%)

series210.0ms (5.7%)

simplify121.0ms (3.3%)

prune136.0ms (3.7%)

localize8.0ms (0.2%)

rewrite44.0ms (1.2%)

series231.0ms (6.2%)

simplify71.0ms (1.9%)

prune100.0ms (2.7%)

localize10.0ms (0.3%)

rewrite107.0ms (2.9%)

series301.0ms (8.1%)

simplify166.0ms (4.5%)

prune234.0ms (6.3%)

regimes38.0ms (1%)

bsearch0.0ms (0%)

simplify10.0ms (0.3%)

end0.0ms (0%)

sample737.0ms (19.9%)

Profiling