Details

analyze255.0ms (7.1%)

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)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
6.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify264.0ms (7.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5013	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 4 expressions with local error:

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

rewrite64.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

20.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
14.0ms	(*.f64 m (-.f64 1 m))
10.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series201.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
58.0ms	(*.f64 m (-.f64 1 m))
51.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
32.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify80.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4960	1907
1	4960	1907

prune143.0ms (4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	7	111

Merged error: 0b

Counts

111 → 7

Compiler

Compiled 2287 to 1601 computations (30% 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))))
0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.2b	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))

rewrite66.0ms (1.8%)

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`
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 → 110

Calls

4 calls:

24.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
11.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
10.0ms	(+.f64 m (/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m)))
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series209.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
56.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
52.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
41.0ms	(+.f64 m (/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m)))

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4971	2870
1	4971	2870

prune151.0ms (4.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	122	7	129

Merged error: 0b

Counts

129 → 7

Compiler

Compiled 3567 to 2012 computations (43.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite80.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`frac-times_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64` `flip3--_binary64` `flip--_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-*l/_binary64`
14×	`associate-r_binary64`
12×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
11×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`
8×	`associate-l_binary64` `difference-of-squares_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `distribute-lft-out--_binary64` `sqrt-prod_binary64`
3×	`associate-/r*_binary64` `sub-neg_binary64` `times-frac_binary64`
2×	`associate-/l/_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 124

Calls

4 calls:

24.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
20.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
10.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series244.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
75.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
44.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
31.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify66.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5031	4003

prune198.0ms (5.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	136	7	143

Merged error: 0b

Counts

143 → 7

Compiler

Compiled 4106 to 2607 computations (36.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m))
0.1b	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v)) 1) (-.f64 1 m))
0.2b	(/.f64 m (sqrt.f64 v))
0.4b	(/.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v))

rewrite76.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
44×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
29×	`associate-l_binary64`
28×	`sqrt-prod_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-/r_binary64` `associate-r*_binary64`
10×	`flip3--_binary64` `flip--_binary64`
8×	`pow1_binary64` `frac-times_binary64`
6×	`cbrt-undiv_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `div-exp_binary64`
5×	`associate-/l/_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `associate-l/_binary64`
3×	`distribute-lft-out--_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`difference-of-sqr-1_binary64`

Counts

4 → 159

Calls

4 calls:

23.0ms	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v)) 1) (-.f64 1 m))
14.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m))
13.0ms	(/.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v))
5.0ms	(/.f64 m (sqrt.f64 v))

series303.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v)) 1) (-.f64 1 m))
82.0ms	(/.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v))
71.0ms	(/.f64 m (sqrt.f64 v))
59.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m))

simplify76.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4961	3021
1	4961	3021

prune160.0ms (4.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	171	7	178

Merged error: 0b

Counts

178 → 7

Compiler

Compiled 3957 to 1905 computations (51.9% saved)

regimes54.0ms (1.5%)

Compiler: Compiled 465 to 375 computations (19.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	31
1	31	31

end0.0ms (0%)

sample773.0ms (21.5%)

Algorithm

1×

intervals

Results

278.0ms	8000×	body	128	valid
165.0ms	8056×	pre	128	true
2.0ms	56×	body	128	invalid

Compiler

Compiled 189 to 150 computations (20.6% saved)

Details

analyze255.0ms (7.1%)

sample24.0ms (0.7%)

simplify264.0ms (7.4%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite64.0ms (1.8%)

series201.0ms (5.6%)

simplify80.0ms (2.2%)

prune143.0ms (4%)

localize13.0ms (0.4%)

rewrite66.0ms (1.8%)

series209.0ms (5.8%)

simplify58.0ms (1.6%)

prune151.0ms (4.2%)

localize11.0ms (0.3%)

rewrite80.0ms (2.2%)

series244.0ms (6.8%)

simplify66.0ms (1.8%)

prune198.0ms (5.5%)

localize9.0ms (0.3%)

rewrite76.0ms (2.1%)

series303.0ms (8.4%)

simplify76.0ms (2.1%)

prune160.0ms (4.4%)

regimes54.0ms (1.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample773.0ms (21.5%)

Profiling