Details

analyze410.0ms (11.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4946	38
1	4946	38
0	2	2
1	2	2

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)

sample30.0ms (0.8%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify95.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4924	19
1	4924	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

Error

0.1b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.2%)

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))

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64`
10×	`associate-l_binary64`
8×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_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` `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 → 95

Calls

3 calls:

17.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
7.0ms	(*.f64 m (-.f64 1 m))

series90.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

34.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
30.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
26.0ms	(*.f64 m (-.f64 1 m))

simplify67.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5029	1776

prune124.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	100	5	105

Error

Counts

105 → 5

Compiler

Compiled 2099 to 1424 computations (32.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite61.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`*-un-lft-identity_binary64`
14×	`associate-r_binary64`
13×	`associate-l_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64` `associate-*r/_binary64`
8×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
7×	`cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64`
5×	`difference-of-squares_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `associate-*l/_binary64`
1×	`associate-/r_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 114

Calls

4 calls:

20.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (.f64 1 1) (.f64 m m))) (*.f64 v (+.f64 m 1))) 1) (-.f64 1 m))
12.0ms	(/.f64 (.f64 m (-.f64 (.f64 1 1) (.f64 m m))) (.f64 v (+.f64 m 1)))
8.0ms	(.f64 m (-.f64 (.f64 1 1) (*.f64 m m)))
6.0ms	(*.f64 v (+.f64 m 1))

series147.0ms (4%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(/.f64 (.f64 m (-.f64 (.f64 1 1) (.f64 m m))) (.f64 v (+.f64 m 1)))
40.0ms	(.f64 m (-.f64 (.f64 1 1) (*.f64 m m)))
38.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (.f64 1 1) (.f64 m m))) (*.f64 v (+.f64 m 1))) 1) (-.f64 1 m))
25.0ms	(*.f64 v (+.f64 m 1))

simplify90.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4963	2509
1	4963	2509

prune154.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	126	5	131

Error

Counts

131 → 5

Compiler

Compiled 3313 to 2286 computations (31% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite65.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 144

Calls

4 calls:

22.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
17.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
5.0ms	(-.f64 1 (sqrt.f64 m))

series118.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
35.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
22.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
15.0ms	(-.f64 1 (sqrt.f64 m))

simplify93.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5003	4463

prune216.0ms (5.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	156	5	161

Error

Counts

161 → 5

Compiler

Compiled 4566 to 2889 computations (36.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
0.2b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
0.3b	(/.f64 m (sqrt.f64 v))
0.4b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

rewrite84.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

150×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
118×	`*-un-lft-identity_binary64`
76×	`add-cube-cbrt_binary64`
66×	`sqrt-prod_binary64`
46×	`associate-r_binary64`
28×	`difference-of-squares_binary64`
25×	`associate-l_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`distribute-lft-out--_binary64`
12×	`associate-/r*_binary64`
10×	`unswap-sqr_binary64`
9×	`associate-/l*_binary64`
8×	`pow1_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64`
4×	`add-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-inv_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`div-sub_binary64`

Counts

4 → 230

Calls

4 calls:

30.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
19.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
7.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
4.0ms	(/.f64 m (sqrt.f64 v))

series132.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
37.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
35.0ms	(/.f64 m (sqrt.f64 v))
21.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))

simplify78.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5677	4737

prune257.0ms (7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	242	5	247

Error

Counts

247 → 5

Compiler

Compiled 5867 to 2839 computations (51.6% saved)

regimes156.0ms (4.2%)

Accuracy

Total 0.1b remaining (98%)

Threshold costs 0.1b (98%)

Compiler

Compiled 1941 to 1527 computations (21.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	19
1	33	19

end0.0ms (0%)

sample1.1s (30.6%)

Algorithm

1×

intervals

Results

269.0ms	8000×	body	128	valid
158.0ms	8065×	pre	128	true
2.0ms	65×	body	128	invalid

Compiler

Compiled 673 to 530 computations (21.2% saved)

Details

analyze410.0ms (11.1%)

sample30.0ms (0.8%)

simplify95.0ms (2.6%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

rewrite40.0ms (1.1%)

series90.0ms (2.4%)

simplify67.0ms (1.8%)

prune124.0ms (3.4%)

localize12.0ms (0.3%)

rewrite61.0ms (1.7%)

series147.0ms (4%)

simplify90.0ms (2.4%)

prune154.0ms (4.2%)

localize13.0ms (0.4%)

rewrite65.0ms (1.8%)

series118.0ms (3.2%)

simplify93.0ms (2.5%)

prune216.0ms (5.9%)

localize9.0ms (0.2%)

rewrite84.0ms (2.3%)

series132.0ms (3.6%)

simplify78.0ms (2.1%)

prune257.0ms (7%)

regimes156.0ms (4.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (30.6%)

Profiling