Details

analyze257.0ms (4.7%)

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)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
6.0ms	259×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify272.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4905	19
1	4905	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)
0.0b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

rewrite64.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`
10×	`associate-l_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`pow1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_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` `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 → 113

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

series208.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(*.f64 m (-.f64 1 m))
59.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
57.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
32.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4978	2142
1	4978	2142

prune142.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Merged error: 0.0b

Counts

126 → 5

Compiler

Compiled 2530 to 1735 computations (31.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite124.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 226

Calls

4 calls:

43.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
37.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
11.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
6.0ms	(/.f64 v (-.f64 1 m))

series191.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(/.f64 v (-.f64 1 m))
56.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
47.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
30.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4954	5059
1	4954	5059

prune276.0ms (5.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	238	5	243

Merged error: 0.0b

Counts

243 → 5

Compiler

Compiled 5355 to 3332 computations (37.8% saved)

localize11.0ms (0.2%)

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)))

rewrite81.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64` `frac-times_binary64`
28×	`*-un-lft-identity_binary64`
23×	`flip3--_binary64` `flip--_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-*l/_binary64`
15×	`cancel-sign-sub-inv_binary64`
14×	`associate-r_binary64` `add-cube-cbrt_binary64`
12×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
11×	`pow1_binary64`
10×	`sqrt-prod_binary64`
8×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_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`
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` `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 → 139

Calls

4 calls:

25.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
18.0ms	(.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)

series245.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
76.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
49.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
27.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5020	4520

prune228.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	151	5	156

Merged error: 0.0b

Counts

156 → 5

Compiler

Compiled 4522 to 2900 computations (35.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite100.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

168×	`cbrt-div_binary64`
148×	`frac-times_binary64`
126×	`flip3--_binary64` `flip--_binary64`
50×	`associate-r/_binary64` `associate-l/_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`pow1/3_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 162

Calls

4 calls:

18.0ms	(cbrt.f64 (.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))
15.0ms	(cbrt.f64 (.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))
14.0ms	(cbrt.f64 (.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))
12.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (cbrt.f64 (.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))))

series726.0ms (13.4%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (cbrt.f64 (.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))))
174.0ms	(cbrt.f64 (.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))
172.0ms	(cbrt.f64 (.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))
164.0ms	(cbrt.f64 (.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))

simplify165.0ms (3%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4925	10729
1	4925	10729

prune696.0ms (12.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	173	6	179

Merged error: 0b

Counts

179 → 6

Compiler

Compiled 11506 to 8164 computations (29% saved)

regimes155.0ms (2.9%)

Compiler: Compiled 1932 to 1515 computations (21.6% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	130	31
1	130	31

end0.0ms (0%)

sample1.2s (21.5%)

Algorithm

1×

intervals

Results

282.0ms	8000×	body	128	valid
169.0ms	8060×	pre	128	true
2.0ms	60×	body	128	invalid

Compiler

Compiled 678 to 531 computations (21.7% saved)

Details

analyze257.0ms (4.7%)

sample25.0ms (0.5%)

simplify272.0ms (5%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite64.0ms (1.2%)

series208.0ms (3.8%)

simplify70.0ms (1.3%)

prune142.0ms (2.6%)

localize7.0ms (0.1%)

rewrite124.0ms (2.3%)

series191.0ms (3.5%)

simplify96.0ms (1.8%)

prune276.0ms (5.1%)

localize11.0ms (0.2%)

rewrite81.0ms (1.5%)

series245.0ms (4.5%)

simplify89.0ms (1.6%)

prune228.0ms (4.2%)

localize12.0ms (0.2%)

rewrite100.0ms (1.8%)

series726.0ms (13.4%)

simplify165.0ms (3%)

prune696.0ms (12.8%)

regimes155.0ms (2.9%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.2s (21.5%)

Profiling