Details

analyze261.0ms (6%)

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 (0.6%)

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)

simplify198.0ms (4.6%)

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)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite42.0ms (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:

18.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
7.0ms	(*.f64 m (-.f64 1 m))

series93.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

34.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
33.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
26.0ms	(*.f64 m (-.f64 1 m))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5029	1776

prune129.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Error

0.0b

Counts

105 → 7

Compiler

Compiled 2158 to 1469 computations (31.9% saved)

localize7.0ms (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)))
0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))

rewrite77.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

171×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
139×	`*-un-lft-identity_binary64`
83×	`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` `cancel-sign-sub-inv_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_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` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

3 → 202

Calls

3 calls:

41.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
9.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
6.0ms	(/.f64 v (-.f64 1 m))

series71.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

25.0ms	(/.f64 v (-.f64 1 m))
24.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
23.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))

simplify116.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4973	4468
1	4973	4468

prune240.0ms (5.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	213	5	218

Error

0.0b

Counts

218 → 5

Compiler

Compiled 4804 to 2967 computations (38.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite64.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`
41×	`times-frac_binary64`
34×	`add-exp-log_binary64`
32×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`
22×	`add-cbrt-cube_binary64`
18×	`difference-of-squares_binary64`
11×	`div-exp_binary64`
10×	`associate-l_binary64`
9×	`pow1_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64`
8×	`flip3--_binary64` `flip--_binary64`
7×	`associate-/r*_binary64`
6×	`cbrt-undiv_binary64` `associate-/r/_binary64` `cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
5×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `frac-times_binary64`
3×	`1-exp_binary64` `rec-exp_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `clear-num_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`difference-of-sqr-1_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 160

Calls

4 calls:

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

series86.0ms (2%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(*.f64 v (/.f64 1 (-.f64 1 m)))
26.0ms	(/.f64 m (*.f64 v (/.f64 1 (-.f64 1 m))))
23.0ms	(.f64 (-.f64 (/.f64 m (.f64 v (/.f64 1 (-.f64 1 m)))) 1) (-.f64 1 m))
9.0ms	(/.f64 1 (-.f64 1 m))

simplify82.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4970	2674
1	4970	2674

prune184.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	172	5	177

Error

0.0b

Counts

177 → 5

Compiler

Compiled 3630 to 2602 computations (28.3% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 m m) (.f64 1 m))
0.0b	(/.f64 m (/.f64 v (-.f64 1 m)))
0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 (pow.f64 m 3)))
2.6b	(/.f64 (.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 (pow.f64 m 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m))))

rewrite142.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

157×	`times-frac_binary64`
148×	`add-sqr-sqrt_binary64`
128×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`
28×	`associate-/r*_binary64`
24×	`cancel-sign-sub-inv_binary64`
16×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
14×	`distribute-lft-out--_binary64`
13×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64`
12×	`associate-r_binary64`
11×	`associate-/r/_binary64`
8×	`associate-/l/_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `frac-times_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `div-inv_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-r/_binary64` `sqr-pow_binary64` `associate-/l_binary64` `associate-*l/_binary64`
3×	`difference-of-sqr-1_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `distribute-rgt-out_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 230

Calls

4 calls:

51.0ms	(/.f64 (.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 (pow.f64 m 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m))))
43.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 (pow.f64 m 3)))
10.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
4.0ms	(+.f64 (.f64 m m) (.f64 1 m))

series119.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(/.f64 (.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 (pow.f64 m 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 m m) (.f64 1 m))))
29.0ms	(+.f64 (.f64 m m) (.f64 1 m))
23.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 (pow.f64 m 3)))
22.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))

simplify109.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5084	6242

prune459.0ms (10.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	241	6	247

Error

Counts

247 → 6

Compiler

Compiled 8775 to 5785 computations (34.1% saved)

regimes237.0ms (5.5%)

Accuracy

Total 0.1b remaining (98.5%)

Threshold costs 0.1b (98.5%)

Compiler

Compiled 3078 to 2400 computations (22% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	22
1	34	22

end0.0ms (0%)

sample1.5s (34.4%)

Algorithm

1×

intervals

Results

273.0ms	8000×	body	128	valid
173.0ms	8063×	pre	128	true
2.0ms	63×	body	128	invalid

Compiler

Compiled 1054 to 823 computations (21.9% saved)

Details

analyze261.0ms (6%)

sample25.0ms (0.6%)

simplify198.0ms (4.6%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite42.0ms (1%)

series93.0ms (2.1%)

simplify71.0ms (1.6%)

prune129.0ms (3%)

localize7.0ms (0.2%)

rewrite77.0ms (1.8%)

series71.0ms (1.6%)

simplify116.0ms (2.7%)

prune240.0ms (5.5%)

localize8.0ms (0.2%)

rewrite64.0ms (1.5%)

series86.0ms (2%)

simplify82.0ms (1.9%)

prune184.0ms (4.2%)

localize16.0ms (0.4%)

rewrite142.0ms (3.3%)

series119.0ms (2.7%)

simplify109.0ms (2.5%)

prune459.0ms (10.6%)

regimes237.0ms (5.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (34.4%)

Profiling