Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample39.0ms (1.4%)

Algorithm

1×

intervals

Results

13.0ms	59×	body	1024	valid
9.0ms	32×	body	512	valid
8.0ms	142×	body	128	valid
2.0ms	5×	body	2048	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 27.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.1b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
4.8b	(log.f64 (+.f64 N 1))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
11×	`log-prod_binary64`
8×	`pow1_binary64` `add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64` `log-pow_binary64`
4×	`cancel-sign-sub-inv_binary64` `distribute-lft-out--_binary64` `log-div_binary64` `associate--l+_binary64`
3×	`associate--r+_binary64` `add-exp-log_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `associate--l-_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `difference-of-squares_binary64` `flip--_binary64`

Counts

2 → 44

Calls

2 calls:

8.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.0ms	(log.f64 (+.f64 N 1))

series72.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

47.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
24.0ms	(log.f64 (+.f64 N 1))

simplify103.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4863	664
1	4863	664

prune124.0ms (4.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	2	51

Merged error: 0.0b

Counts

51 → 2

Compiler

Compiled 1561 to 1180 computations (24.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

2.1b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`log-prod_binary64`
15×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
9×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-exp-log_binary64`
3×	`distribute-lft-out_binary64`
2×	`pow1_binary64` `rem-log-exp_binary64`
1×	`add-log-exp_binary64` `log-pow_binary64` `add-cbrt-cube_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64`

Counts

1 → 27

Calls

1 calls:

5.0ms

(log.f64 (/.f64 (+.f64 N 1) N))

series45.0ms (1.6%)

Counts

1 → 3

Calls

1 calls:

45.0ms

(log.f64 (/.f64 (+.f64 N 1) N))

simplify83.0ms (3%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4848	488
1	4848	488

prune26.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	30	2	32

Merged error: 0.0b

Counts

32 → 2

Compiler

Compiled 381 to 267 computations (29.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))
0.7b	(/.f64 1/2 (*.f64 N N))
0.7b	(/.f64 1/3 (pow.f64 N 3))
11.8b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))

rewrite89.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
45×	`times-frac_binary64`
37×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-/r*_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
7×	`cancel-sign-sub-inv_binary64`
6×	`associate-/l*_binary64`
5×	`distribute-lft-out_binary64` `div-inv_binary64` `div-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`cbrt-undiv_binary64` `distribute-lft-out--_binary64` `frac-sub_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `associate--l+_binary64`

Counts

4 → 129

Calls

4 calls:

35.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))
32.0ms	(+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))
6.0ms	(/.f64 1/3 (pow.f64 N 3))
5.0ms	(/.f64 1/2 (*.f64 N N))

series186.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))
42.0ms	(/.f64 1/3 (pow.f64 N 3))
33.0ms	(/.f64 1/2 (*.f64 N N))
27.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))

simplify51.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5180	2222

prune159.0ms (5.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	140	3	143

Merged error: 0b

Counts

143 → 3

Compiler

Compiled 2941 to 2047 computations (30.4% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 1/2 (*.f64 N N))
0.7b	(/.f64 1/3 (pow.f64 N 3))
11.8b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))
26.1b	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N))) 3))

rewrite103.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64`
48×	`add-sqr-sqrt_binary64`
45×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
22×	`cbrt-prod_binary64`
20×	`unpow-prod-down_binary64` `cube-prod_binary64`
14×	`add-exp-log_binary64`
13×	`associate-/r*_binary64`
11×	`add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
7×	`cancel-sign-sub-inv_binary64`
6×	`distribute-lft-out_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `div-inv_binary64` `frac-sub_binary64`
5×	`cbrt-div_binary64` `sqr-pow_binary64` `cube-div_binary64` `div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
4×	`pow1_binary64`
3×	`cbrt-undiv_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `prod-exp_binary64` `pow-exp_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 150

Calls

4 calls:

39.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))
37.0ms	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N))) 3))
6.0ms	(/.f64 1/3 (pow.f64 N 3))
5.0ms	(/.f64 1/2 (*.f64 N N))

series149.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(/.f64 1/3 (pow.f64 N 3))
40.0ms	(/.f64 1/2 (*.f64 N N))
34.0ms	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N))) 3))
28.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))

simplify63.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5720	3368

prune227.0ms (8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	162	3	165

Merged error: 0b

Counts

165 → 3

Compiler

Compiled 3965 to 2875 computations (27.5% saved)

regimes17.0ms (0.6%)

Compiler: Compiled 41 to 34 computations (17.1% saved)

bsearch18.0ms (0.7%)

Steps

Iters	Range		Point
10	4.354027438608079	111837815101329.58	10832.711036711009

Compiler

Compiled 1 to 1 computations (0% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	37
1	39	37

end0.0ms (0%)

sample1.2s (42.4%)

Algorithm

1×

intervals

Results

452.0ms	2013×	body	1024	valid
242.0ms	4225×	body	128	valid
143.0ms	1011×	body	512	valid
102.0ms	268×	body	2048	valid
45.0ms	483×	body	256	valid

Compiler

Compiled 72 to 59 computations (18.1% saved)

Details

analyze2.0ms (0.1%)

sample39.0ms (1.4%)

simplify10.0ms (0.4%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite14.0ms (0.5%)

series72.0ms (2.5%)

simplify103.0ms (3.7%)

prune124.0ms (4.4%)

localize4.0ms (0.2%)

rewrite7.0ms (0.2%)

series45.0ms (1.6%)

simplify83.0ms (3%)

prune26.0ms (0.9%)

localize10.0ms (0.3%)

rewrite89.0ms (3.1%)

series186.0ms (6.6%)

simplify51.0ms (1.8%)

prune159.0ms (5.6%)

localize14.0ms (0.5%)

rewrite103.0ms (3.7%)

series149.0ms (5.3%)

simplify63.0ms (2.2%)

prune227.0ms (8%)

regimes17.0ms (0.6%)

bsearch18.0ms (0.7%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (42.4%)

Profiling