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)

sample35.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	59×	body	1024	valid
8.0ms	144×	body	128	valid
5.0ms	32×	body	512	valid
3.0ms	8×	body	2048	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify11.0ms (0.3%)

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: 28.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.7b	(log.f64 (+.f64 N 1))
2.9b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
11×	`log-prod_binary64`
7×	`pow1_binary64` `add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64` `log-pow_binary64`
4×	`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 → 40

Calls

2 calls:

8.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
4.0ms	(log.f64 (+.f64 N 1))

series78.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

54.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
23.0ms	(log.f64 (+.f64 N 1))

simplify105.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4866	648
1	4866	648

prune48.0ms (1.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Merged error: 0.1b

Counts

47 → 2

Compiler

Compiled 611 to 401 computations (34.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
2.6b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`log-prod_binary64`
7×	`distribute-lft-out_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64` `pow1_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64`

Counts

2 → 60

Calls

2 calls:

6.0ms	(/.f64 (+.f64 N 1) N)
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

series106.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

60.0ms	(/.f64 (+.f64 N 1) N)
45.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify73.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5305	940

prune50.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Merged error: 0.1b

Counts

68 → 4

Compiler

Compiled 824 to 559 computations (32.2% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
0.3b	(cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) 3))
0.4b	(pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) 3)
2.6b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
16×	`log-prod_binary64`
14×	`cbrt-prod_binary64`
10×	`pow1_binary64` `add-exp-log_binary64`
8×	`unpow-prod-down_binary64` `cube-prod_binary64`
7×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
5×	`log-pow_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64`
2×	`associate-/l/_binary64` `rem-log-exp_binary64` `sqr-pow_binary64` `div-inv_binary64` `div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `rem-cbrt-cube_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `pow-pow_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 108

Calls

4 calls:

6.0ms	(/.f64 (+.f64 N 1) N)
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))
3.0ms	(pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) 3)
3.0ms	(cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) 3))

series198.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) 3)
60.0ms	(/.f64 (+.f64 N 1) N)
39.0ms	(cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) 3))
38.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify63.0ms (2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5083	1793

prune109.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	119	5	124

Merged error: 0.1b

Counts

124 → 5

Compiler

Compiled 1762 to 1329 computations (24.6% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (pow.f64 (pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3)))
0.5b	(pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) (*.f64 (cbrt.f64 3) (cbrt.f64 3)))
1.8b	(pow.f64 (pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
2.6b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite26.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`unpow-prod-down_binary64`
26×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`log-prod_binary64`
15×	`cbrt-prod_binary64`
12×	`times-frac_binary64`
10×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`pow-unpow_binary64`
5×	`sqr-pow_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `log-pow_binary64` `add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `distribute-lft-out_binary64`
2×	`rem-log-exp_binary64` `pow-pow_binary64`
1×	`pow1/3_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 90

Calls

4 calls:

5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))
5.0ms	(pow.f64 (pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
5.0ms	(cbrt.f64 (pow.f64 (pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3)))
3.0ms	(pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) (*.f64 (cbrt.f64 3) (cbrt.f64 3)))

series724.0ms (22.6%)

Counts

4 → 12

Calls

4 calls:

325.0ms	(cbrt.f64 (pow.f64 (pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3)))
224.0ms	(pow.f64 (pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
137.0ms	(pow.f64 (log.f64 (/.f64 (+.f64 N 1) N)) (*.f64 (cbrt.f64 3) (cbrt.f64 3)))
38.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5352	3261

prune169.0ms (5.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	102	5	107

Merged error: 0.1b

Counts

107 → 5

Compiler

Compiled 2718 to 2284 computations (16% saved)

regimes20.0ms (0.6%)

Compiler: Compiled 66 to 57 computations (13.6% saved)

bsearch14.0ms (0.4%)

Steps

Iters	Range		Point
7	992.3880738714992	85055.98833229704	9362.610851426467

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 (38.1%)

Algorithm

1×

intervals

Results

455.0ms	1987×	body	1024	valid
238.0ms	4241×	body	128	valid
146.0ms	1011×	body	512	valid
97.0ms	256×	body	2048	valid
46.0ms	505×	body	256	valid

Compiler

Compiled 97 to 82 computations (15.5% saved)

Details

analyze2.0ms (0.1%)

sample35.0ms (1.1%)

simplify11.0ms (0.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite14.0ms (0.4%)

series78.0ms (2.4%)

simplify105.0ms (3.3%)

prune48.0ms (1.5%)

localize5.0ms (0.1%)

rewrite16.0ms (0.5%)

series106.0ms (3.3%)

simplify73.0ms (2.3%)

prune50.0ms (1.5%)

localize8.0ms (0.3%)

rewrite25.0ms (0.8%)

series198.0ms (6.2%)

simplify63.0ms (2%)

prune109.0ms (3.4%)

localize15.0ms (0.5%)

rewrite26.0ms (0.8%)

series724.0ms (22.6%)

simplify61.0ms (1.9%)

prune169.0ms (5.3%)

regimes20.0ms (0.6%)

bsearch14.0ms (0.4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (38.1%)

Profiling