Details

analyze2.0ms (0%)

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)

sample41.0ms (0.9%)

Algorithm

1×

intervals

Results

18.0ms	61×	body	1024	valid
8.0ms	138×	body	128	valid
5.0ms	34×	body	512	valid
3.0ms	7×	body	2048	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify92.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0%)

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

Error

28.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(log.f64 (+.f64 N 1))
2.0b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
2.0b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.8b	(log.f64 (+.f64 N 1))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_419`
11×	`log-prod_binary64_505`
8×	`add-sqr-sqrt_binary64_441` `pow1_binary64_480`
6×	`add-cube-cbrt_binary64_454` `log-pow_binary64_508`
4×	`associate--l+_binary64_356` `distribute-lft-out--_binary64_371` `cancel-sign-sub-inv_binary64_385` `log-div_binary64_506`
3×	`add-exp-log_binary64_457` `associate--r+_binary64_355`
2×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `distribute-lft-out_binary64_370` `flip-+_binary64_393` `add-cbrt-cube_binary64_455` `associate--l-_binary64_357`
1×	`sub-neg_binary64_412` `difference-of-squares_binary64_388` `rem-log-exp_binary64_460` `flip3--_binary64_423` `diff-log_binary64_511` `flip--_binary64_394`

Counts

2 → 44

Calls

4 calls:

7.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.0ms	(log.f64 (+.f64 N 1))
0.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
0.0ms	(log.f64 (+.f64 N 1))

series73.0ms (1.5%)

Counts

2 → 16

Calls

2 calls:

48.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
25.0ms	(log.f64 (+.f64 N 1))

Compiler

Compiled 242 to 211 computations (12.8% saved)

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4906	769
1	4906	769

prune93.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	3	61

Error

0.1b

Counts

61 → 3

Compiler

Compiled 757 to 485 computations (35.9% saved)

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(log.f64 (/.f64 (+.f64 N 1) N))
0.0b	(/.f64 (+.f64 N 1) N)
0.0b	(/.f64 (+.f64 N 1) N)
1.9b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_419`
24×	`times-frac_binary64_425`
19×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
16×	`log-prod_binary64_505`
7×	`distribute-lft-out_binary64_370` `add-exp-log_binary64_457`
4×	`add-cbrt-cube_binary64_455` `associate-/l*_binary64_364`
3×	`associate-/r*_binary64_363` `pow1_binary64_480`
2×	`add-log-exp_binary64_458` `rem-log-exp_binary64_460` `div-inv_binary64_416` `div-exp_binary64_470` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `clear-num_binary64_418` `log-pow_binary64_508` `frac-2neg_binary64_430` `flip-+_binary64_393` `log-div_binary64_506` `cbrt-undiv_binary64_453`

Counts

2 → 60

Calls

4 calls:

5.0ms	(/.f64 (+.f64 N 1) N)
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))
0.0ms	(/.f64 (+.f64 N 1) N)
0.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

series76.0ms (1.6%)

Counts

2 → 16

Calls

2 calls:

42.0ms	(log.f64 (/.f64 (+.f64 N 1) N))
34.0ms	(/.f64 (+.f64 N 1) N)

Compiler

Compiled 182 to 169 computations (7.1% saved)

simplify66.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5344	1038

prune61.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	75	4	79

Error

0.1b

Counts

79 → 4

Compiler

Compiled 920 to 626 computations (32% saved)

localize16.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.3b	(cbrt.f64 (+.f64 N 1))
0.2b	(/.f64 (cbrt.f64 (+.f64 N 1)) (sqrt.f64 N))
0.0b	(log.f64 (sqrt.f64 N))
0.0b	(log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (sqrt.f64 N)))
0.3b	(cbrt.f64 (+.f64 N 1))
0.4b	(-.f64 (*.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N)))
3.6b	(log.f64 (cbrt.f64 (+.f64 N 1)))
22.3b	(+.f64 (-.f64 (*.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N))) (log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (sqrt.f64 N))))

rewrite59.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`log-prod_binary64_505`
73×	`*-un-lft-identity_binary64_419`
48×	`cbrt-prod_binary64_450`
46×	`associate-+r+_binary64_351` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
42×	`times-frac_binary64_425`
28×	`associate--l+_binary64_356`
24×	`sqrt-prod_binary64_435`
21×	`associate-+l+_binary64_352`
14×	`distribute-rgt-in_binary64_369` `distribute-lft-out_binary64_370` `distribute-lft-in_binary64_368`
12×	`cancel-sign-sub-inv_binary64_385`
10×	`pow1_binary64_480`
9×	`log-pow_binary64_508`
7×	`add-log-exp_binary64_458`
6×	`associate--r+_binary64_355`
5×	`add-exp-log_binary64_457`
4×	`cbrt-div_binary64_451` `add-cbrt-cube_binary64_455`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `log-div_binary64_506`
2×	`pow1/3_binary64_501` `sub-neg_binary64_412` `pow1/2_binary64_499` `sum-log_binary64_510` `diff-log_binary64_511` `sqrt-pow1_binary64_437`
1×	`rem-log-exp_binary64_460` `div-inv_binary64_416` `associate-+l-_binary64_354` `flip3--_binary64_423` `associate-+r-_binary64_353` `flip--_binary64_394` `+-commutative_binary64_349`

Counts

4 → 153

Calls

8 calls:

21.0ms	(+.f64 (-.f64 (*.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N))) (log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (sqrt.f64 N))))
9.0ms	(-.f64 (*.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N)))
4.0ms	(log.f64 (cbrt.f64 (+.f64 N 1)))
3.0ms	(cbrt.f64 (+.f64 N 1))
0.0ms	(log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (sqrt.f64 N)))

series206.0ms (4.4%)

Counts

4 → 20

Calls

4 calls:

81.0ms	(+.f64 (-.f64 (*.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N))) (log.f64 (/.f64 (cbrt.f64 (+.f64 N 1)) (sqrt.f64 N))))
42.0ms	(-.f64 (*.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N)))
41.0ms	(cbrt.f64 (+.f64 N 1))
41.0ms	(log.f64 (cbrt.f64 (+.f64 N 1)))

Compiler

Compiled 788 to 666 computations (15.5% saved)

simplify102.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4913	3636
1	4913	3636

prune264.0ms (5.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	174	3	177

Error

0.1b

Counts

177 → 3

Compiler

Compiled 4378 to 2960 computations (32.4% saved)

localize18.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.2b	(cbrt.f64 (sqrt.f64 (+.f64 N 1)))
0.2b	(cbrt.f64 (sqrt.f64 (+.f64 N 1)))
0.0b	(log.f64 (sqrt.f64 N))
0.0b	(log.f64 (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 N 1))) (cbrt.f64 (sqrt.f64 (+.f64 N 1)))) (sqrt.f64 N)))
0.3b	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 N 1))) (cbrt.f64 (sqrt.f64 (+.f64 N 1))))
0.4b	(-.f64 (*.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N)))
3.6b	(log.f64 (cbrt.f64 (+.f64 N 1)))
22.0b	(+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N))) (log.f64 (/.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 N 1))) (cbrt.f64 (sqrt.f64 (+.f64 N 1)))) (sqrt.f64 N))))

rewrite77.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-prod_binary64_450`
60×	`*-un-lft-identity_binary64_419`
55×	`add-sqr-sqrt_binary64_441`
51×	`log-prod_binary64_505`
34×	`sqrt-prod_binary64_435`
33×	`add-cube-cbrt_binary64_454`
28×	`associate--l+_binary64_356`
21×	`associate-+l+_binary64_352`
17×	`pow1_binary64_480`
14×	`cbrt-div_binary64_451` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `swap-sqr_binary64_386`
13×	`distribute-lft-out_binary64_370`
12×	`sqrt-div_binary64_436` `cancel-sign-sub-inv_binary64_385`
10×	`associate-+r+_binary64_351` `associate-r_binary64_359` `associate-l_binary64_360`
9×	`unswap-sqr_binary64_387` `log-pow_binary64_508`
8×	`flip3-+_binary64_422` `flip-+_binary64_393`
7×	`pow1/3_binary64_501` `add-log-exp_binary64_458` `add-exp-log_binary64_457`
6×	`times-frac_binary64_425` `associate--r+_binary64_355`
4×	`frac-times_binary64_429` `add-cbrt-cube_binary64_455`
3×	`log-div_binary64_506`
2×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `sub-neg_binary64_412` `pow1/2_binary64_499` `sum-log_binary64_510` `associate-r/_binary64_361` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `pow-sqr_binary64_392` `pow-prod-up_binary64_489`
1×	`rem-log-exp_binary64_460` `div-inv_binary64_416` `associate-+l-_binary64_354` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip3--_binary64_423` `pow-plus_binary64_482` `*-commutative_binary64_350` `associate-+r-_binary64_353` `flip--_binary64_394` `+-commutative_binary64_349` `pow2_binary64_500`

Counts

4 → 172

Calls

8 calls:

22.0ms	(+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N))) (log.f64 (/.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 N 1))) (cbrt.f64 (sqrt.f64 (+.f64 N 1)))) (sqrt.f64 N))))
15.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 N 1))) (cbrt.f64 (sqrt.f64 (+.f64 N 1))))
10.0ms	(-.f64 (*.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N)))
4.0ms	(log.f64 (cbrt.f64 (+.f64 N 1)))
0.0ms	(log.f64 (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 N 1))) (cbrt.f64 (sqrt.f64 (+.f64 N 1)))) (sqrt.f64 N)))

series216.0ms (4.6%)

Counts

4 → 20

Calls

4 calls:

85.0ms	(+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N))) (log.f64 (/.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 N 1))) (cbrt.f64 (sqrt.f64 (+.f64 N 1)))) (sqrt.f64 N))))
47.0ms	(log.f64 (cbrt.f64 (+.f64 N 1)))
43.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 N 1))) (cbrt.f64 (sqrt.f64 (+.f64 N 1))))
41.0ms	(-.f64 (*.f64 2 (log.f64 (cbrt.f64 (+.f64 N 1)))) (log.f64 (sqrt.f64 N)))

Compiler

Compiled 886 to 750 computations (15.3% saved)

simplify88.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4962	3799
1	4962	3799

prune360.0ms (7.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	192	3	195

Error

0.1b

Counts

195 → 3

Compiler

Compiled 5708 to 4043 computations (29.2% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	290	803
1	290	803

regimes139.0ms (3%)

Compiler: Compiled 1049 to 858 computations (18.2% saved)

bsearch2.0ms (0%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

regimes110.0ms (2.3%)

Compiler: Compiled 697 to 582 computations (16.5% saved)

bsearch14.0ms (0.3%)

Steps

Iters	Range		Point
6	302.52702270046814	3300.8171630890365	929.9693967107072

Compiler

Compiled 1 to 1 computations (0% saved)

regimes102.0ms (2.2%)

Compiler: Compiled 617 to 516 computations (16.4% saved)

bsearch15.0ms (0.3%)

Steps

Iters	Range		Point
6	302.52702270046814	3300.8171630890365	929.9693967107072

Compiler

Compiled 1 to 1 computations (0% saved)

regimes90.0ms (1.9%)

Compiler: Compiled 483 to 414 computations (14.3% saved)

bsearch13.0ms (0.3%)

Steps

Iters	Range		Point
6	302.52702270046814	3300.8171630890365	1274.9763547642451

Compiler

Compiled 1 to 1 computations (0% saved)

regimes53.0ms (1.1%)

Compiler: Compiled 140 to 128 computations (8.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

regimes19.0ms (0.4%)

Compiler: Compiled 30 to 29 computations (3.3% saved)

bsearch14.0ms (0.3%)

Steps

Iters	Range		Point
7	127662.57638432007	23020028.068672698	158463.51741184632

Compiler

Compiled 1 to 1 computations (0% saved)

regimes18.0ms (0.4%)

Compiler: Compiled 24 to 24 computations (0% saved)

bsearch17.0ms (0.4%)

Steps

Iters	Range		Point
10	1.2571684454435198e-15	1.2251308373656755	0.686945551724479

Compiler

Compiled 1 to 1 computations (0% saved)

regimes17.0ms (0.4%)

Compiler: Compiled 17 to 18 computations (-5.9% saved)

bsearch17.0ms (0.4%)

Steps

Iters	Range		Point
10	1.2571684454435198e-15	1.2251308373656755	0.9058357690173492

Compiler

Compiled 1 to 1 computations (0% saved)

regimes15.0ms (0.3%)

Compiler: Compiled 8 to 11 computations (-37.5% saved)

bsearch16.0ms (0.3%)

Steps

Iters	Range		Point
10	1.2571684454435198e-15	1.2251308373656755	1.0062406200728051

Compiler

Compiled 1 to 1 computations (0% saved)

regimes7.0ms (0.2%)

Accuracy

Total 0.0b remaining (47.3%)

Threshold costs 0.0b (47.3%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch14.0ms (0.3%)

Compiler: Compiled 265 to 208 computations (21.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	132	403
1	132	403

end0.0ms (0%)

sample2.0s (41.9%)

Algorithm

1×

intervals

Results

454.0ms	1995×	body	1024	valid
241.0ms	4275×	body	128	valid
141.0ms	983×	body	512	valid
96.0ms	258×	body	2048	valid
43.0ms	489×	body	256	valid

Compiler

Compiled 773 to 622 computations (19.5% saved)

Pareto

0.9442631289547355

Details

analyze2.0ms (0%)

sample41.0ms (0.9%)

simplify92.0ms (2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite14.0ms (0.3%)

series73.0ms (1.5%)

simplify70.0ms (1.5%)

prune93.0ms (2%)

localize5.0ms (0.1%)

rewrite14.0ms (0.3%)

series76.0ms (1.6%)

simplify66.0ms (1.4%)

prune61.0ms (1.3%)

localize16.0ms (0.3%)

rewrite59.0ms (1.3%)

series206.0ms (4.4%)

simplify102.0ms (2.2%)

prune264.0ms (5.6%)

localize18.0ms (0.4%)

rewrite77.0ms (1.6%)

series216.0ms (4.6%)

simplify88.0ms (1.9%)

prune360.0ms (7.7%)

simplify14.0ms (0.3%)

regimes139.0ms (3%)

bsearch2.0ms (0%)

regimes110.0ms (2.3%)

bsearch14.0ms (0.3%)

regimes102.0ms (2.2%)

bsearch15.0ms (0.3%)

regimes90.0ms (1.9%)

bsearch13.0ms (0.3%)

regimes53.0ms (1.1%)

bsearch1.0ms (0%)

regimes19.0ms (0.4%)

bsearch14.0ms (0.3%)

regimes18.0ms (0.4%)

bsearch17.0ms (0.4%)

regimes17.0ms (0.4%)

bsearch17.0ms (0.4%)

regimes15.0ms (0.3%)

bsearch16.0ms (0.3%)

regimes7.0ms (0.2%)

bsearch14.0ms (0.3%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.0s (41.9%)

Profiling