Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample29.0ms (1.3%)

Algorithm

1×

intervals

Results

13.0ms	72×	body	2048	valid
5.0ms	38×	body	1024	valid
4.0ms	120×	body	128	valid
1.0ms	15×	body	512	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify100.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0.1%)

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

Error

17.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.3b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
4×	`add-log-exp_binary64_2504`
3×	`add-cube-cbrt_binary64_2500` `cancel-sign-sub-inv_binary64_2431`
2×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
1×	`diff-atan_binary64_2622` `difference-of-squares_binary64_2434` `flip--_binary64_2440` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `diff-log_binary64_2557` `flip3--_binary64_2469`

Counts

2 → 24

Calls

2 calls:

4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms	(atan.f64 (+.f64 N 1))

series17.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

12.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms	(atan.f64 (+.f64 N 1))

simplify70.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4998	391
1	4998	391

prune21.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	2	31

Error

0.4b

Counts

31 → 2

Compiler

Compiled 351 to 229 computations (34.8% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (*.f64 N (+.f64 N 1)))
0.0b	(*.f64 N (+.f64 N 1))
0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
5×	`add-log-exp_binary64_2504` `add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
4×	`associate-r_binary64_2405`
3×	`associate-l_binary64_2406`
2×	`flip3-+_binary64_2468` `distribute-lft-in_binary64_2414` `flip-+_binary64_2439` `associate-*r/_binary64_2407` `distribute-rgt-in_binary64_2415` `associate-+r+_binary64_2397`
1×	`*-commutative_binary64_2396` `+-commutative_binary64_2395` `sum-log_binary64_2556` `unswap-sqr_binary64_2433` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416` `cbrt-unprod_binary64_2498`

Counts

3 → 43

Calls

3 calls:

6.0ms	(*.f64 N (+.f64 N 1))
3.0ms	(+.f64 1 (*.f64 N (+.f64 N 1)))
0.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series50.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

34.0ms	(*.f64 N (+.f64 N 1))
9.0ms	(+.f64 1 (*.f64 N (+.f64 N 1)))
8.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify74.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4920	599
1	4920	599

prune54.0ms (2.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	49	5	54

Error

0.3b

Counts

54 → 5

Compiler

Compiled 777 to 607 computations (21.9% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N)))) (sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N)))))
0.4b	(atan2.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N)))) (sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))))
15.7b	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
15.7b	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))

rewrite25.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2487`
24×	`sqrt-prod_binary64_2481`
21×	`pow1_binary64_2526`
16×	`sqrt-div_binary64_2482`
14×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
10×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483`
8×	`flip3-+_binary64_2468` `swap-sqr_binary64_2432` `flip-+_binary64_2439`
6×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `associate-r_binary64_2405` `associate-l_binary64_2406`
5×	`pow-prod-up_binary64_2535`
4×	`add-log-exp_binary64_2504` `frac-times_binary64_2475` `unswap-sqr_binary64_2433` `rem-sqrt-square_binary64_2478`
3×	`pow-prod-down_binary64_2536` `pow-sqr_binary64_2438`
2×	`associate-l/_binary64_2408` `associate-r/_binary64_2407`
1×	`sqr-abs_binary64_2480` `*-commutative_binary64_2396` `pow-plus_binary64_2528` `sqrt-unprod_binary64_2485` `rem-square-sqrt_binary64_2477` `pow2_binary64_2546` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`

Counts

4 → 95

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N)))) (sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.0ms	(atan2.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N)))) (sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))))

series46.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
13.0ms	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
10.0ms	(.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N)))) (sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N)))))
10.0ms	(atan2.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N)))) (sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))))

simplify52.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5021	1787

prune131.0ms (6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	106	6	112

Error

0.3b

Counts

112 → 6

Compiler

Compiled 2352 to 1885 computations (19.9% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b	(atan2.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N)))) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
15.7b	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
15.7b	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
15.7b	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))

rewrite14.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2487`
9×	`sqrt-prod_binary64_2481`
7×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
6×	`sqrt-div_binary64_2482`
4×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`flip3-+_binary64_2468` `pow1/2_binary64_2545` `flip-+_binary64_2439` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`

Counts

4 → 52

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.0ms	(atan2.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N)))) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))))))

series51.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
12.0ms	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))
12.0ms	(atan2.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N)))) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
12.0ms	(sqrt.f64 (+.f64 1 (*.f64 N (+.f64 1 N))))

simplify73.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5395	1023

prune107.0ms (4.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	64	6	70

Error

0.3b

Counts

70 → 6

Compiler

Compiled 2101 to 1693 computations (19.4% saved)

regimes51.0ms (2.3%)

Accuracy

Total 0.0b remaining (13.5%)

Threshold costs 0.0b (13.5%)

Compiler

Compiled 542 to 454 computations (16.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	29
1	13	29

end0.0ms (0%)

sample1.2s (53.1%)

Algorithm

1×

intervals

Results

374.0ms	2091×	body	2048	valid
151.0ms	4177×	body	128	valid
125.0ms	988×	body	1024	valid
45.0ms	491×	body	512	valid
16.0ms	253×	body	256	valid

Compiler

Compiled 300 to 253 computations (15.7% saved)

Details

analyze2.0ms (0.1%)

sample29.0ms (1.3%)

simplify100.0ms (4.6%)

prune2.0ms (0.1%)

localize10.0ms (0.4%)

rewrite6.0ms (0.3%)

series17.0ms (0.8%)

simplify70.0ms (3.2%)

prune21.0ms (1%)

localize5.0ms (0.2%)

rewrite12.0ms (0.6%)

series50.0ms (2.3%)

simplify74.0ms (3.4%)

prune54.0ms (2.5%)

localize8.0ms (0.4%)

rewrite25.0ms (1.2%)

series46.0ms (2.1%)

simplify52.0ms (2.4%)

prune131.0ms (6%)

localize11.0ms (0.5%)

rewrite14.0ms (0.6%)

series51.0ms (2.3%)

simplify73.0ms (3.3%)

prune107.0ms (4.9%)

regimes51.0ms (2.3%)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample1.2s (53.1%)

Profiling