Details

analyze97.0ms (2.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11
0	1	1
1	1	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 (0.8%)

Algorithm

1×

intervals

Results

10.0ms	58×	body	2048	valid
5.0ms	43×	body	1024	valid
4.0ms	131×	body	128	valid
2.0ms	19×	body	512	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune6.0ms (0.2%)

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

17.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
0.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite27.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

16.9b

Rules

5×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163`
3×	`add-cube-cbrt_binary64_2159` `cancel-sign-sub-inv_binary64_2090`
2×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
1×	`diff-atan_binary64_2281` `diff-log_binary64_2216` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`

Counts

2 → 24

Calls

2 calls:

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

Compiler

Compiled 348 to 227 computations (34.8% saved)

series28.0ms (0.8%)

Error

17.3b

Counts

2 → 6

Calls

2 calls:

16.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
8.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 126 to 98 computations (22.2% saved)

simplify72.0ms (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 (0.6%)

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

0.2b

Counts

31 → 2

Compiler

Compiled 351 to 229 computations (34.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.2b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite42.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

6×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `add-cube-cbrt_binary64_2159` `associate-r_binary64_2064`
3×	`associate-l_binary64_2065`
2×	`add-log-exp_binary64_2163` `associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `flip3-+_binary64_2127` `flip-+_binary64_2098` `distribute-lft-out_binary64_2075` `*-commutative_binary64_2055`

Counts

2 → 30

Calls

2 calls:

7.0ms	(*.f64 N (+.f64 N 1))
0.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 468 to 361 computations (22.9% saved)

series58.0ms (1.6%)

Error

0.2b

Counts

2 → 9

Calls

2 calls:

37.0ms	(*.f64 N (+.f64 N 1))
13.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 200 to 174 computations (13% saved)

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4927	392
1	4927	392

prune39.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	35	6	41

Error

0.2b

Counts

41 → 6

Compiler

Compiled 578 to 369 computations (36.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
0.5b	(cbrt.f64 N)
0.5b	(cbrt.f64 N)
0.5b	(cbrt.f64 N)

rewrite85.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

25×	`cbrt-prod_binary64_2155`
23×	`add-sqr-sqrt_binary64_2146`
15×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
11×	`pow1_binary64_2185`
9×	`pow1/3_binary64_2206`
6×	`add-exp-log_binary64_2162` `swap-sqr_binary64_2091` `associate-l_binary64_2065` `associate-r_binary64_2064`
4×	`add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160` `unswap-sqr_binary64_2092`
2×	`pow-prod-down_binary64_2195` `pow-prod-up_binary64_2194` `pow-sqr_binary64_2097`
1×	`pow2_binary64_2205` `pow-plus_binary64_2187` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `*-commutative_binary64_2055`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)

Compiler

Compiled 1524 to 743 computations (51.2% saved)

series320.0ms (9%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

91.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
77.0ms	(cbrt.f64 N)
73.0ms	(cbrt.f64 N)
69.0ms	(cbrt.f64 N)

Compiler

Compiled 663 to 513 computations (22.6% saved)

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

prune83.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	85	6	91

Error

0.2b

Counts

91 → 6

Compiler

Compiled 1649 to 949 computations (42.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
0.7b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (.f64 N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
12.4b	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
12.4b	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))

rewrite145.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

30×	`add-sqr-sqrt_binary64_2146`
24×	`sqrt-prod_binary64_2140`
21×	`pow1_binary64_2185`
14×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
10×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142`
8×	`swap-sqr_binary64_2091`
6×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `associate-l_binary64_2065` `associate-r_binary64_2064`
5×	`pow-prod-up_binary64_2194`
4×	`add-log-exp_binary64_2163` `rem-sqrt-square_binary64_2137` `unswap-sqr_binary64_2092`
3×	`pow-prod-down_binary64_2195` `pow-sqr_binary64_2097`
1×	`pow2_binary64_2205` `pow-plus_binary64_2187` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `sqrt-unprod_binary64_2144` `sqr-abs_binary64_2139` `rem-square-sqrt_binary64_2136` `*-commutative_binary64_2055`

Counts

4 → 83

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (.f64 N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
1.0ms	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))

Compiler

Compiled 2606 to 1704 computations (34.6% saved)

series108.0ms (3.1%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
33.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
16.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (.f64 N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
16.0ms	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))

Compiler

Compiled 648 to 512 computations (21% saved)

simplify81.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5095	1475

prune105.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	3	1	4
Picked	0	1	1
Done	1	0	1
Total	94	7	101

Error

0.1b

Counts

101 → 7

Compiler

Compiled 1987 to 1281 computations (35.5% saved)

regimes163.0ms (4.6%)

Accuracy

Total 0.1b remaining (17.1%)

Threshold costs 0.1b (17.1%)

Compiler

Compiled 2084 to 1512 computations (27.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	10	13

end0.0ms (0%)

sample1.8s (51.8%)

Algorithm

1×

intervals

Results

359.0ms	2029×	body	2048	valid
138.0ms	4129×	body	128	valid
122.0ms	1049×	body	1024	valid
48.0ms	549×	body	512	valid
19.0ms	244×	body	256	valid

Compiler

Compiled 1046 to 760 computations (27.3% saved)

Details

analyze97.0ms (2.7%)

sample29.0ms (0.8%)

simplify10.0ms (0.3%)

prune6.0ms (0.2%)

localize5.0ms (0.1%)

rewrite27.0ms (0.8%)

series28.0ms (0.8%)

simplify72.0ms (2%)

prune21.0ms (0.6%)

localize6.0ms (0.2%)

rewrite42.0ms (1.2%)

series58.0ms (1.6%)

simplify75.0ms (2.1%)

prune39.0ms (1.1%)

localize12.0ms (0.3%)

rewrite85.0ms (2.4%)

series320.0ms (9%)

simplify75.0ms (2.1%)

prune83.0ms (2.4%)

localize8.0ms (0.2%)

rewrite145.0ms (4.1%)

series108.0ms (3.1%)

simplify81.0ms (2.3%)

prune105.0ms (3%)

regimes163.0ms (4.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.8s (51.8%)

Profiling