Details

analyze1.0ms (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%)

Algorithm

1×

intervals

Results

12.0ms	74×	body	2048	valid
5.0ms	46×	body	1024	valid
4.0ms	108×	body	128	valid
2.0ms	18×	body	512	valid
1.0ms	10×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify100.0ms (3.5%)

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

Merged error: 19.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

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

series16.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

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

simplify73.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4998	391
1	4998	391

prune21.0ms (0.8%)

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

Merged error: 0.3b

Counts

31 → 2

Compiler

Compiled 351 to 229 computations (34.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.3b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

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

series36.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

29.0ms	(*.f64 N (+.f64 N 1))
8.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify74.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4927	383
1	4927	383

prune38.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	32	4	36
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	32	6	38

Merged error: 0.3b

Counts

38 → 6

Compiler

Compiled 557 to 435 computations (21.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

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×	`swap-sqr_binary64_2091` `associate-l_binary64_2065` `associate-r_binary64_2064` `add-exp-log_binary64_2162`
4×	`unswap-sqr_binary64_2092` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
2×	`pow-prod-down_binary64_2195` `pow-prod-up_binary64_2194` `pow-sqr_binary64_2097`
1×	`*-commutative_binary64_2055` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `pow2_binary64_2205` `cbrt-unprod_binary64_2157`

Counts

4 → 73

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)

series349.0ms (12.3%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
88.0ms	(cbrt.f64 N)
85.0ms	(cbrt.f64 N)
79.0ms	(cbrt.f64 N)

simplify65.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4892	563
1	4892	563

prune89.0ms (3.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	82	9	91

Merged error: 0.3b

Counts

91 → 9

Compiler

Compiled 1722 to 1016 computations (41% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)
0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 N)) 4)

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod_binary64_2155`
11×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
9×	`unpow-prod-down_binary64_2203`
5×	`pow1_binary64_2185` `add-exp-log_binary64_2162`
4×	`add-log-exp_binary64_2163` `pow1/3_binary64_2206` `add-cbrt-cube_binary64_2160`
3×	`pow-unpow_binary64_2201`
2×	`pow-pow_binary64_2196`
1×	`pow-exp_binary64_2192` `sqr-pow_binary64_2096` `pow-to-exp_binary64_2193`

Counts

4 → 57

Calls

4 calls:

4.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 N)) 4)
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)

series396.0ms (13.9%)

Counts

4 → 12

Calls

4 calls:

153.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 N)) 4)
82.0ms	(cbrt.f64 N)
81.0ms	(cbrt.f64 N)
80.0ms	(cbrt.f64 N)

simplify39.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5100	547

prune76.0ms (2.7%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	69	9	78

Merged error: 0.3b

Counts

78 → 9

Compiler

Compiled 1814 to 971 computations (46.5% saved)

regimes52.0ms (1.8%)

Compiler: Compiled 540 to 426 computations (21.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample1.3s (45.8%)

Algorithm

1×

intervals

Results

355.0ms	2107×	body	2048	valid
136.0ms	4084×	body	128	valid
122.0ms	1050×	body	1024	valid
46.0ms	501×	body	512	valid
16.0ms	258×	body	256	valid

Compiler

Compiled 289 to 231 computations (20.1% saved)

Details

analyze1.0ms (0.1%)

sample29.0ms (1%)

simplify100.0ms (3.5%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite7.0ms (0.2%)

series16.0ms (0.6%)

simplify73.0ms (2.6%)

prune21.0ms (0.8%)

localize5.0ms (0.2%)

rewrite9.0ms (0.3%)

series36.0ms (1.3%)

simplify74.0ms (2.6%)

prune38.0ms (1.3%)

localize10.0ms (0.3%)

rewrite18.0ms (0.6%)

series349.0ms (12.3%)

simplify65.0ms (2.3%)

prune89.0ms (3.1%)

localize14.0ms (0.5%)

rewrite13.0ms (0.4%)

series396.0ms (13.9%)

simplify39.0ms (1.4%)

prune76.0ms (2.7%)

regimes52.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (45.8%)

Profiling