Details

analyze1.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample31.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms	62×	body	2048	valid
6.0ms	141×	body	128	valid
4.0ms	28×	body	1024	valid
2.0ms	17×	body	512	valid
1.0ms	8×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify172.0ms (4.7%)

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

Merged error: 13.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.0b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_2165` `*-un-lft-identity_binary64_2143`
4×	`add-log-exp_binary64_2182`
3×	`add-cube-cbrt_binary64_2178` `cancel-sign-sub-inv_binary64_2109`
2×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
1×	`diff-log_binary64_2235` `flip--_binary64_2118` `sub-neg_binary64_2136` `distribute-lft-out--_binary64_2095` `flip3--_binary64_2147` `diff-atan_binary64_2300` `difference-of-squares_binary64_2112`

Counts

2 → 24

Calls

2 calls:

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

series36.0ms (1%)

Counts

2 → 6

Calls

2 calls:

28.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
7.0ms	(atan.f64 (+.f64 N 1))

simplify73.0ms (2%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4971	391
1	4971	391

prune44.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	3	31

Merged error: 0.3b

Counts

31 → 3

Compiler

Compiled 592 to 423 computations (28.5% saved)

localize7.0ms (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))))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_2165` `*-un-lft-identity_binary64_2143`
4×	`pow1_binary64_2204` `associate-r_binary64_2083` `add-exp-log_binary64_2181` `add-cube-cbrt_binary64_2178` `add-cbrt-cube_binary64_2179`
3×	`associate-l_binary64_2084`
2×	`add-log-exp_binary64_2182` `associate-*r/_binary64_2085`
1×	`distribute-rgt-in_binary64_2093` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `distribute-lft-out_binary64_2094` `unswap-sqr_binary64_2111` `flip3-+_binary64_2146` `flip-+_binary64_2117` `*-commutative_binary64_2074` `distribute-lft-in_binary64_2092`

Counts

2 → 30

Calls

2 calls:

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

series70.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

55.0ms	(*.f64 N (+.f64 N 1))
15.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify82.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4877	383
1	4877	383

prune80.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	32	4	36
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	33	6	39

Merged error: 0.2b

Counts

39 → 6

Compiler

Compiled 1175 to 958 computations (18.5% 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)

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_2174`
23×	`add-sqr-sqrt_binary64_2165`
15×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
11×	`pow1_binary64_2204`
9×	`pow1/3_binary64_2225`
6×	`associate-r_binary64_2083` `add-exp-log_binary64_2181` `associate-l_binary64_2084` `swap-sqr_binary64_2110`
4×	`add-log-exp_binary64_2182` `unswap-sqr_binary64_2111` `add-cbrt-cube_binary64_2179`
2×	`pow-sqr_binary64_2116` `pow-prod-up_binary64_2213` `pow-prod-down_binary64_2214`
1×	`pow2_binary64_2224` `pow-plus_binary64_2206` `cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `*-commutative_binary64_2074`

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)

series642.0ms (17.6%)

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt.f64 N)
167.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
153.0ms	(cbrt.f64 N)
143.0ms	(cbrt.f64 N)

simplify53.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5245	563

prune93.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	84	7	91

Merged error: 0.2b

Counts

91 → 7

Compiler

Compiled 1805 to 1087 computations (39.8% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`cbrt-prod_binary64_2174`
10×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
9×	`unpow-prod-down_binary64_2222`
5×	`pow1_binary64_2204` `add-exp-log_binary64_2181`
4×	`add-log-exp_binary64_2182` `add-cbrt-cube_binary64_2179` `pow1/3_binary64_2225`
3×	`pow-unpow_binary64_2220`
2×	`pow-pow_binary64_2215`
1×	`pow-to-exp_binary64_2212` `sqr-pow_binary64_2115` `pow-exp_binary64_2211`

Counts

4 → 55

Calls

4 calls:

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

series795.0ms (21.8%)

Counts

4 → 12

Calls

4 calls:

278.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 N)) 4)
240.0ms	(cbrt.f64 (*.f64 (cbrt.f64 N) (cbrt.f64 N)))
143.0ms	(cbrt.f64 N)
134.0ms	(cbrt.f64 N)

simplify82.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4705	558
1	4705	558

prune90.0ms (2.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	66	8	74

Merged error: 0.2b

Counts

74 → 8

Compiler

Compiled 1902 to 1068 computations (43.8% saved)

regimes36.0ms (1%)

Compiler: Compiled 338 to 260 computations (23.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample1.2s (32.1%)

Algorithm

1×

intervals

Results

435.0ms	2119×	body	2048	valid
181.0ms	4096×	body	128	valid
147.0ms	1019×	body	1024	valid
56.0ms	520×	body	512	valid
19.0ms	246×	body	256	valid

Compiler

Compiled 188 to 148 computations (21.3% saved)

Details

analyze1.0ms (0%)

sample31.0ms (0.8%)

simplify172.0ms (4.7%)

prune6.0ms (0.2%)

localize6.0ms (0.2%)

rewrite7.0ms (0.2%)

series36.0ms (1%)

simplify73.0ms (2%)

prune44.0ms (1.2%)

localize7.0ms (0.2%)

rewrite10.0ms (0.3%)

series70.0ms (1.9%)

simplify82.0ms (2.3%)

prune80.0ms (2.2%)

localize10.0ms (0.3%)

rewrite16.0ms (0.5%)

series642.0ms (17.6%)

simplify53.0ms (1.4%)

prune93.0ms (2.5%)

localize15.0ms (0.4%)

rewrite16.0ms (0.4%)

series795.0ms (21.8%)

simplify82.0ms (2.3%)

prune90.0ms (2.5%)

regimes36.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (32.1%)

Profiling