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)

sample31.0ms (1.3%)

Algorithm

1×

intervals

Results

15.0ms	75×	body	2048	valid
5.0ms	133×	body	128	valid
4.0ms	28×	body	1024	valid
1.0ms	12×	body	512	valid
1.0ms	8×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify107.0ms (4.4%)

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: 12.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481`
3×	`cancel-sign-sub-inv_binary64_1408` `add-cube-cbrt_binary64_1477`
2×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
1×	`sub-neg_binary64_1435` `flip3--_binary64_1446` `diff-atan_binary64_1599` `flip--_binary64_1417` `diff-log_binary64_1534` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`

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 (0.7%)

Counts

2 → 6

Calls

2 calls:

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

simplify68.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4998	391
1	4998	391

prune22.0ms (0.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.3b

Counts

31 → 1

Compiler

Compiled 351 to 229 computations (34.8% saved)

localize9.0ms (0.4%)

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 (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
4×	`associate-r_binary64_1382` `add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
3×	`associate-l_binary64_1383`
2×	`associate-*r/_binary64_1384` `add-log-exp_binary64_1481`
1×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `distribute-lft-in_binary64_1391` `flip3-+_binary64_1445` `distribute-rgt-in_binary64_1392` `flip-+_binary64_1416` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`

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))))

series33.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

25.0ms	(*.f64 N (+.f64 N 1))
8.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify71.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4927	383
1	4927	383

prune38.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	32	4	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	5	37

Merged error: 0.3b

Counts

37 → 5

Compiler

Compiled 557 to 437 computations (21.5% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (*.f64 N (+.f64 1 N))))
17.7b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
17.7b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
17.7b	(cbrt.f64 (*.f64 N (+.f64 1 N)))

rewrite27.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*r/_binary64_1384`
18×	`cbrt-div_binary64_1474`
11×	`pow1_binary64_1503`
10×	`add-sqr-sqrt_binary64_1464`
9×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/3_binary64_1524`
8×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
7×	`cbrt-prod_binary64_1473`
6×	`add-exp-log_binary64_1480`
4×	`associate-r_binary64_1382` `add-cbrt-cube_binary64_1478` `swap-sqr_binary64_1409` `associate-l_binary64_1383` `add-log-exp_binary64_1481` `frac-times_binary64_1452`
2×	`pow-prod-down_binary64_1513` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512` `associate-*l/_binary64_1385`
1×	`pow2_binary64_1523` `cbrt-unprod_binary64_1475` `pow-plus_binary64_1505` `*-commutative_binary64_1373` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`

Counts

4 → 72

Calls

4 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (*.f64 N (+.f64 1 N))))
4.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
4.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
4.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))

series151.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (*.f64 N (+.f64 1 N))))
37.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
37.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
33.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))

simplify67.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4960	1357
1	4960	1357

prune128.0ms (5.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	83	6	89

Merged error: 0.3b

Counts

89 → 6

Compiler

Compiled 2509 to 1930 computations (23.1% saved)

localize23.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 N (+.f64 N 1)))) 4)
17.7b	(cbrt.f64 (*.f64 N (+.f64 N 1)))
17.7b	(cbrt.f64 (*.f64 N (+.f64 N 1)))
17.7b	(cbrt.f64 (*.f64 N (+.f64 1 N)))

rewrite24.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`cbrt-prod_binary64_1473`
7×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442` `unpow-prod-down_binary64_1521`
6×	`associate-*r/_binary64_1384` `cbrt-div_binary64_1474`
5×	`add-exp-log_binary64_1480` `pow1_binary64_1503`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `pow1/3_binary64_1524`
3×	`pow-unpow_binary64_1519` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`pow-pow_binary64_1514`
1×	`pow-exp_binary64_1510` `sqr-pow_binary64_1414` `pow-to-exp_binary64_1511`

Counts

4 → 55

Calls

4 calls:

5.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
5.0ms	(cbrt.f64 (*.f64 N (+.f64 N 1)))
5.0ms	(cbrt.f64 (*.f64 N (+.f64 N 1)))
4.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 N (+.f64 N 1)))) 4)

series238.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 N (+.f64 N 1)))) 4)
38.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
37.0ms	(cbrt.f64 (*.f64 N (+.f64 N 1)))
33.0ms	(cbrt.f64 (*.f64 N (+.f64 N 1)))

simplify50.0ms (2%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4902	1225
1	4902	1225

prune128.0ms (5.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	67	6	73

Merged error: 0.3b

Counts

73 → 6

Compiler

Compiled 2478 to 2008 computations (19% saved)

regimes43.0ms (1.7%)

Compiler: Compiled 430 to 348 computations (19.1% 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%)

sample1.1s (46.5%)

Algorithm

1×

intervals

Results

402.0ms	2100×	body	2048	valid
163.0ms	4204×	body	128	valid
132.0ms	995×	body	1024	valid
47.0ms	466×	body	512	valid
17.0ms	235×	body	256	valid

Compiler

Compiled 234 to 191 computations (18.4% saved)

Details

analyze2.0ms (0.1%)

sample31.0ms (1.3%)

simplify107.0ms (4.4%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

rewrite6.0ms (0.2%)

series16.0ms (0.7%)

simplify68.0ms (2.8%)

prune22.0ms (0.9%)

localize9.0ms (0.4%)

rewrite9.0ms (0.4%)

series33.0ms (1.3%)

simplify71.0ms (2.9%)

prune38.0ms (1.6%)

localize11.0ms (0.4%)

rewrite27.0ms (1.1%)

series151.0ms (6.2%)

simplify67.0ms (2.7%)

prune128.0ms (5.2%)

localize23.0ms (0.9%)

rewrite24.0ms (1%)

series238.0ms (9.7%)

simplify50.0ms (2%)

prune128.0ms (5.2%)

regimes43.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (46.5%)

Profiling