Details

analyze108.0ms (3.2%)

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)

sample32.0ms (0.9%)

Algorithm

1×

intervals

Results

12.0ms	64×	body	2048	valid
5.0ms	141×	body	128	valid
5.0ms	34×	body	1024	valid
2.0ms	14×	body	512	valid
0.0ms	3×	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

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

13.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
0.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite38.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

13.2b

Rules

5×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
4×	`add-log-exp_binary64_1140`
3×	`add-cube-cbrt_binary64_1136` `cancel-sign-sub-inv_binary64_1067`
2×	`pow1_binary64_1162` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
1×	`diff-atan_binary64_1258` `diff-log_binary64_1193` `flip3--_binary64_1105` `sub-neg_binary64_1094` `flip--_binary64_1076` `difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053`

Counts

2 → 24

Calls

2 calls:

7.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
2.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 348 to 227 computations (34.8% saved)

series31.0ms (0.9%)

Error

13.8b

Counts

2 → 6

Calls

2 calls:

20.0ms	(-.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)

simplify93.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4998	391
1	4998	391

prune22.0ms (0.6%)

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

Error

0.3b

Counts

31 → 1

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))))

rewrite44.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

6×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
4×	`pow1_binary64_1162` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `add-cube-cbrt_binary64_1136` `associate-r_binary64_1041`
3×	`associate-l_binary64_1042`
2×	`add-log-exp_binary64_1140` `associate-*r/_binary64_1043`
1×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `flip3-+_binary64_1104` `flip-+_binary64_1075` `distribute-lft-out_binary64_1052` `*-commutative_binary64_1032`

Counts

2 → 30

Calls

2 calls:

8.0ms	(*.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)

series69.0ms (2%)

Error

0.3b

Counts

2 → 9

Calls

2 calls:

48.0ms	(*.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)

simplify94.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4927	392
1	4927	392

prune49.0ms (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	2	40

Error

0.3b

Counts

40 → 2

Compiler

Compiled 507 to 318 computations (37.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
0.6b	(.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))))))
13.8b	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
13.8b	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))

rewrite160.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

30×	`add-sqr-sqrt_binary64_1123`
24×	`sqrt-prod_binary64_1117`
21×	`pow1_binary64_1162`
14×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
10×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119`
8×	`swap-sqr_binary64_1068`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-l_binary64_1042` `associate-r_binary64_1041`
5×	`pow-prod-up_binary64_1171`
4×	`add-log-exp_binary64_1140` `rem-sqrt-square_binary64_1114` `unswap-sqr_binary64_1069`
3×	`pow-prod-down_binary64_1172` `pow-sqr_binary64_1074`
1×	`pow2_binary64_1182` `pow-plus_binary64_1164` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `sqrt-unprod_binary64_1121` `sqr-abs_binary64_1116` `rem-square-sqrt_binary64_1113` `*-commutative_binary64_1032`

Counts

4 → 83

Calls

4 calls:

9.0ms	(.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)

series117.0ms (3.4%)

Error

0.3b

Counts

4 → 12

Calls

4 calls:

36.0ms	(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)))))
17.0ms	(.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))))))
15.0ms	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))

Compiler

Compiled 648 to 512 computations (21% saved)

simplify101.0ms (3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5095	1475

prune130.0ms (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	92	5	97

Error

0.3b

Counts

97 → 5

Compiler

Compiled 2058 to 1334 computations (35.2% saved)

localize21.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
0.3b	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
13.8b	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
13.8b	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))

rewrite99.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

8×	`add-sqr-sqrt_binary64_1123`
6×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `sqrt-prod_binary64_1117` `*-un-lft-identity_binary64_1101`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
2×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114`

Counts

4 → 40

Calls

4 calls:

3.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
2.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
1.0ms	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
1.0ms	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))

Compiler

Compiled 1356 to 934 computations (31.1% saved)

series144.0ms (4.2%)

Error

0.3b

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
34.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
21.0ms	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
17.0ms	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))

Compiler

Compiled 900 to 734 computations (18.4% saved)

simplify92.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4895	862
1	4895	862

prune77.0ms (2.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	52	5	57

Error

0.3b

Counts

57 → 5

Compiler

Compiled 1552 to 1074 computations (30.8% saved)

regimes109.0ms (3.2%)

Accuracy

Total 0.1b remaining (12.4%)

Threshold costs 0.1b (12.4%)

Compiler

Compiled 1042 to 788 computations (24.4% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample1.7s (51.2%)

Algorithm

1×

intervals

Results

448.0ms	2102×	body	2048	valid
163.0ms	4173×	body	128	valid
150.0ms	989×	body	1024	valid
54.0ms	509×	body	512	valid
17.0ms	227×	body	256	valid

Compiler

Compiled 525 to 399 computations (24% saved)

Details

analyze108.0ms (3.2%)

sample32.0ms (0.9%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite38.0ms (1.1%)

series31.0ms (0.9%)

simplify93.0ms (2.7%)

prune22.0ms (0.6%)

localize5.0ms (0.2%)

rewrite44.0ms (1.3%)

series69.0ms (2%)

simplify94.0ms (2.8%)

prune49.0ms (1.4%)

localize8.0ms (0.2%)

rewrite160.0ms (4.7%)

series117.0ms (3.4%)

simplify101.0ms (3%)

prune130.0ms (3.8%)

localize21.0ms (0.6%)

rewrite99.0ms (2.9%)

series144.0ms (4.2%)

simplify92.0ms (2.7%)

prune77.0ms (2.3%)

regimes109.0ms (3.2%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.7s (51.2%)

Profiling