Details

analyze221.0ms (2.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample27.0ms (0.3%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify142.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5241	29

prune4.0ms (0%)

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

14.0b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
1.3b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
3.7b	(-.f64 (.f64 b b) (.f64 a a))
8.9b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite537.0ms (6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

251×	`times-frac_binary64_766`
178×	`add-sqr-sqrt_binary64_782`
153×	`*-un-lft-identity_binary64_760`
121×	`add-cube-cbrt_binary64_795`
58×	`associate-l_binary64_701`
46×	`difference-of-squares_binary64_729`
40×	`cancel-sign-sub-inv_binary64_726`
22×	`div-inv_binary64_757`
19×	`associate-r_binary64_700`
18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
14×	`distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `distribute-lft-out--_binary64_712`
13×	`associate-/l*_binary64_705`
8×	`add-log-exp_binary64_799`
6×	`pow1_binary64_821` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `flip3--_binary64_764` `flip--_binary64_735`
4×	`sub-neg_binary64_753` `associate-/r/_binary64_706` `associate-/r*_binary64_704`
3×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `frac-sub_binary64_769` `frac-times_binary64_770` `unswap-sqr_binary64_728` `associate-*r/_binary64_702`
2×	`diff-log_binary64_852`
1×	`pow-prod-down_binary64_831` `associate-l/_binary64_703` `-commutative_binary64_691` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

Counts

4 → 270

Calls

4 calls:

49.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
15.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

Compiler

Compiled 8765 to 4259 computations (51.4% saved)

series513.0ms (5.7%)

Error

9.9b

Counts

4 → 63

Calls

4 calls:

154.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
139.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
90.0ms	(-.f64 (.f64 b b) (.f64 a a))
61.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 3183 to 2466 computations (22.5% saved)

simplify134.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4991	9357
1	4991	9357

prune451.0ms (5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	325	8	333
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	326	9	335

Error

0.0b

Counts

335 → 9

Compiler

Compiled 9510 to 4536 computations (52.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (-.f64 b a))
0.2b	(/.f64 PI.f64 (+.f64 b a))
0.2b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
0.3b	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))

rewrite362.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

87×	`*-un-lft-identity_binary64_760`
86×	`add-sqr-sqrt_binary64_782`
73×	`times-frac_binary64_766`
43×	`add-cube-cbrt_binary64_795`
37×	`associate-l_binary64_701`
34×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
22×	`associate-r_binary64_700`
16×	`frac-times_binary64_770` `difference-of-squares_binary64_729`
14×	`distribute-lft-out--_binary64_712`
12×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
11×	`pow1_binary64_821`
10×	`associate-l/_binary64_703` `associate-r/_binary64_702`
9×	`associate-/r*_binary64_704`
8×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `flip3--_binary64_764` `flip--_binary64_735` `div-inv_binary64_757` `associate-/r/_binary64_706`
7×	`distribute-lft-out_binary64_711`
6×	`frac-sub_binary64_769` `associate-/l*_binary64_705`
4×	`pow-prod-down_binary64_831` `add-log-exp_binary64_799`
2×	`unswap-sqr_binary64_728` `*-commutative_binary64_691` `flip3-+_binary64_763` `flip-+_binary64_734` `frac-2neg_binary64_771` `clear-num_binary64_759`

Counts

4 → 188

Calls

4 calls:

49.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
29.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
5.0ms	(/.f64 1/2 (-.f64 b a))
5.0ms	(/.f64 PI.f64 (+.f64 b a))

Compiler

Compiled 5512 to 2805 computations (49.1% saved)

series540.0ms (6%)

Error

0.0b

Counts

4 → 78

Calls

4 calls:

138.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
115.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
97.0ms	(/.f64 PI.f64 (+.f64 b a))
95.0ms	(/.f64 1/2 (-.f64 b a))

Compiler

Compiled 4320 to 3090 computations (28.5% saved)

simplify107.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

266 → 266

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4998	6023
1	4998	6023

prune326.0ms (3.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	261	5	266
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	267	8	275

Error

Counts

275 → 8

Compiler

Compiled 6984 to 3431 computations (50.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 1/2 (/.f64 PI.f64 (+.f64 a b)))
0.2b	(/.f64 (.f64 1/2 (/.f64 PI.f64 (+.f64 a b))) (.f64 a b))
0.2b	(/.f64 PI.f64 (+.f64 a b))

rewrite116.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

35×	`*-un-lft-identity_binary64_760`
31×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
26×	`add-sqr-sqrt_binary64_782` `times-frac_binary64_766`
21×	`add-cube-cbrt_binary64_795`
18×	`associate-r_binary64_700`
10×	`div-exp_binary64_811` `cbrt-undiv_binary64_794`
9×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
7×	`distribute-lft-out_binary64_711`
5×	`pow1_binary64_821` `associate-/r*_binary64_704`
4×	`associate-/r/_binary64_706` `associate-/l*_binary64_705`
3×	`add-log-exp_binary64_799` `div-inv_binary64_757` `associate-l_binary64_701`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-*r/_binary64_702` `unswap-sqr_binary64_728`
1×	`associate-/l/_binary64_707` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

3 → 96

Calls

3 calls:

10.0ms	(*.f64 1/2 (/.f64 PI.f64 (+.f64 a b)))
10.0ms	(/.f64 (.f64 1/2 (/.f64 PI.f64 (+.f64 a b))) (.f64 a b))
5.0ms	(/.f64 PI.f64 (+.f64 a b))

Compiler

Compiled 1854 to 618 computations (66.7% saved)

series411.0ms (4.6%)

Error

Counts

3 → 72

Calls

3 calls:

134.0ms	(/.f64 (.f64 1/2 (/.f64 PI.f64 (+.f64 a b))) (.f64 a b))
112.0ms	(*.f64 1/2 (/.f64 PI.f64 (+.f64 a b)))
87.0ms	(/.f64 PI.f64 (+.f64 a b))

Compiler

Compiled 3408 to 2349 computations (31.1% saved)

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4964	3423
1	4964	3423

prune140.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	170	6	176

Error

Counts

176 → 6

Compiler

Compiled 3125 to 1120 computations (64.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (-.f64 b a))
0.2b	(/.f64 PI.f64 (+.f64 a b))
0.2b	(.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 PI.f64 (+.f64 a b))) (/.f64 1/2 (-.f64 b a)))
0.3b	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 PI.f64 (+.f64 a b)))

rewrite324.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

87×	`*-un-lft-identity_binary64_760`
86×	`add-sqr-sqrt_binary64_782`
73×	`times-frac_binary64_766`
43×	`add-cube-cbrt_binary64_795`
39×	`associate-r_binary64_700`
34×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
20×	`associate-l_binary64_701`
16×	`frac-times_binary64_770` `associate-*l/_binary64_703` `difference-of-squares_binary64_729`
14×	`distribute-lft-out--_binary64_712`
12×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
11×	`pow1_binary64_821`
9×	`associate-/r*_binary64_704`
8×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `flip3--_binary64_764` `flip--_binary64_735` `div-inv_binary64_757` `associate-/r/_binary64_706`
7×	`distribute-lft-out_binary64_711`
6×	`frac-sub_binary64_769` `associate-/l*_binary64_705`
4×	`pow-prod-down_binary64_831` `add-log-exp_binary64_799` `associate-*r/_binary64_702`
2×	`unswap-sqr_binary64_728` `flip3-+_binary64_763` `flip-+_binary64_734` `*-commutative_binary64_691` `frac-2neg_binary64_771` `clear-num_binary64_759`

Counts

4 → 188

Calls

4 calls:

33.0ms	(.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 PI.f64 (+.f64 a b))) (/.f64 1/2 (-.f64 b a)))
29.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 PI.f64 (+.f64 a b)))
5.0ms	(/.f64 1/2 (-.f64 b a))
5.0ms	(/.f64 PI.f64 (+.f64 a b))

Compiler

Compiled 5512 to 2786 computations (49.5% saved)

series571.0ms (6.4%)

Error

Counts

4 → 96

Calls

4 calls:

147.0ms	(.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 PI.f64 (+.f64 a b))) (/.f64 1/2 (-.f64 b a)))
116.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 PI.f64 (+.f64 a b)))
96.0ms	(/.f64 1/2 (-.f64 b a))
92.0ms	(/.f64 PI.f64 (+.f64 a b))

Compiler

Compiled 5334 to 3745 computations (29.8% saved)

simplify129.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4957	6895
1	4957	6895

prune340.0ms (3.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	284	6	290

Error

Counts

290 → 6

Compiler

Compiled 7442 to 3549 computations (52.3% saved)

regimes608.0ms (6.8%)

Accuracy

Total 0.2b remaining (99.9%)

Threshold costs 0.2b (99.9%)

Compiler

Compiled 8182 to 6168 computations (24.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	17
1	13	17

end0.0ms (0%)

sample2.8s (31.4%)

Algorithm

1×

intervals

Results

453.0ms	8000×	body	128	valid
24.0ms	330×	body	128	invalid

Compiler

Compiled 2745 to 2071 computations (24.6% saved)

Details

analyze221.0ms (2.5%)

sample27.0ms (0.3%)

simplify142.0ms (1.6%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite537.0ms (6%)

series513.0ms (5.7%)

simplify134.0ms (1.5%)

prune451.0ms (5%)

localize14.0ms (0.2%)

rewrite362.0ms (4%)

series540.0ms (6%)

simplify107.0ms (1.2%)

prune326.0ms (3.6%)

localize7.0ms (0.1%)

rewrite116.0ms (1.3%)

series411.0ms (4.6%)

simplify81.0ms (0.9%)

prune140.0ms (1.6%)

localize12.0ms (0.1%)

rewrite324.0ms (3.6%)

series571.0ms (6.4%)

simplify129.0ms (1.4%)

prune340.0ms (3.8%)

regimes608.0ms (6.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (31.4%)

Profiling