Details

analyze1.0s (13.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
14.9%	84.9%	0.2%	13
16.2%	83.5%	0.3%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample33.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	223×	body	128	valid
2.0ms	42×	body	128	invalid
1.0ms	9×	body	1024	valid
1.0ms	12×	body	512	valid
1.0ms	11×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify180.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4915	19
1	4915	19

prune2.0ms (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

28.9b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y x) (-.f64 z t))
2.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
22.1b	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_16446` `add-sqr-sqrt_binary64_16468`
13×	`flip3--_binary64_16450` `flip--_binary64_16421`
10×	`add-exp-log_binary64_16484` `add-cbrt-cube_binary64_16482`
9×	`add-cube-cbrt_binary64_16481`
8×	`associate-/l/_binary64_16393` `frac-times_binary64_16456`
6×	`cancel-sign-sub-inv_binary64_16412`
5×	`times-frac_binary64_16452` `pow1_binary64_16507` `add-log-exp_binary64_16485` `associate-r_binary64_16386` `associate-l_binary64_16387` `associate-/r*_binary64_16390`
4×	`associate-r/_binary64_16388` `distribute-lft-out--_binary64_16398` `distribute-rgt-in_binary64_16396` `distribute-lft-in_binary64_16395` `associate-l/_binary64_16389` `difference-of-squares_binary64_16415`
2×	`cbrt-undiv_binary64_16480` `cbrt-unprod_binary64_16479` `prod-exp_binary64_16495` `sub-neg_binary64_16439` `associate-/r/_binary64_16392` `div-exp_binary64_16497`
1×	`+-commutative_binary64_16376` `clear-num_binary64_16445` `unswap-sqr_binary64_16414` `distribute-lft-out_binary64_16397` `pow-prod-down_binary64_16517` `-commutative_binary64_16377` `div-inv_binary64_16443` `flip3-+_binary64_16449` `associate-/l_binary64_16391` `sum-log_binary64_16537` `flip-+_binary64_16420` `frac-2neg_binary64_16457`

Counts

3 → 85

Calls

3 calls:

16.0ms	(*.f64 (-.f64 y x) (-.f64 z t))
14.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
8.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

series429.0ms (5.7%)

Counts

3 → 9

Calls

3 calls:

234.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
162.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
33.0ms	(*.f64 (-.f64 y x) (-.f64 z t))

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4998	1705
1	4998	1705

prune100.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Error

3.2b

Counts

95 → 10

Compiler

Compiled 2072 to 535 computations (74.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
1.9b	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
2.5b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64_16468`
73×	`*-un-lft-identity_binary64_16446`
51×	`times-frac_binary64_16452`
31×	`associate-r_binary64_16386`
27×	`add-cube-cbrt_binary64_16481`
23×	`distribute-lft-out--_binary64_16398` `difference-of-squares_binary64_16415`
10×	`add-exp-log_binary64_16484` `add-cbrt-cube_binary64_16482`
5×	`pow1_binary64_16507` `add-log-exp_binary64_16485` `associate-/l_binary64_16391` `flip3--_binary64_16450` `associate-l_binary64_16387` `flip--_binary64_16421` `associate-/r_binary64_16390`
4×	`associate-/r/_binary64_16392`
2×	`cbrt-undiv_binary64_16480` `unswap-sqr_binary64_16414` `associate-/l/_binary64_16393` `cbrt-unprod_binary64_16479` `div-inv_binary64_16443` `prod-exp_binary64_16495` `associate-*l/_binary64_16389` `div-exp_binary64_16497` `frac-times_binary64_16456`
1×	`associate-r/_binary64_16388` `div-sub_binary64_16451` `+-commutative_binary64_16376` `clear-num_binary64_16445` `pow-prod-down_binary64_16517` `-commutative_binary64_16377` `flip3-+_binary64_16449` `sum-log_binary64_16537` `flip-+_binary64_16420` `frac-2neg_binary64_16457`

Counts

3 → 119

Calls

3 calls:

19.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
8.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
4.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))

series453.0ms (6%)

Counts

3 → 9

Calls

3 calls:

235.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))
176.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
42.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5753	2426

prune113.0ms (1.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	124	14	138

Error

3.2b

Counts

138 → 14

Compiler

Compiled 2956 to 657 computations (77.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
2.3b	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
2.5b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))

rewrite112.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

330×	`times-frac_binary64_16452`
323×	`*-un-lft-identity_binary64_16446`
321×	`add-sqr-sqrt_binary64_16468`
113×	`add-cube-cbrt_binary64_16481`
104×	`distribute-lft-out--_binary64_16398` `difference-of-squares_binary64_16415`
36×	`associate-/r*_binary64_16390`
15×	`associate-/r/_binary64_16392`
10×	`add-exp-log_binary64_16484` `associate-/l*_binary64_16391` `add-cbrt-cube_binary64_16482`
9×	`flip3--_binary64_16450` `flip--_binary64_16421`
8×	`div-inv_binary64_16443`
5×	`add-log-exp_binary64_16485`
4×	`cbrt-undiv_binary64_16480` `associate-/l/_binary64_16393` `div-exp_binary64_16497`
3×	`div-sub_binary64_16451` `pow1_binary64_16507`
2×	`clear-num_binary64_16445` `frac-2neg_binary64_16457`
1×	`+-commutative_binary64_16376` `distribute-lft-out_binary64_16397` `flip3-+_binary64_16449` `sum-log_binary64_16537` `flip-+_binary64_16420` `associate-+r-_binary64_16380`

Counts

3 → 274

Calls

3 calls:

47.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
17.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
9.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

series498.0ms (6.6%)

Counts

3 → 9

Calls

3 calls:

230.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
228.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
40.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

simplify123.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5145	8451

prune215.0ms (2.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	280	3	283
Fresh	4	8	12
Picked	1	0	1
Done	1	0	1
Total	286	11	297

Error

3.0b

Counts

297 → 11

Compiler

Compiled 7204 to 1042 computations (85.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.5b	(+.f64 x (.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))))
2.7b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
2.7b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
2.7b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`*-un-lft-identity_binary64_16446` `add-sqr-sqrt_binary64_16468`
93×	`cbrt-prod_binary64_16477`
75×	`times-frac_binary64_16452`
37×	`add-cube-cbrt_binary64_16481`
30×	`distribute-lft-out--_binary64_16398` `difference-of-squares_binary64_16415`
6×	`add-log-exp_binary64_16485` `associate-/r/_binary64_16392`
4×	`add-exp-log_binary64_16484` `pow1_binary64_16507` `add-cbrt-cube_binary64_16482`
3×	`pow1/3_binary64_16528` `div-inv_binary64_16443` `cbrt-div_binary64_16478` `flip3--_binary64_16450` `flip--_binary64_16421`
1×	`+-commutative_binary64_16376` `flip3-+_binary64_16449` `sum-log_binary64_16537` `flip-+_binary64_16420`

Counts

4 → 131

Calls

4 calls:

8.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
8.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
8.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
4.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))))

series1.1s (15.1%)

Counts

4 → 12

Calls

4 calls:

298.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
296.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
282.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
260.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))))

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5080	3639

prune141.0ms (1.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	143	11	154

Error

3.0b

Counts

154 → 11

Compiler

Compiled 5723 to 767 computations (86.6% saved)

regimes835.0ms (11.1%)

Accuracy

Total 4.2b remaining (51.3%)

Threshold costs 0b (0%)

Compiler

Compiled 7242 to 4750 computations (34.4% saved)

bsearch3.0ms (0%)

Compiler: Compiled 13 to 11 computations (15.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	88	88
1	88	88

end0.0ms (0%)

sample1.7s (22.6%)

Algorithm

1×

intervals

Results

286.0ms	6667×	body	128	valid
64.0ms	412×	body	1024	valid
59.0ms	509×	body	512	valid
56.0ms	1219×	body	128	invalid
27.0ms	351×	body	256	valid
11.0ms	61×	body	2048	valid

Compiler

Compiled 1312 to 842 computations (35.8% saved)

Details

analyze1.0s (13.8%)

sample33.0ms (0.4%)

simplify180.0ms (2.4%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite45.0ms (0.6%)

series429.0ms (5.7%)

simplify64.0ms (0.9%)

prune100.0ms (1.3%)

localize10.0ms (0.1%)

rewrite45.0ms (0.6%)

series453.0ms (6%)

simplify70.0ms (0.9%)

prune113.0ms (1.5%)

localize9.0ms (0.1%)

rewrite112.0ms (1.5%)

series498.0ms (6.6%)

simplify123.0ms (1.6%)

prune215.0ms (2.9%)

localize18.0ms (0.2%)

rewrite45.0ms (0.6%)

series1.1s (15.1%)

simplify76.0ms (1%)

prune141.0ms (1.9%)

regimes835.0ms (11.1%)

bsearch3.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.7s (22.6%)

Profiling