Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample19.0ms (0.9%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify97.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	14	16
1	14	16

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.0b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize7.0ms (0.3%)

Local error

Found 6 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))

rewrite56.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_4170`
41×	`times-frac_binary64_4176`
40×	`add-sqr-sqrt_binary64_4192`
24×	`add-cube-cbrt_binary64_4205`
12×	`distribute-lft-out_binary64_4121`
11×	`associate-/r*_binary64_4114`
9×	`add-exp-log_binary64_4208`
8×	`difference-of-squares_binary64_4139`
7×	`add-cbrt-cube_binary64_4206`
6×	`associate-/l*_binary64_4115` `distribute-lft-out--_binary64_4122`
5×	`add-log-exp_binary64_4209`
4×	`pow1_binary64_4231` `associate-/r/_binary64_4116` `difference-of-sqr-1_binary64_4140`
3×	`div-inv_binary64_4167` `div-exp_binary64_4221`
2×	`flip-+_binary64_4144` `frac-2neg_binary64_4181` `flip3-+_binary64_4173` `cbrt-undiv_binary64_4204` `clear-num_binary64_4169`
1×	`1-exp_binary64_4214` `flip3--_binary64_4174` `pow-flip_binary64_4244` `inv-pow_binary64_4255` `rec-exp_binary64_4220` `+-commutative_binary64_4100` `sum-log_binary64_4261` `flip--_binary64_4145` `frac-add_binary64_4178`

Counts

3 → 100

Calls

6 calls:

36.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
6.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))
0.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0ms	(/.f64 1 (-.f64 x 1))

series57.0ms (2.6%)

Counts

3 → 15

Calls

3 calls:

22.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
20.0ms	(/.f64 x (+.f64 x 1))
15.0ms	(/.f64 1 (-.f64 x 1))

Compiler

Compiled 243 to 213 computations (12.3% saved)

simplify88.0ms (4%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4917	1486
1	4917	1486

prune121.0ms (5.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	2	116

Error

Counts

116 → 2

Compiler

Compiled 1854 to 1367 computations (26.3% saved)

localize10.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 1 (+.f64 x -1))
0.0b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (+.f64 x -1)))
0.0b	(pow.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (+.f64 x -1))) 3)
0.0b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (+.f64 x -1))) 3))
0.0b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (+.f64 x -1)))
0.0b	(pow.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (+.f64 x -1))) 3)
0.0b	(/.f64 1 (+.f64 x -1))
0.0b	(/.f64 x (+.f64 x 1))

rewrite82.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Rules

111×	`*-un-lft-identity_binary64_4170`
51×	`times-frac_binary64_4176`
38×	`distribute-lft-out_binary64_4121`
30×	`add-sqr-sqrt_binary64_4192`
26×	`add-cube-cbrt_binary64_4205`
11×	`add-exp-log_binary64_4208`
9×	`add-cbrt-cube_binary64_4206` `cube-prod_binary64_4198` `unpow-prod-down_binary64_4249` `associate-/r*_binary64_4114`
6×	`pow1_binary64_4231` `associate-/l*_binary64_4115` `add-log-exp_binary64_4209`
5×	`div-inv_binary64_4167`
4×	`flip-+_binary64_4144` `associate-/r/_binary64_4116` `flip3-+_binary64_4173` `difference-of-sqr--1_binary64_4141`
3×	`pow-unpow_binary64_4247` `cube-div_binary64_4199` `div-exp_binary64_4221`
2×	`frac-2neg_binary64_4181` `cbrt-undiv_binary64_4204` `clear-num_binary64_4169` `frac-add_binary64_4178`
1×	`pow-to-exp_binary64_4239` `1-exp_binary64_4214` `cube-mult_binary64_4200` `sqr-pow_binary64_4142` `pow-flip_binary64_4244` `inv-pow_binary64_4255` `pow-exp_binary64_4238` `rec-exp_binary64_4220` `pow-pow_binary64_4242` `+-commutative_binary64_4100` `unpow3_binary64_4236` `rem-cube-cbrt_binary64_4193` `sum-log_binary64_4261`

Counts

4 → 130

Calls

8 calls:

33.0ms	(pow.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (+.f64 x -1))) 3)
27.0ms	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (+.f64 x -1)))
6.0ms	(/.f64 1 (+.f64 x -1))
5.0ms	(/.f64 x (+.f64 x 1))
0.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (+.f64 x -1))) 3))

series93.0ms (4.3%)

Counts

4 → 19

Calls

4 calls:

31.0ms	(pow.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (+.f64 x -1))) 3)
23.0ms	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (+.f64 x -1)))
22.0ms	(/.f64 x (+.f64 x 1))
17.0ms	(/.f64 1 (+.f64 x -1))

Compiler

Compiled 365 to 337 computations (7.7% saved)

simplify74.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4939	2257
1	4939	2257

prune159.0ms (7.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	149	2	151

Error

Counts

151 → 2

Compiler

Compiled 2810 to 2200 computations (21.7% saved)

localize9.0ms (0.4%)

Local error

Found 8 expressions with local error:

11.6b	(.f64 (/.f64 1 (-.f64 (.f64 x x) 1)) (+.f64 x 1))
0.5b	(/.f64 1 (-.f64 (*.f64 x x) 1))
0.0b	(/.f64 x (+.f64 x 1))
0.0b	(+.f64 (.f64 (/.f64 1 (-.f64 (.f64 x x) 1)) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(+.f64 (.f64 (/.f64 1 (-.f64 (.f64 x x) 1)) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(/.f64 x (+.f64 x 1))
0.5b	(/.f64 1 (-.f64 (*.f64 x x) 1))
11.6b	(.f64 (/.f64 1 (-.f64 (.f64 x x) 1)) (+.f64 x 1))

rewrite63.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64_4170`
50×	`times-frac_binary64_4176`
49×	`add-sqr-sqrt_binary64_4192`
35×	`add-cube-cbrt_binary64_4205`
24×	`associate-l_binary64_4111`
19×	`add-exp-log_binary64_4208`
14×	`difference-of-squares_binary64_4139`
13×	`add-cbrt-cube_binary64_4206`
10×	`associate-/r*_binary64_4114`
7×	`pow1_binary64_4231` `difference-of-sqr-1_binary64_4140`
6×	`flip-+_binary64_4144` `associate-/l*_binary64_4115` `associate-/r/_binary64_4116` `flip3-+_binary64_4173` `add-log-exp_binary64_4209`
5×	`distribute-lft-out_binary64_4121` `frac-add_binary64_4178` `div-exp_binary64_4221`
4×	`frac-times_binary64_4180` `associate-r/_binary64_4112` `prod-exp_binary64_4219` `associate-r*_binary64_4110`
3×	`div-inv_binary64_4167` `cbrt-undiv_binary64_4204` `unswap-sqr_binary64_4138`
2×	`distribute-lft-in_binary64_4119` `distribute-rgt-in_binary64_4120` `1-exp_binary64_4214` `flip3--_binary64_4174` `cbrt-unprod_binary64_4203` `associate-*l/_binary64_4113` `frac-2neg_binary64_4181` `rec-exp_binary64_4220` `associate-+l+_binary64_4103` `flip--_binary64_4145` `clear-num_binary64_4169`
1×	`pow-flip_binary64_4244` `inv-pow_binary64_4255` `+-commutative_binary64_4100` `*-commutative_binary64_4101` `sum-log_binary64_4261` `pow-prod-down_binary64_4241`

Counts

4 → 149

Calls

8 calls:

18.0ms	(+.f64 (.f64 (/.f64 1 (-.f64 (.f64 x x) 1)) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
16.0ms	(.f64 (/.f64 1 (-.f64 (.f64 x x) 1)) (+.f64 x 1))
7.0ms	(/.f64 1 (-.f64 (*.f64 x x) 1))
5.0ms	(/.f64 x (+.f64 x 1))
0.0ms	(+.f64 (.f64 (/.f64 1 (-.f64 (.f64 x x) 1)) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))

series87.0ms (4%)

Counts

4 → 19

Calls

4 calls:

28.0ms	(+.f64 (.f64 (/.f64 1 (-.f64 (.f64 x x) 1)) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
21.0ms	(/.f64 x (+.f64 x 1))
19.0ms	(/.f64 1 (-.f64 (*.f64 x x) 1))
18.0ms	(.f64 (/.f64 1 (-.f64 (.f64 x x) 1)) (+.f64 x 1))

Compiler

Compiled 416 to 345 computations (17.1% saved)

simplify102.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5005	2389

prune185.0ms (8.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	168	2	170

Error

Counts

170 → 2

Compiler

Compiled 3548 to 2430 computations (31.5% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	88	187
1	88	187

regimes21.0ms (1%)

Compiler: Compiled 131 to 109 computations (16.8% saved)

bsearch0.0ms (0%)

regimes21.0ms (1%)

Compiler: Compiled 117 to 97 computations (17.1% saved)

bsearch0.0ms (0%)

regimes15.0ms (0.7%)

Compiler: Compiled 66 to 57 computations (13.6% saved)

bsearch0.0ms (0%)

regimes27.0ms (1.3%)

Compiler: Compiled 44 to 41 computations (6.8% saved)

bsearch33.0ms (1.5%)

Steps

Iters	Range		Point
11	2.307904188735251e-08	144708799448604.4	1.0121555451085444
10	-187239288387.4265	-5.458083995085865e-08	-1.0171651250769214

Compiler

Compiled 1 to 1 computations (0% saved)

regimes17.0ms (0.8%)

Compiler: Compiled 5 to 8 computations (-60% saved)

bsearch31.0ms (1.4%)

Steps

Iters	Range		Point
11	2.307904188735251e-08	144708799448604.4	1.0121555451085444
10	-187239288387.4265	-5.458083995085865e-08	-1.0171651250769214

Compiler

Compiled 1 to 1 computations (0% saved)

regimes7.0ms (0.3%)

Accuracy

Total 0.5b remaining (99.9%)

Threshold costs 0.5b (99.9%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch5.0ms (0.2%)

Compiler: Compiled 71 to 60 computations (15.5% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	69	102
1	69	102

end0.0ms (0%)

sample665.0ms (30.7%)

Algorithm

1×

intervals

Results

251.0ms

8000×

body

128

valid

Compiler

Compiled 212 to 178 computations (16% saved)

Pareto

0.9371358839029874

Details

analyze4.0ms (0.2%)

sample19.0ms (0.9%)

simplify97.0ms (4.5%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

rewrite56.0ms (2.6%)

series57.0ms (2.6%)

simplify88.0ms (4%)

prune121.0ms (5.6%)

localize10.0ms (0.4%)

rewrite82.0ms (3.8%)

series93.0ms (4.3%)

simplify74.0ms (3.4%)

prune159.0ms (7.4%)

localize9.0ms (0.4%)

rewrite63.0ms (2.9%)

series87.0ms (4%)

simplify102.0ms (4.7%)

prune185.0ms (8.5%)

simplify5.0ms (0.2%)

regimes21.0ms (1%)

bsearch0.0ms (0%)

regimes21.0ms (1%)

bsearch0.0ms (0%)

regimes15.0ms (0.7%)

bsearch0.0ms (0%)

regimes27.0ms (1.3%)

bsearch33.0ms (1.5%)

regimes17.0ms (0.8%)

bsearch31.0ms (1.4%)

regimes7.0ms (0.3%)

bsearch5.0ms (0.2%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample665.0ms (30.7%)

Profiling