Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.6%	25.4%	0
0%	74.6%	25.4%	1
37.3%	37.3%	25.4%	2
37.3%	18.7%	44%	3
46.7%	9.3%	44%	4
46.7%	4.7%	48.7%	5
49%	2.3%	48.7%	6
49%	1.2%	49.8%	7
49.6%	0.6%	49.8%	8
49.9%	0.3%	49.8%	9
49.9%	0.1%	50%	10
49.9%	0.1%	50.1%	11
49.9%	0%	50.1%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample32.0ms (1.3%)

Algorithm

1×

intervals

Results

14.0ms	119×	body	1024	valid
5.0ms	88×	body	512	valid
3.0ms	256×	pre	128	true
2.0ms	12×	body	2048	valid
1.0ms	29×	body	256	valid
0.0ms	8×	body	128	valid

Compiler

Compiled 11 to 11 computations (0% saved)

simplify100.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	6
1	9	6

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

59.7b

Counts

2 → 1

Compiler

Compiled 8 to 8 computations (0% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.7b	(-.f64 (exp.f64 x) 1)
2.7b	(-.f64 (exp.f64 x) 1)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_782`
5×	`*-un-lft-identity_binary64_760`
3×	`cancel-sign-sub-inv_binary64_726` `add-log-exp_binary64_799`
2×	`add-cube-cbrt_binary64_795` `difference-of-squares_binary64_729`
1×	`diff-log_binary64_852` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712` `pow1_binary64_821` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

1 → 18

Calls

2 calls:

5.0ms	(-.f64 (exp.f64 x) 1)
0.0ms	(-.f64 (exp.f64 x) 1)

series19.0ms (0.7%)

Counts

1 → 6

Calls

1 calls:

18.0ms

(-.f64 (exp.f64 x) 1)

Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify78.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4922	232
1	4922	232

prune42.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	2	25

Error

Counts

25 → 2

Compiler

Compiled 220 to 138 computations (37.3% saved)

localize10.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
0.0b	(.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))))
0.0b	(+.f64 1/6 (*.f64 x 1/24))
0.0b	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
0.0b	(.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))))
0.0b	(+.f64 1/6 (*.f64 x 1/24))
0.3b	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
0.3b	(*.f64 x 1/24)

rewrite25.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `pow1_binary64_821` `add-sqr-sqrt_binary64_782`
9×	`-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `associate-l*_binary64_701`
7×	`associate-r_binary64_700`
6×	`add-log-exp_binary64_799` `associate-*r/_binary64_702`
5×	`prod-exp_binary64_809` `distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `*-commutative_binary64_691`
2×	`unswap-sqr_binary64_728`
1×	`+-commutative_binary64_690` `sum-log_binary64_851`

Counts

4 → 75

Calls

8 calls:

7.0ms	(.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))))
6.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
4.0ms	(*.f64 x 1/24)
3.0ms	(+.f64 1/6 (*.f64 x 1/24))
0.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))

series128.0ms (5%)

Counts

4 → 20

Calls

4 calls:

49.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
36.0ms	(.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))))
27.0ms	(+.f64 1/6 (*.f64 x 1/24))
16.0ms	(*.f64 x 1/24)

Compiler

Compiled 454 to 347 computations (23.6% saved)

simplify75.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4868	1156
1	4868	1156

prune84.0ms (3.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	95	2	97

Error

Counts

97 → 2

Compiler

Compiled 1789 to 1244 computations (30.5% saved)

localize9.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 3)
0.0b	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1)))
0.0b	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))
0.0b	(pow.f64 (exp.f64 x) 3)
0.0b	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
2.6b	(-.f64 (pow.f64 (exp.f64 x) 3) 1)

rewrite48.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64_782`
64×	`*-un-lft-identity_binary64_760`
48×	`times-frac_binary64_766`
40×	`difference-of-squares_binary64_729`
32×	`add-cube-cbrt_binary64_795`
20×	`difference-of-sqr-1_binary64_730`
18×	`cube-prod_binary64_788` `unpow-prod-down_binary64_839`
16×	`associate-/l*_binary64_705` `sqr-pow_binary64_732`
9×	`add-cbrt-cube_binary64_796`
7×	`add-exp-log_binary64_798` `pow1_binary64_821`
6×	`add-log-exp_binary64_799`
5×	`distribute-lft-out--_binary64_712`
4×	`associate-r_binary64_700` `pow-pow_binary64_832`
3×	`exp-prod_binary64_812` `cancel-sign-sub-inv_binary64_726` `associate-/r_binary64_704` `associate-l*_binary64_701` `pow-unpow_binary64_837`
2×	`associate-/r/_binary64_706` `flip3-+_binary64_763` `associate-/l/_binary64_707` `flip-+_binary64_734` `associate-*r/_binary64_702` `flip--_binary64_735` `flip3--_binary64_764`
1×	`cube-mult_binary64_790` `diff-log_binary64_852` `unswap-sqr_binary64_728` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `distribute-lft-out_binary64_711` `prod-exp_binary64_809` `unpow3_binary64_826` `distribute-lft-in_binary64_709` `pow-exp_binary64_828` `div-inv_binary64_757` `rem-cube-cbrt_binary64_783` `distribute-rgt-in_binary64_710` `pow-to-exp_binary64_829` `div-sub_binary64_765` `cbrt-unprod_binary64_793` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 160

Calls

8 calls:

14.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
8.0ms	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))
7.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)
3.0ms	(pow.f64 (exp.f64 x) 3)
0.0ms	(+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1)))

series217.0ms (8.5%)

Counts

4 → 24

Calls

4 calls:

115.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
40.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)
33.0ms	(pow.f64 (exp.f64 x) 3)
28.0ms	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))

Compiler

Compiled 536 to 428 computations (20.1% saved)

simplify97.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4986	4762
1	4986	4762

prune230.0ms (9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	184	2	186

Error

Counts

186 → 2

Compiler

Compiled 4551 to 2984 computations (34.4% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	181
1	75	181

regimes72.0ms (2.8%)

Compiler: Compiled 499 to 434 computations (13% saved)

bsearch0.0ms (0%)

regimes12.0ms (0.5%)

Compiler: Compiled 24 to 22 computations (8.3% saved)

bsearch0.0ms (0%)

regimes9.0ms (0.3%)

Compiler: Compiled 13 to 14 computations (-7.7% saved)

bsearch0.0ms (0%)

regimes8.0ms (0.3%)

Compiler: Compiled 6 to 9 computations (-50% saved)

bsearch0.0ms (0%)

regimes9.0ms (0.4%)

Accuracy

Total 0.4b remaining (96.2%)

Threshold costs 0.4b (96.2%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 36 to 29 computations (19.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	51
1	36	51

end0.0ms (0%)

sample1.2s (48.1%)

Algorithm

1×

intervals

Results

479.0ms	3981×	body	1024	valid
125.0ms	2037×	body	512	valid
101.0ms	8000×	pre	128	true
52.0ms	397×	body	2048	valid
42.0ms	1041×	body	256	valid
11.0ms	544×	body	128	valid

Compiler

Compiled 176 to 147 computations (16.5% saved)

Pareto

0.5677011342662979

Details

analyze3.0ms (0.1%)

sample32.0ms (1.3%)

simplify100.0ms (3.9%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

rewrite6.0ms (0.2%)

series19.0ms (0.7%)

simplify78.0ms (3.1%)

prune42.0ms (1.6%)

localize10.0ms (0.4%)

rewrite25.0ms (1%)

series128.0ms (5%)

simplify75.0ms (2.9%)

prune84.0ms (3.3%)

localize9.0ms (0.3%)

rewrite48.0ms (1.9%)

series217.0ms (8.5%)

simplify97.0ms (3.8%)

prune230.0ms (9%)

simplify4.0ms (0.2%)

regimes72.0ms (2.8%)

bsearch0.0ms (0%)

regimes12.0ms (0.5%)

bsearch0.0ms (0%)

regimes9.0ms (0.3%)

bsearch0.0ms (0%)

regimes8.0ms (0.3%)

bsearch0.0ms (0%)

regimes9.0ms (0.4%)

bsearch4.0ms (0.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (48.1%)

Profiling