Details

analyze236.0ms (5.7%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 7 to 7 computations (0% saved)

sample38.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms	47×	body	2048	valid
7.0ms	50×	body	1024	valid
3.0ms	39×	body	512	valid
3.0ms	96×	body	128	valid
1.0ms	24×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify167.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4875	9
1	4875	9

prune4.0ms (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

30.9b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.0b	(-.f64 (exp.f64 (*.f64 a x)) 1)
0.0b	(exp.f64 (*.f64 a x))
0.0b	(exp.f64 (*.f64 a x))
5.0b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
3×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
2×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

2 → 28

Calls

4 calls:

6.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
1.0ms	(exp.f64 (*.f64 a x))
0.0ms	(exp.f64 (*.f64 a x))
0.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

series93.0ms (2.3%)

Counts

2 → 22

Calls

2 calls:

57.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
36.0ms	(exp.f64 (*.f64 a x))

Compiler

Compiled 348 to 316 computations (9.2% saved)

simplify75.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4936	572
1	4936	572

prune66.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	5	51

Error

0.2b

Counts

51 → 5

Compiler

Compiled 582 to 293 computations (49.7% saved)

localize8.0ms (0.2%)

Local error

Found 8 expressions with local error:

6.4b	(.f64 a (.f64 x x))
0.8b	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
0.2b	(.f64 1/2 (.f64 a (*.f64 x x)))
0.0b	(+.f64 x (.f64 1/2 (.f64 a (*.f64 x x))))
0.0b	(+.f64 x (.f64 1/2 (.f64 a (*.f64 x x))))
0.2b	(.f64 1/2 (.f64 a (*.f64 x x)))
0.8b	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
6.4b	(.f64 a (.f64 x x))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`associate-l_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
5×	`associate-r_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `flip-+_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 73

Calls

8 calls:

7.0ms	(.f64 1/2 (.f64 a (*.f64 x x)))
6.0ms	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
6.0ms	(.f64 a (.f64 x x))
4.0ms	(+.f64 x (.f64 1/2 (.f64 a (*.f64 x x))))
0.0ms	(+.f64 x (.f64 1/2 (.f64 a (*.f64 x x))))

series365.0ms (8.9%)

Counts

4 → 36

Calls

4 calls:

137.0ms	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
101.0ms	(+.f64 x (.f64 1/2 (.f64 a (*.f64 x x))))
66.0ms	(.f64 1/2 (.f64 a (*.f64 x x)))
60.0ms	(.f64 a (.f64 x x))

Compiler

Compiled 636 to 536 computations (15.7% saved)

simplify47.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5023	1426

prune83.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Error

0.1b

Counts

114 → 5

Compiler

Compiled 1642 to 715 computations (56.5% saved)

localize7.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.8b	(.f64 a (+.f64 x (.f64 1/2 (.f64 (.f64 a x) x))))
0.2b	(.f64 1/2 (.f64 (*.f64 a x) x))
0.1b	(.f64 (.f64 a x) x)
0.0b	(+.f64 x (.f64 1/2 (.f64 (*.f64 a x) x)))
0.0b	(+.f64 x (.f64 1/2 (.f64 (*.f64 a x) x)))
0.1b	(.f64 (.f64 a x) x)
0.2b	(.f64 1/2 (.f64 (*.f64 a x) x))
0.8b	(.f64 a (+.f64 x (.f64 1/2 (.f64 (.f64 a x) x))))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 72

Calls

8 calls:

9.0ms	(.f64 1/2 (.f64 (*.f64 a x) x))
6.0ms	(.f64 a (+.f64 x (.f64 1/2 (.f64 (.f64 a x) x))))
5.0ms	(.f64 (.f64 a x) x)
4.0ms	(+.f64 x (.f64 1/2 (.f64 (*.f64 a x) x)))
0.0ms	(+.f64 x (.f64 1/2 (.f64 (*.f64 a x) x)))

series369.0ms (9%)

Counts

4 → 36

Calls

4 calls:

139.0ms	(.f64 a (+.f64 x (.f64 1/2 (.f64 (.f64 a x) x))))
105.0ms	(+.f64 x (.f64 1/2 (.f64 (*.f64 a x) x)))
74.0ms	(.f64 1/2 (.f64 (*.f64 a x) x))
51.0ms	(.f64 (.f64 a x) x)

Compiler

Compiled 636 to 536 computations (15.7% saved)

simplify87.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4993	1414
1	4993	1414

prune82.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	108	5	113

Error

0.1b

Counts

113 → 5

Compiler

Compiled 1603 to 711 computations (55.6% saved)

localize8.0ms (0.2%)

Local error

Found 8 expressions with local error:

5.4b	(+.f64 (.f64 a x) (.f64 a (.f64 1/2 (.f64 x (*.f64 a x)))))
4.4b	(.f64 a (.f64 1/2 (.f64 x (.f64 a x))))
0.2b	(.f64 1/2 (.f64 x (*.f64 a x)))
0.1b	(.f64 x (.f64 a x))
0.1b	(.f64 x (.f64 a x))
0.2b	(.f64 1/2 (.f64 x (*.f64 a x)))
4.4b	(.f64 a (.f64 1/2 (.f64 x (.f64 a x))))
5.4b	(+.f64 (.f64 a x) (.f64 a (.f64 1/2 (.f64 x (*.f64 a x)))))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`associate-l_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64`
3×	`associate-r_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 75

Calls

8 calls:

9.0ms	(.f64 a (.f64 1/2 (.f64 x (.f64 a x))))
7.0ms	(.f64 1/2 (.f64 x (*.f64 a x)))
5.0ms	(+.f64 (.f64 a x) (.f64 a (.f64 1/2 (.f64 x (*.f64 a x)))))
5.0ms	(.f64 x (.f64 a x))
0.0ms	(.f64 x (.f64 a x))

series355.0ms (8.6%)

Counts

4 → 30

Calls

4 calls:

144.0ms	(+.f64 (.f64 a x) (.f64 a (.f64 1/2 (.f64 x (*.f64 a x)))))
89.0ms	(.f64 a (.f64 1/2 (.f64 x (.f64 a x))))
67.0ms	(.f64 1/2 (.f64 x (*.f64 a x)))
54.0ms	(.f64 x (.f64 a x))

Compiler

Compiled 666 to 546 computations (18% saved)

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4980	1312
1	4980	1312

prune73.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	105	5	110

Error

0.1b

Counts

110 → 5

Compiler

Compiled 1589 to 628 computations (60.5% saved)

regimes425.0ms (10.3%)

Accuracy

Total 0.3b remaining (81.8%)

Threshold costs 0.3b (81.8%)

Compiler

Compiled 1596 to 1180 computations (26.1% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	51
1	29	51

end2.0ms (0%)

Compiler: Compiled 34 to 19 computations (44.1% saved)

sample1.3s (32.6%)

Algorithm

1×

intervals

Results

425.0ms	1443×	body	2048	valid
252.0ms	1737×	body	1024	valid
96.0ms	1142×	body	512	valid
80.0ms	3056×	body	128	valid
32.0ms	622×	body	256	valid
4.0ms	144×	body	128	invalid

Compiler

Compiled 291 to 208 computations (28.5% saved)

Pareto

Details

analyze236.0ms (5.7%)

sample38.0ms (0.9%)

simplify167.0ms (4.1%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

rewrite10.0ms (0.3%)

series93.0ms (2.3%)

simplify75.0ms (1.8%)

prune66.0ms (1.6%)

localize8.0ms (0.2%)

rewrite28.0ms (0.7%)

series365.0ms (8.9%)

simplify47.0ms (1.2%)

prune83.0ms (2%)

localize7.0ms (0.2%)

rewrite29.0ms (0.7%)

series369.0ms (9%)

simplify87.0ms (2.1%)

prune82.0ms (2%)

localize8.0ms (0.2%)

rewrite32.0ms (0.8%)

series355.0ms (8.6%)

simplify71.0ms (1.7%)

prune73.0ms (1.8%)

regimes425.0ms (10.3%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end2.0ms (0%)

sample1.3s (32.6%)

Profiling