Details

analyze8.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample187.0ms (1.7%)

Algorithm

1×

intervals

Results

136.0ms	138×	body	2048	valid
24.0ms	59×	body	1024	valid
11.0ms	32×	body	512	valid
2.0ms	19×	body	256	valid
1.0ms	8×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify304.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (151.0ms)

Iter	Nodes	Cost
0	4809	13
1	4809	13

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

29.6b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.2b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
0.0b	(-.f64 (exp.f64 x) 2)
0.0b	(-.f64 (exp.f64 x) 2)
4.2b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_737`
9×	`add-log-exp_binary64_776`
6×	`add-sqr-sqrt_binary64_759` `cancel-sign-sub-inv_binary64_703`
4×	`add-cube-cbrt_binary64_772` `frac-add_binary64_745` `associate-+l+_binary64_670`
3×	`flip3--_binary64_741` `flip--_binary64_712`
2×	`add-cbrt-cube_binary64_773` `diff-log_binary64_829` `add-exp-log_binary64_775` `distribute-lft-out--_binary64_689` `pow1_binary64_798` `sub-neg_binary64_730` `neg-sub0_binary64_732` `sum-log_binary64_828` `distribute-lft-out_binary64_688` `exp-diff_binary64_785` `exp-neg_binary64_784`
1×	`flip3-+_binary64_740` `flip-+_binary64_711` `+-commutative_binary64_667` `associate-+l-_binary64_672` `difference-of-squares_binary64_706`

Counts

2 → 39

Calls

4 calls:

18.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
9.0ms	(-.f64 (exp.f64 x) 2)
0.0ms	(-.f64 (exp.f64 x) 2)
0.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series81.0ms (0.7%)

Counts

2 → 10

Calls

2 calls:

49.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
32.0ms	(-.f64 (exp.f64 x) 2)

Compiler

Compiled 137 to 120 computations (12.4% saved)

simplify113.0ms (1%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4943	673
1	4943	673

prune143.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	2	50

Error

0.0b

Counts

50 → 2

Compiler

Compiled 623 to 319 computations (48.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/12 (pow.f64 x 4))
0.0b	(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
0.0b	(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_759`
7×	`add-exp-log_binary64_775` `associate-r_binary64_677`
5×	`add-cube-cbrt_binary64_772` `*-un-lft-identity_binary64_737`
4×	`add-cbrt-cube_binary64_773` `add-log-exp_binary64_776` `unpow-prod-down_binary64_816`
3×	`unswap-sqr_binary64_705` `prod-exp_binary64_786` `associate-l_binary64_678`
2×	`pow1_binary64_798` `sqr-pow_binary64_709`
1×	`flip3-+_binary64_740` `cbrt-unprod_binary64_770` `pow-exp_binary64_805` `flip-+_binary64_711` `+-commutative_binary64_667` `sum-log_binary64_828` `pow-to-exp_binary64_806` `*-commutative_binary64_668`

Counts

2 → 36

Calls

4 calls:

11.0ms	(*.f64 1/12 (pow.f64 x 4))
8.0ms	(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
0.0ms	(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
0.0ms	(*.f64 1/12 (pow.f64 x 4))

series197.0ms (1.8%)

Counts

2 → 9

Calls

2 calls:

137.0ms	(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
60.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 121 to 103 computations (14.9% saved)

simplify118.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4951	522
1	4951	522

prune70.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	44	3	47

Error

0.0b

Counts

47 → 3

Compiler

Compiled 610 to 391 computations (35.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

6.6b	(+.f64 -1 (exp.f64 (neg.f64 x)))
6.6b	(+.f64 -1 (exp.f64 (neg.f64 x)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_776` `*-un-lft-identity_binary64_737`
1×	`add-cbrt-cube_binary64_773` `flip3-+_binary64_740` `add-exp-log_binary64_775` `add-cube-cbrt_binary64_772` `pow1_binary64_798` `add-sqr-sqrt_binary64_759` `flip-+_binary64_711` `+-commutative_binary64_667` `sum-log_binary64_828` `distribute-lft-out_binary64_688`

Counts

1 → 12

Calls

2 calls:

7.0ms	(+.f64 -1 (exp.f64 (neg.f64 x)))
0.0ms	(+.f64 -1 (exp.f64 (neg.f64 x)))

series25.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

24.0ms

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

Compiler

Compiled 32 to 31 computations (3.1% saved)

simplify126.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4933	162
1	4933	162

prune19.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	15	0	15
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	15	3	18

Error

0.0b

Counts

18 → 3

Compiler

Compiled 154 to 94 computations (39% saved)

localize29.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 1/144 (.f64 x x))
0.1b	(.f64 (pow.f64 x 6) (-.f64 (.f64 1/144 (*.f64 x x)) 1/12))
0.0b	(*.f64 1/1728 (pow.f64 x 12))
0.0b	(-.f64 (.f64 1/144 (.f64 x x)) 1/12)
0.0b	(*.f64 1/1728 (pow.f64 x 12))
0.1b	(.f64 (pow.f64 x 6) (-.f64 (.f64 1/144 (*.f64 x x)) 1/12))
0.2b	(.f64 1/144 (.f64 x x))
51.3b	(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 12)) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (.f64 (pow.f64 x 6) (-.f64 (.f64 1/144 (.f64 x x)) 1/12))))

rewrite86.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_759`
21×	`add-exp-log_binary64_775` `add-cube-cbrt_binary64_772` `*-un-lft-identity_binary64_737`
15×	`add-cbrt-cube_binary64_773`
13×	`associate-l_binary64_678`
11×	`associate-r_binary64_677`
9×	`prod-exp_binary64_786` `pow1_binary64_798` `times-frac_binary64_743`
8×	`unpow-prod-down_binary64_816`
7×	`unswap-sqr_binary64_705`
6×	`cancel-sign-sub-inv_binary64_703`
5×	`cbrt-unprod_binary64_770`
4×	`add-log-exp_binary64_776` `distribute-lft-in_binary64_686` `distribute-rgt-in_binary64_687` `sqr-pow_binary64_709`
3×	`associate-/l_binary64_682` `associate-/r_binary64_681` `pow-prod-down_binary64_808` `*-commutative_binary64_668`
2×	`associate-/r/_binary64_683` `flip3-+_binary64_740` `pow-exp_binary64_805` `sub-neg_binary64_730` `flip-+_binary64_711` `pow-to-exp_binary64_806` `associate-/l/_binary64_684` `associate-*r/_binary64_679`
1×	`frac-2neg_binary64_748` `clear-num_binary64_736` `div-inv_binary64_734` `flip3--_binary64_741` `cbrt-undiv_binary64_771` `div-exp_binary64_788` `flip--_binary64_712`

Counts

4 → 110

Calls

8 calls:

24.0ms	(.f64 (pow.f64 x 6) (-.f64 (.f64 1/144 (*.f64 x x)) 1/12))
20.0ms	(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 12)) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (.f64 (pow.f64 x 6) (-.f64 (.f64 1/144 (.f64 x x)) 1/12))))
11.0ms	(*.f64 1/1728 (pow.f64 x 12))
10.0ms	(.f64 1/144 (.f64 x x))
0.0ms	(-.f64 (.f64 1/144 (.f64 x x)) 1/12)

series754.0ms (6.9%)

Counts

4 → 18

Calls

4 calls:

414.0ms	(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 12)) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (.f64 (pow.f64 x 6) (-.f64 (.f64 1/144 (.f64 x x)) 1/12))))
202.0ms	(.f64 (pow.f64 x 6) (-.f64 (.f64 1/144 (*.f64 x x)) 1/12))
87.0ms	(*.f64 1/1728 (pow.f64 x 12))
51.0ms	(.f64 1/144 (.f64 x x))

Compiler

Compiled 574 to 481 computations (16.2% saved)

simplify141.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5110	2834

prune398.0ms (3.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	128	3	131

Error

Counts

131 → 3

Compiler

Compiled 4024 to 2979 computations (26% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	153	416
1	153	416

regimes65.0ms (0.6%)

Accuracy

Total 0.7b remaining (93.1%)

Threshold costs 0.7b (93.1%)

Compiler

Compiled 270 to 212 computations (21.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	10	13

end0.0ms (0%)

sample7.9s (72.7%)

Algorithm

1×

intervals

Results

4.0s	4153×	body	2048	valid
835.0ms	1972×	body	1024	valid
232.0ms	1016×	body	512	valid
70.0ms	518×	body	256	valid
24.0ms	341×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 821 to 647 computations (21.2% saved)

Pareto

0.13854376179880842

Details

analyze8.0ms (0.1%)

sample187.0ms (1.7%)

simplify304.0ms (2.8%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite33.0ms (0.3%)

series81.0ms (0.7%)

simplify113.0ms (1%)

prune143.0ms (1.3%)

localize12.0ms (0.1%)

rewrite25.0ms (0.2%)

series197.0ms (1.8%)

simplify118.0ms (1.1%)

prune70.0ms (0.6%)

localize7.0ms (0.1%)

rewrite9.0ms (0.1%)

series25.0ms (0.2%)

simplify126.0ms (1.1%)

prune19.0ms (0.2%)

localize29.0ms (0.3%)

rewrite86.0ms (0.8%)

series754.0ms (6.9%)

simplify141.0ms (1.3%)

prune398.0ms (3.6%)

simplify14.0ms (0.1%)

regimes65.0ms (0.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.9s (72.7%)

Profiling