Details

analyze572.0ms (8.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample46.0ms (0.7%)

Algorithm

1×

intervals

Results

22.0ms	95×	body	1024	valid
5.0ms	40×	body	512	valid
4.0ms	90×	body	128	valid
3.0ms	10×	body	2048	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify153.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

prune8.0ms (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

43.3b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.8b	(-.f64 (exp.f64 x) 1)
0.7b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
0.7b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.8b	(-.f64 (exp.f64 x) 1)

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_759`
30×	`*-un-lft-identity_binary64_737`
21×	`times-frac_binary64_743`
15×	`add-cube-cbrt_binary64_772`
10×	`difference-of-squares_binary64_706`
7×	`associate-/r*_binary64_681`
5×	`distribute-lft-out--_binary64_689` `difference-of-sqr-1_binary64_707`
4×	`add-cbrt-cube_binary64_773` `add-log-exp_binary64_776`
3×	`add-exp-log_binary64_775` `associate-/l*_binary64_682` `cancel-sign-sub-inv_binary64_703`
2×	`associate-/r/_binary64_683` `pow1_binary64_798` `flip3--_binary64_741` `flip--_binary64_712`
1×	`diff-log_binary64_829` `frac-2neg_binary64_748` `clear-num_binary64_736` `sub-neg_binary64_730` `div-inv_binary64_734` `cbrt-undiv_binary64_771` `div-exp_binary64_788`

Counts

2 → 63

Calls

4 calls:

13.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
7.0ms	(-.f64 (exp.f64 x) 1)
0.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
0.0ms	(-.f64 (exp.f64 x) 1)

series103.0ms (1.6%)

Counts

2 → 12

Calls

2 calls:

72.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
30.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 140 to 111 computations (20.7% saved)

simplify109.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5105	1195

prune176.0ms (2.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	3	76

Error

Counts

76 → 3

Compiler

Compiled 1016 to 511 computations (49.7% saved)

localize23.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
0.0b	(+.f64 1/6 (*.f64 1/24 x))
0.0b	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))))
0.0b	(+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x))))))
0.0b	(+.f64 1/6 (*.f64 1/24 x))
0.1b	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
0.3b	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
0.3b	(*.f64 1/24 x)

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_759`
13×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775` `pow1_binary64_798`
9×	`add-cube-cbrt_binary64_772` `-un-lft-identity_binary64_737` `associate-r*_binary64_677`
7×	`associate-l_binary64_678`
6×	`add-log-exp_binary64_776`
5×	`cbrt-unprod_binary64_770` `prod-exp_binary64_786` `pow-prod-down_binary64_808`
4×	`associate-*r/_binary64_679`
3×	`unswap-sqr_binary64_705` `flip3-+_binary64_740` `flip-+_binary64_711` `*-commutative_binary64_668`
2×	`distribute-lft-in_binary64_686` `distribute-rgt-in_binary64_687`
1×	`+-commutative_binary64_667` `sum-log_binary64_828`

Counts

4 → 74

Calls

8 calls:

14.0ms	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
10.0ms	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
7.0ms	(*.f64 1/24 x)
5.0ms	(+.f64 1/6 (*.f64 1/24 x))
0.0ms	(+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x))))))

series250.0ms (3.8%)

Counts

4 → 20

Calls

4 calls:

98.0ms	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
67.0ms	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
54.0ms	(+.f64 1/6 (*.f64 1/24 x))
30.0ms	(*.f64 1/24 x)

Compiler

Compiled 550 to 411 computations (25.3% saved)

simplify92.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4986	1168
1	4986	1168

prune156.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	94	3	97

Error

Counts

97 → 3

Compiler

Compiled 2087 to 1268 computations (39.2% saved)

localize12.0ms (0.2%)

Local error

Found 6 expressions with local error:

0.3b	(*.f64 x 1/12)
0.0b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.0b	(+.f64 1/2 (/.f64 1 x))
0.0b	(+.f64 1/2 (/.f64 1 x))
0.0b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.3b	(*.f64 x 1/12)

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64_776`
8×	`*-un-lft-identity_binary64_737`
7×	`add-sqr-sqrt_binary64_759`
5×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775` `add-cube-cbrt_binary64_772` `pow1_binary64_798`
4×	`sum-log_binary64_828`
3×	`associate-l_binary64_678` `associate-r_binary64_677`
2×	`flip3-+_binary64_740` `flip-+_binary64_711` `+-commutative_binary64_667` `distribute-lft-out_binary64_688`
1×	`unswap-sqr_binary64_705` `cbrt-unprod_binary64_770` `prod-exp_binary64_786` `div-inv_binary64_734` `associate-+l+_binary64_670` `pow-prod-down_binary64_808` `*-commutative_binary64_668`

Counts

3 → 44

Calls

6 calls:

16.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
11.0ms	(+.f64 1/2 (/.f64 1 x))
6.0ms	(*.f64 x 1/12)
0.0ms	(+.f64 1/2 (/.f64 1 x))
0.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))

series127.0ms (1.9%)

Counts

3 → 18

Calls

3 calls:

69.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
29.0ms	(+.f64 1/2 (/.f64 1 x))
29.0ms	(*.f64 x 1/12)

Compiler

Compiled 203 to 184 computations (9.4% saved)

simplify135.0ms (2%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4880	618
1	4880	618

prune81.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	62	3	65

Error

Counts

65 → 3

Compiler

Compiled 746 to 597 computations (20% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.8b	(-.f64 1 (exp.f64 (neg.f64 x)))
0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
2.8b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_759` `*-un-lft-identity_binary64_737`
18×	`times-frac_binary64_743`
14×	`add-cube-cbrt_binary64_772`
10×	`difference-of-squares_binary64_706`
6×	`add-exp-log_binary64_775` `associate-/r*_binary64_681`
5×	`distribute-lft-out--_binary64_689`
4×	`add-cbrt-cube_binary64_773` `add-log-exp_binary64_776`
3×	`associate-/l*_binary64_682` `pow1_binary64_798` `cancel-sign-sub-inv_binary64_703`
2×	`associate-/r/_binary64_683` `flip3--_binary64_741` `div-exp_binary64_788` `flip--_binary64_712`
1×	`diff-log_binary64_829` `frac-2neg_binary64_748` `clear-num_binary64_736` `1-exp_binary64_781` `sub-neg_binary64_730` `inv-pow_binary64_822` `pow-flip_binary64_811` `div-inv_binary64_734` `cbrt-undiv_binary64_771` `rec-exp_binary64_787`

Counts

2 → 62

Calls

4 calls:

12.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
8.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))
0.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
0.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

series104.0ms (1.6%)

Counts

2 → 12

Calls

2 calls:

69.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
34.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 140 to 131 computations (6.4% saved)

simplify135.0ms (2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4951	1118
1	4951	1118

prune93.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	74	3	77

Error

Counts

77 → 3

Compiler

Compiled 917 to 587 computations (36% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	210	433
1	210	433

regimes219.0ms (3.3%)

Accuracy

Total 1.0b remaining (98.8%)

Threshold costs 1.0b (98.8%)

Compiler

Compiled 1021 to 764 computations (25.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	27
1	20	27

end0.0ms (0%)

sample3.8s (58%)

Algorithm

1×

intervals

Results

693.0ms	2709×	body	1024	valid
176.0ms	1256×	body	512	valid
132.0ms	3120×	body	128	valid
89.0ms	261×	body	2048	valid
59.0ms	654×	body	256	valid
0.0ms	1×	body	2048	invalid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 855 to 644 computations (24.7% saved)

Pareto

-0.2008896320921186

Details

analyze572.0ms (8.7%)

sample46.0ms (0.7%)

simplify153.0ms (2.3%)

prune8.0ms (0.1%)

localize7.0ms (0.1%)

rewrite29.0ms (0.4%)

series103.0ms (1.6%)

simplify109.0ms (1.7%)

prune176.0ms (2.7%)

localize23.0ms (0.3%)

rewrite50.0ms (0.8%)

series250.0ms (3.8%)

simplify92.0ms (1.4%)

prune156.0ms (2.4%)

localize12.0ms (0.2%)

rewrite38.0ms (0.6%)

series127.0ms (1.9%)

simplify135.0ms (2%)

prune81.0ms (1.2%)

localize9.0ms (0.1%)

rewrite28.0ms (0.4%)

series104.0ms (1.6%)

simplify135.0ms (2%)

prune93.0ms (1.4%)

simplify15.0ms (0.2%)

regimes219.0ms (3.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.8s (58%)

Profiling