Details

analyze261.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample77.0ms

Algorithm

intervals

Results

38.0ms	74×	body	1280	valid
15.0ms	53×	body	640	valid
9.0ms	26×	body	2560	valid
5.0ms	30×	body	320	valid
2.0ms	58×	body	80	valid
1.0ms	15×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	9
1	10	9

prune2.0ms

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

Merged error: 53.4b

Counts

2 → 1

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 x x) 1)
1.5b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.6b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
12.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
5×	`add-exp-log_binary64`
4×	`flip3-+_binary64` `log-prod_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`sqrt-prod_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `+-commutative_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 53

Calls

4 calls:

4.0ms	(+.f64 (*.f64 x x) 1)
7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series21.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 (*.f64 x x) 1)
5.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
8.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify71.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4858	656
1	4858	656

prune88.0ms

Filtered

52 candidates to 65 candidates (-25.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	5	66

Merged error: 0.0b

Counts

66 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
0.1b	(*.f64 3/40 (pow.f64 x 5))
0.3b	(*.f64 (pow.f64 x 3) 1/6)
18.4b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `cube-prod_binary64`
2×	`pow-to-exp_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `unpow3_binary64` `associate--l+_binary64` `cube-mult_binary64`

Counts

4 → 80

Calls

4 calls:

6.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
5.0ms	(*.f64 3/40 (pow.f64 x 5))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

series30.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
5.0ms	(*.f64 3/40 (pow.f64 x 5))
5.0ms	(*.f64 (pow.f64 x 3) 1/6)
7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

simplify55.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5032	815

prune89.0ms

Filtered

60 candidates to 92 candidates (-53.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	92	5	97

Merged error: 0.0b

Counts

97 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (-.f64 (.f64 3/40 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/6)))
0.1b	(*.f64 3/40 (pow.f64 x 5))
0.3b	(*.f64 (pow.f64 x 3) 1/6)
18.4b	(-.f64 (.f64 3/40 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/6))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
14×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `cube-prod_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 82

Calls

4 calls:

6.0ms	(+.f64 x (-.f64 (.f64 3/40 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/6)))
6.0ms	(*.f64 3/40 (pow.f64 x 5))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
5.0ms	(-.f64 (.f64 3/40 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/6))

series30.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 x (-.f64 (.f64 3/40 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/6)))
5.0ms	(*.f64 3/40 (pow.f64 x 5))
4.0ms	(*.f64 (pow.f64 x 3) 1/6)
14.0ms	(-.f64 (.f64 3/40 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/6))

simplify56.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5097	905

prune87.0ms

Filtered

61 candidates to 94 candidates (-54.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	94	5	99

Merged error: 0.0b

Counts

99 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1/16 (pow.f64 x 5))
0.8b	(/.f64 1/8 (pow.f64 x 3))
15.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
19.1b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
71×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
11×	`log-prod_binary64`
10×	`sqr-pow_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-sub_binary64`
5×	`pow1_binary64` `log-div_binary64`
4×	`distribute-lft-out_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sum-log_binary64`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/.f64 1/16 (pow.f64 x 5))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
34.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
39.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 1/16 (pow.f64 x 5))
4.0ms	(/.f64 1/8 (pow.f64 x 3))
8.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
6.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify59.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5315	2408

prune174.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	171	5	176

Merged error: 0.0b

Counts

176 → 5

regimes42.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.3b

bsearch34.0ms

Steps

Iters	Range		Point
10	0.5010622809105568	3829239748214.2065	1.0246936005954463
10	-6.1724443159130615	-9.838195072127243e-15	-1.0707837615459106

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	275	54
1	275	54

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2299×	body	1280	valid
438.0ms	1594×	body	640	valid
273.0ms	820×	body	2560	valid
141.0ms	847×	body	320	valid
85.0ms	2060×	body	80	valid
39.0ms	380×	body	160	valid

Details

analyze261.0ms

sample77.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite23.0ms

series21.0ms

simplify71.0ms

prune88.0ms

localize9.0ms

rewrite26.0ms

series30.0ms

simplify55.0ms

prune89.0ms

localize9.0ms

rewrite25.0ms

series30.0ms

simplify56.0ms

prune87.0ms

localize11.0ms

rewrite91.0ms

series25.0ms

simplify59.0ms

prune174.0ms

regimes42.0ms

bsearch34.0ms

simplify5.0ms

end0.0ms

sample2.2s

Profiling