Details

analyze6.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample26.0ms

Algorithm

intervals

Results

7.0ms	54×	body	640	valid
5.0ms	132×	body	80	valid
3.0ms	32×	body	320	valid
3.0ms	17×	body	1280	valid
2.0ms	21×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	191	15
1	191	15

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 11.7b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
18×	`distribute-lft-out--_binary64`
17×	`distribute-lft-out_binary64`
14×	`difference-of-squares_binary64`
12×	`add-exp-log_binary64`
11×	`associate-/r*_binary64` `add-log-exp_binary64`
8×	`add-cbrt-cube_binary64` `div-inv_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`difference-of-sqr-1_binary64` `associate-/r/_binary64` `div-exp_binary64`
3×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

6.0ms	(/.f64 1 (+.f64 x 1))
6.0ms	(/.f64 1 (-.f64 x 1))
20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
36.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series16.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/.f64 1 (+.f64 x 1))
2.0ms	(/.f64 1 (-.f64 x 1))
3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
8.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

simplify64.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4987	1726
1	4987	1726

prune148.0ms

Filtered

88 candidates to 147 candidates (-67.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	3	148

Merged error: 0.2b

Counts

148 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (/.f64 1 (-.f64 x 1)))
0.3b	(cbrt.f64 (/.f64 1 (-.f64 x 1)))
0.3b	(cbrt.f64 (/.f64 1 (-.f64 x 1)))
18.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (.f64 (.f64 (cbrt.f64 (/.f64 1 (-.f64 x 1))) (cbrt.f64 (/.f64 1 (-.f64 x 1)))) (cbrt.f64 (/.f64 1 (-.f64 x 1)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

81×	`cbrt-prod_binary64`
73×	`add-sqr-sqrt_binary64`
64×	`*-un-lft-identity_binary64`
63×	`times-frac_binary64`
39×	`cbrt-div_binary64`
37×	`add-cube-cbrt_binary64`
21×	`frac-add_binary64`
18×	`difference-of-squares_binary64`
15×	`frac-times_binary64` `associate-*l/_binary64`
10×	`flip3--_binary64` `flip--_binary64`
9×	`add-log-exp_binary64` `associate-*r/_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
7×	`frac-sub_binary64`
6×	`associate-/r/_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64` `div-inv_binary64`
2×	`sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 143

Calls

4 calls:

6.0ms	(cbrt.f64 (/.f64 1 (-.f64 x 1)))
6.0ms	(cbrt.f64 (/.f64 1 (-.f64 x 1)))
6.0ms	(cbrt.f64 (/.f64 1 (-.f64 x 1)))
26.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (.f64 (.f64 (cbrt.f64 (/.f64 1 (-.f64 x 1))) (cbrt.f64 (/.f64 1 (-.f64 x 1)))) (cbrt.f64 (/.f64 1 (-.f64 x 1)))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(cbrt.f64 (/.f64 1 (-.f64 x 1)))
7.0ms	(cbrt.f64 (/.f64 1 (-.f64 x 1)))
7.0ms	(cbrt.f64 (/.f64 1 (-.f64 x 1)))
13.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (.f64 (.f64 (cbrt.f64 (/.f64 1 (-.f64 x 1))) (cbrt.f64 (/.f64 1 (-.f64 x 1)))) (cbrt.f64 (/.f64 1 (-.f64 x 1)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4951	3041
1	4951	3041

prune192.0ms

Filtered

91 candidates to 155 candidates (-70.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	155	3	158

Merged error: 0.2b

Counts

158 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
16.5b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
42×	`associate-*r/_binary64`
35×	`*-un-lft-identity_binary64`
32×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
27×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64` `frac-times_binary64`
18×	`flip3-+_binary64` `associate-/l/_binary64` `difference-of-squares_binary64` `flip-+_binary64`
10×	`associate-*l/_binary64`
9×	`associate-/r*_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-l_binary64`
6×	`pow1_binary64`
5×	`sub-neg_binary64` `distribute-lft-out--_binary64`
4×	`distribute-rgt-out--_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `unpow3_binary64`
3×	`associate-r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64`
2×	`associate-+l+_binary64` `associate-/r/_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 145

Calls

4 calls:

20.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
11.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
12.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

series12.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
3.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
1.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify90.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4940	4416
1	4940	4416

prune276.0ms

Filtered

126 candidates to 157 candidates (-24.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	157	3	160

Merged error: 0.2b

Counts

160 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3))))
0.1b	(/.f64 2 (pow.f64 x 7))
0.2b	(/.f64 2 (pow.f64 x 5))
0.2b	(/.f64 2 (pow.f64 x 3))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64`
64×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
36×	`unpow-prod-down_binary64`
26×	`associate-/r*_binary64`
19×	`add-exp-log_binary64`
12×	`sqr-pow_binary64` `cube-prod_binary64`
11×	`distribute-lft-out_binary64`
10×	`add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `associate-/l*_binary64` `div-exp_binary64`
6×	`div-inv_binary64`
4×	`pow1_binary64` `frac-add_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`+-commutative_binary64` `associate-+r+_binary64`

Counts

4 → 177

Calls

4 calls:

57.0ms	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3))))
5.0ms	(/.f64 2 (pow.f64 x 7))
5.0ms	(/.f64 2 (pow.f64 x 5))
5.0ms	(/.f64 2 (pow.f64 x 3))

series22.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3))))
6.0ms	(/.f64 2 (pow.f64 x 7))
5.0ms	(/.f64 2 (pow.f64 x 5))
4.0ms	(/.f64 2 (pow.f64 x 3))

simplify38.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5408	2067

prune201.0ms

Filtered

124 candidates to 189 candidates (-52.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	185	7	192

Merged error: 0b

Counts

192 → 7

regimes50.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 26.0b

bsearch35.0ms

Steps

Iters	Range		Point
10	1.0235308815651651e-07	4185487.207633421	724.9671878446854
9	-144812915860.9967	-1762098.6286223363	-133969169.14947066

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	104	69
1	104	69

end0.0ms

sample732.0ms

Algorithm

intervals

Results

267.0ms	1926×	body	640	valid
150.0ms	4133×	body	80	valid
96.0ms	931×	body	320	valid
90.0ms	529×	body	1280	valid
35.0ms	481×	body	160	valid

Details

analyze6.0ms

sample26.0ms

simplify10.0ms

prune8.0ms

localize9.0ms

rewrite73.0ms

series16.0ms

simplify64.0ms

prune148.0ms

localize13.0ms

rewrite50.0ms

series35.0ms

simplify75.0ms

prune192.0ms

localize13.0ms

rewrite53.0ms

series12.0ms

simplify90.0ms

prune276.0ms

localize12.0ms

rewrite78.0ms

series22.0ms

simplify38.0ms

prune201.0ms

regimes50.0ms

bsearch35.0ms

simplify3.0ms

end0.0ms

sample732.0ms

Profiling