Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.8%	89.9%	0.2%	11
14.1%	85.7%	0.2%	12
22.6%	77.1%	0.2%	13
23.7%	76%	0.2%	14

sample26.0ms

Algorithm

intervals

Results

8.0ms	208×	body	128	valid
3.0ms	18×	body	1024	valid
2.0ms	14×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	24×	body	128	invalid
0.0ms	2×	body	2048	valid

simplify132.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4870	19
1	4870	19

prune3.0ms

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: 16.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 z t) y)
2.3b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
10.8b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `associate-l*_binary64` `distribute-lft-out--_binary64` `times-frac_binary64`
4×	`flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64` `associate-*l/_binary64`
3×	`associate-r_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 69

Calls

3 calls:

7.0ms	(*.f64 (-.f64 z t) y)
12.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
11.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

series586.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(*.f64 (-.f64 z t) y)
366.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
159.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

simplify36.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4986	1273
1	4986	1273

prune79.0ms

Filtered

57 candidates to 78 candidates (-36.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	70	8	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	8	79

Merged error: 4.4b

Counts

79 → 8

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a t) y)
3.3b	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
11.7b	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

203×	`times-frac_binary64`
180×	`add-sqr-sqrt_binary64`
176×	`*-un-lft-identity_binary64`
87×	`add-cube-cbrt_binary64`
45×	`difference-of-squares_binary64`
44×	`distribute-lft-out--_binary64`
22×	`associate-/r*_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
8×	`add-log-exp_binary64` `div-inv_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64` `flip3--_binary64` `div-sub_binary64` `flip--_binary64`
2×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-sub_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `associate--r-_binary64` `associate-/r/_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

3 → 196

Calls

3 calls:

6.0ms	(/.f64 (-.f64 a t) y)
44.0ms	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
14.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))

series703.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/.f64 (-.f64 a t) y)
376.0ms	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
274.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))

simplify93.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5324	5092

prune153.0ms

Filtered

138 candidates to 205 candidates (-48.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	198	7	205
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	203	10	213

Merged error: 3.3b

Counts

213 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
1.2b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) (cbrt.f64 y))))
5.3b	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) (cbrt.f64 y)))
8.2b	(-.f64 (+.f64 x y) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) (cbrt.f64 y)))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

675×	`times-frac_binary64`
541×	`add-sqr-sqrt_binary64`
532×	`*-un-lft-identity_binary64`
262×	`add-cube-cbrt_binary64`
175×	`associate-r_binary64`
169×	`cbrt-prod_binary64`
135×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
34×	`associate-/r*_binary64`
30×	`add-exp-log_binary64`
21×	`add-cbrt-cube_binary64`
13×	`div-inv_binary64`
9×	`add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
5×	`associate-/l*_binary64`
4×	`unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `associate-*r/_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `diff-log_binary64` `associate-/r/_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/3_binary64` `associate-l_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 456

Calls

4 calls:

1.0ms	(cbrt.f64 y)
70.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) (cbrt.f64 y))))
18.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) (cbrt.f64 y)))
8.0ms	(-.f64 (+.f64 x y) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) (cbrt.f64 y)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt.f64 y)
221.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) (cbrt.f64 y))))
301.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) (cbrt.f64 y)))
394.0ms	(-.f64 (+.f64 x y) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) (cbrt.f64 y)))))

simplify167.0ms

Algorithm

egg-herbie

Counts

468 → 468

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5379	13062

prune334.0ms

Filtered

307 candidates to 468 candidates (-52.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	468	0	468
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	468	10	478

Merged error: 3.3b

Counts

478 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (-.f64 a t))
0.2b	(/.f64 1 (/.f64 y (-.f64 a t)))
5.5b	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 1 (/.f64 y (-.f64 a t)))))
11.7b	(/.f64 (-.f64 z t) (/.f64 1 (/.f64 y (-.f64 a t))))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`times-frac_binary64`
734×	`add-sqr-sqrt_binary64`
720×	`*-un-lft-identity_binary64`
435×	`add-cube-cbrt_binary64`
145×	`difference-of-squares_binary64`
141×	`distribute-lft-out--_binary64`
94×	`associate-/r*_binary64`
54×	`associate-/r/_binary64`
31×	`div-inv_binary64`
28×	`add-exp-log_binary64`
25×	`flip3--_binary64` `flip--_binary64`
20×	`add-cbrt-cube_binary64`
14×	`div-exp_binary64`
11×	`associate-/l*_binary64`
10×	`cbrt-undiv_binary64`
9×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`rec-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `div-sub_binary64` `frac-sub_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `associate--r-_binary64` `inv-pow_binary64` `pow-flip_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 602

Calls

4 calls:

6.0ms	(/.f64 y (-.f64 a t))
11.0ms	(/.f64 1 (/.f64 y (-.f64 a t)))
142.0ms	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 1 (/.f64 y (-.f64 a t)))))
29.0ms	(/.f64 (-.f64 z t) (/.f64 1 (/.f64 y (-.f64 a t))))

series664.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/.f64 y (-.f64 a t))
70.0ms	(/.f64 1 (/.f64 y (-.f64 a t)))
360.0ms	(-.f64 (+.f64 x y) (/.f64 (-.f64 z t) (/.f64 1 (/.f64 y (-.f64 a t)))))
166.0ms	(/.f64 (-.f64 z t) (/.f64 1 (/.f64 y (-.f64 a t))))

simplify210.0ms

Algorithm

egg-herbie

Counts

614 → 614

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4991	17978
1	4991	17978

prune328.0ms

Filtered

323 candidates to 614 candidates (-90.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	613	1	614
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	614	10	624

Merged error: 3.3b

Counts

624 → 10

regimes184.0ms

Accuracy

24.4% (6.2b remaining)

Error of 9.4b against oracle of 3.2b and baseline of 11.4b

bsearch57.0ms

Steps

Iters	Range		Point
7	7.910175331804046e-42	1.2698716605918806e-39	1.5876893569634118e-41
9	-1.4443952101809879e-87	-1.717435915269629e-94	-4.06012244061433e-89

simplify9.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	259	63
1	259	63

end0.0ms

sample763.0ms

Algorithm

intervals

Results

296.0ms	6774×	body	128	valid
53.0ms	471×	body	512	valid
52.0ms	349×	body	1024	valid
36.0ms	730×	body	128	invalid
27.0ms	355×	body	256	valid
10.0ms	51×	body	2048	valid

Details

analyze1.0s

sample26.0ms

simplify132.0ms

prune3.0ms

localize9.0ms

rewrite36.0ms

series586.0ms

simplify36.0ms

prune79.0ms

localize18.0ms

rewrite97.0ms

series703.0ms

simplify93.0ms

prune153.0ms

localize23.0ms

rewrite188.0ms

series1.1s

simplify167.0ms

prune334.0ms

localize11.0ms

rewrite297.0ms

series664.0ms

simplify210.0ms

prune328.0ms

regimes184.0ms

bsearch57.0ms

simplify9.0ms

end0.0ms

sample763.0ms

Profiling