Details

analyze273.0ms

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

sample70.0ms

Algorithm

intervals

Results

33.0ms	78×	body	1280	valid
12.0ms	46×	body	640	valid
10.0ms	29×	body	2560	valid
4.0ms	24×	body	320	valid
3.0ms	68×	body	80	valid
1.0ms	11×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	9
1	9	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: 52.6b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.7b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
3.1b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
15.4b	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

series24.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
13.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5075	600

prune97.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Merged error: 0.1b

Counts

52 → 7

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))
0.1b	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

50×	`associate-r_binary64`
49×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`unpow-prod-down_binary64` `cube-prod_binary64`
20×	`sqrt-prod_binary64`
10×	`add-exp-log_binary64`
8×	`unswap-sqr_binary64`
6×	`add-log-exp_binary64`
4×	`add-cbrt-cube_binary64` `prod-exp_binary64`
3×	`associate-r/_binary64` `associate-l*_binary64` `cube-div_binary64`
2×	`pow1_binary64` `diff-log_binary64` `sqr-pow_binary64` `div-inv_binary64` `frac-sub_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 90

Calls

2 calls:

15.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))
18.0ms	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))

series34.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))
21.0ms	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))

simplify30.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	4998	1131
1	4998	1131

prune88.0ms

Filtered

47 candidates to 96 candidates (-104.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	95	8	103

Merged error: 0.1b

Counts

103 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 0.0625 (pow.f64 x 5))
0.3b	(/.f64 0.125 (pow.f64 x 3))
10.2b	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
18.0b	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))

rewrite92.0ms

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 0.0625 (pow.f64 x 5))
5.0ms	(/.f64 0.125 (pow.f64 x 3))
37.0ms	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
38.0ms	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 0.0625 (pow.f64 x 5))
5.0ms	(/.f64 0.125 (pow.f64 x 3))
12.0ms	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
7.0ms	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))

simplify55.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5361	2493

prune188.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	171	8	179

Merged error: 0.1b

Counts

179 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 0.25 (*.f64 x x)) (log.f64 2))
0.1b	(/.f64 0.09375 (pow.f64 x 4))
0.6b	(/.f64 0.25 (*.f64 x x))
8.6b	(-.f64 (+.f64 (/.f64 0.25 (*.f64 x x)) (log.f64 2)) (-.f64 (/.f64 0.09375 (pow.f64 x 4)) (log.f64 x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
15×	`distribute-lft-out--_binary64`
14×	`add-exp-log_binary64`
13×	`add-log-exp_binary64`
12×	`unpow-prod-down_binary64`
11×	`pow1_binary64` `add-cbrt-cube_binary64`
8×	`associate-/r*_binary64` `distribute-lft-out_binary64`
7×	`log-pow_binary64`
6×	`diff-log_binary64` `associate-/l*_binary64`
5×	`div-exp_binary64`
4×	`sqr-pow_binary64` `frac-sub_binary64`
3×	`flip3-+_binary64` `flip3--_binary64` `log-prod_binary64` `cbrt-undiv_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64` `sum-log_binary64`
2×	`sub-neg_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-to-exp_binary64` `associate--r+_binary64` `cbrt-unprod_binary64` `associate--r-_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `pow-exp_binary64` `associate--l+_binary64`

Counts

4 → 113

Calls

4 calls:

8.0ms	(+.f64 (/.f64 0.25 (*.f64 x x)) (log.f64 2))
5.0ms	(/.f64 0.09375 (pow.f64 x 4))
5.0ms	(/.f64 0.25 (*.f64 x x))
23.0ms	(-.f64 (+.f64 (/.f64 0.25 (*.f64 x x)) (log.f64 2)) (-.f64 (/.f64 0.09375 (pow.f64 x 4)) (log.f64 x)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 (/.f64 0.25 (*.f64 x x)) (log.f64 2))
5.0ms	(/.f64 0.09375 (pow.f64 x 4))
4.0ms	(/.f64 0.25 (*.f64 x x))
14.0ms	(-.f64 (+.f64 (/.f64 0.25 (*.f64 x x)) (log.f64 2)) (-.f64 (/.f64 0.09375 (pow.f64 x 4)) (log.f64 x)))

simplify33.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5573	1730

prune111.0ms

Filtered

79 candidates to 125 candidates (-58.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	125	8	133

Merged error: 0.1b

Counts

133 → 8

regimes127.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.2b

bsearch25.0ms

Steps

Iters	Range		Point
9	0.2768238907569622	14347100.157384831	0.9662551447614324
7	-14.55571598581285	-0.08183750982964474	-1.0350961389186162

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	306	61
1	306	61

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2359×	body	1280	valid
449.0ms	1560×	body	640	valid
287.0ms	830×	body	2560	valid
134.0ms	777×	body	320	valid
92.0ms	2091×	body	80	valid
38.0ms	383×	body	160	valid

Details

analyze273.0ms

sample70.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite19.0ms

series24.0ms

simplify43.0ms

prune97.0ms

localize18.0ms

rewrite38.0ms

series34.0ms

simplify30.0ms

prune88.0ms

localize11.0ms

rewrite92.0ms

series30.0ms

simplify55.0ms

prune188.0ms

localize12.0ms

rewrite44.0ms

series43.0ms

simplify33.0ms

prune111.0ms

regimes127.0ms

bsearch25.0ms

simplify5.0ms

end0.0ms

sample2.2s

Profiling