Details

analyze100.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
56.2%	43.7%	0.1%	7
56.2%	43.7%	0.1%	8
76.5%	23.4%	0.1%	9
76.5%	23.4%	0.1%	10
87.8%	12.1%	0.1%	11
87.8%	12.1%	0.1%	12
93.8%	6.1%	0.1%	13
93.8%	6.1%	0.1%	14

sample13.0ms

Algorithm

intervals

Results

7.0ms

256×

body

128

valid

simplify150.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	5237	10

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.0b

Counts

2 → 2

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
2×	`distribute-lft-out_binary64` `times-frac_binary64`
1×	`flip3-+_binary64` `pow1_binary64` `frac-add_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

1 → 14

Calls

1 calls:

13.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

simplify79.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4900	239
1	4900	239

prune13.0ms

Filtered

12 candidates to 17 candidates (-41.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	16	3	19

Merged error: 0.0b

Counts

19 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
0.6b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64`
43×	`cbrt-prod_binary64`
33×	`cbrt-div_binary64`
23×	`add-sqr-sqrt_binary64`
16×	`distribute-lft-out_binary64`
15×	`add-cube-cbrt_binary64`
14×	`times-frac_binary64`
11×	`flip3-+_binary64` `pow1_binary64` `frac-add_binary64` `flip-+_binary64`
10×	`swap-sqr_binary64`
9×	`pow1/3_binary64` `frac-times_binary64`
8×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

31.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
15.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
171.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
178.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
177.0ms	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

simplify98.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4963	2939
1	4963	2939

prune166.0ms

Filtered

83 candidates to 123 candidates (-48.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	122	4	126

Merged error: 0.0b

Counts

126 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1/4 (*.f64 x x))
0.3b	(/.f64 1/4 (*.f64 y y))
2.6b	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
26.5b	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

236×	`add-sqr-sqrt_binary64`
191×	`times-frac_binary64`
110×	`*-un-lft-identity_binary64`
84×	`difference-of-squares_binary64`
42×	`distribute-lft-out--_binary64`
28×	`add-cube-cbrt_binary64`
25×	`div-inv_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`associate-/l*_binary64`
11×	`associate-/r*_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`pow1_binary64`
3×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `frac-sub_binary64`
2×	`cbrt-unprod_binary64` `prod-exp_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `div-sub_binary64`

Counts

4 → 178

Calls

4 calls:

5.0ms	(/.f64 1/4 (*.f64 x x))
5.0ms	(/.f64 1/4 (*.f64 y y))
10.0ms	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
27.0ms	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/.f64 1/4 (*.f64 x x))
44.0ms	(/.f64 1/4 (*.f64 y y))
48.0ms	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
95.0ms	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

simplify117.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4941	6365
1	4941	6365

prune231.0ms

Filtered

133 candidates to 190 candidates (-42.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	189	5	194

Merged error: 0.0b

Counts

194 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt_binary64`
71×	`cbrt-prod_binary64`
63×	`*-un-lft-identity_binary64`
42×	`times-frac_binary64`
33×	`cbrt-div_binary64`
28×	`difference-of-squares_binary64`
16×	`distribute-lft-out--_binary64`
15×	`add-cube-cbrt_binary64`
14×	`swap-sqr_binary64`
12×	`associate-r_binary64` `associate-l_binary64`
11×	`pow1_binary64` `flip3--_binary64` `flip--_binary64` `frac-sub_binary64`
9×	`pow1/3_binary64` `frac-times_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

37.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
14.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
14.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
13.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

series761.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
178.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
192.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
186.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

simplify114.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4954	3967
1	4954	3967

prune374.0ms

Filtered

107 candidates to 147 candidates (-37.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	146	6	152

Merged error: 0.0b

Counts

152 → 6

regimes39.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms

sample352.0ms

Algorithm

intervals

Results

214.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Details

analyze100.0ms

sample13.0ms

simplify150.0ms

prune8.0ms

localize5.0ms

rewrite14.0ms

series37.0ms

simplify79.0ms

prune13.0ms

localize9.0ms

rewrite89.0ms

series742.0ms

simplify98.0ms

prune166.0ms

localize12.0ms

rewrite75.0ms

series227.0ms

simplify117.0ms

prune231.0ms

localize16.0ms

rewrite103.0ms

series761.0ms

simplify114.0ms

prune374.0ms

regimes39.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample352.0ms

Profiling