Details

analyze644.0ms

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
3.1%	96.7%	0.2%	8
17.2%	82.7%	0.2%	9
21.8%	78%	0.2%	10
30%	68.8%	1.2%	11
31.8%	65.3%	2.9%	12
40.1%	55.3%	4.6%	13
44.5%	50.1%	5.4%	14

sample19.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
1.0ms	44×	body	80	invalid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	733	9
1	733	9

prune5.0ms

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: 2.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)
5.9b	(*.f64 (/.f64 x y) (-.f64 z t))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64` `times-frac_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `pow1_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

2 → 53

Calls

2 calls:

9.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)
10.0ms	(*.f64 (/.f64 x y) (-.f64 z t))

series29.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)
17.0ms	(*.f64 (/.f64 x y) (-.f64 z t))

simplify49.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4963	583
1	4963	583

prune50.0ms

Filtered

43 candidates to 59 candidates (-37.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	54	5	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	6	60

Merged error: 0.0b

Counts

60 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 y)
0.5b	(cbrt.f64 y)
3.8b	(*.f64 (-.f64 z t) (/.f64 x (cbrt.f64 y)))
4.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (-.f64 z t) (/.f64 x (cbrt.f64 y))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-exp-log_binary64`
46×	`prod-exp_binary64`
35×	`add-cbrt-cube_binary64`
32×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
23×	`associate-r_binary64` `times-frac_binary64`
22×	`add-cube-cbrt_binary64`
20×	`cbrt-unprod_binary64` `div-exp_binary64`
16×	`cbrt-prod_binary64`
12×	`associate-l_binary64`
11×	`pow1_binary64` `frac-times_binary64`
10×	`cbrt-undiv_binary64`
8×	`associate-*r/_binary64`
7×	`associate-*l/_binary64`
6×	`flip3--_binary64` `1-exp_binary64` `rec-exp_binary64` `flip--_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`pow1/3_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`

Counts

4 → 129

Calls

4 calls:

1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)
12.0ms	(*.f64 (-.f64 z t) (/.f64 x (cbrt.f64 y)))
18.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (-.f64 z t) (/.f64 x (cbrt.f64 y))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(cbrt.f64 y)
14.0ms	(cbrt.f64 y)
36.0ms	(*.f64 (-.f64 z t) (/.f64 x (cbrt.f64 y)))
19.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (-.f64 z t) (/.f64 x (cbrt.f64 y))))

simplify61.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4964	1219
1	4964	1219

prune68.0ms

Filtered

92 candidates to 141 candidates (-53.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	140	7	147

Merged error: 0.0b

Counts

147 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 z t))
1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 (-.f64 z t))))
2.9b	(*.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 (-.f64 z t)))
4.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 (-.f64 z t)))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

330×	`cbrt-div_binary64`
301×	`frac-times_binary64`
268×	`add-exp-log_binary64`
176×	`prod-exp_binary64`
165×	`flip3--_binary64` `flip--_binary64`
160×	`associate-*r/_binary64`
89×	`associate-*l/_binary64`
82×	`cbrt-unprod_binary64`
73×	`add-cbrt-cube_binary64`
45×	`div-exp_binary64`
42×	`add-sqr-sqrt_binary64`
36×	`pow1_binary64`
30×	`associate-l_binary64`
26×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
24×	`cbrt-prod_binary64`
23×	`cbrt-undiv_binary64`
22×	`pow-prod-down_binary64` `add-cube-cbrt_binary64`
14×	`1-exp_binary64` `rec-exp_binary64`
10×	`associate-r_binary64`
6×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64`
3×	`*-commutative_binary64`
2×	`difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
1×	`pow1/3_binary64`

Counts

4 → 346

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 z t))
23.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 (-.f64 z t))))
13.0ms	(*.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 (-.f64 z t)))
45.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 (-.f64 z t)))))

series121.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt.f64 (-.f64 z t))
42.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 (-.f64 z t))))
34.0ms	(*.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 (-.f64 z t)))
20.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 (-.f64 z t)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

358 → 358

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5005	9393

prune171.0ms

Filtered

205 candidates to 358 candidates (-74.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	356	2	358
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	358	7	365

Merged error: 0.0b

Counts

365 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
4.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 (cbrt.f64 x) (cbrt.f64 y))))))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

1719×	`add-exp-log_binary64`
1210×	`prod-exp_binary64`
758×	`frac-times_binary64`
648×	`cbrt-div_binary64`
404×	`div-exp_binary64`
401×	`associate-*r/_binary64`
348×	`cbrt-unprod_binary64`
324×	`flip3--_binary64` `flip--_binary64`
283×	`add-cbrt-cube_binary64`
232×	`associate-*l/_binary64`
162×	`1-exp_binary64`
114×	`cbrt-undiv_binary64`
66×	`rec-exp_binary64`
54×	`pow1_binary64`
37×	`pow-prod-down_binary64`
8×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
4×	`add-log-exp_binary64`
3×	`times-frac_binary64`
2×	`associate-r_binary64` `pow1/3_binary64` `*-commutative_binary64`
1×	`div-inv_binary64`

Counts

4 → 729

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
39.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
63.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 (cbrt.f64 x) (cbrt.f64 y))))))

series93.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt.f64 x)
14.0ms	(cbrt.f64 x)
41.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
24.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 (cbrt.f64 x) (cbrt.f64 y))))))

simplify192.0ms

Algorithm

egg-herbie

Counts

741 → 741

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4918	19002
1	4918	19002

prune238.0ms

Filtered

220 candidates to 741 candidates (-236.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	741	0	741
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	741	7	748

Merged error: 0.0b

Counts

748 → 7

regimes324.0ms

Accuracy

1.2% (2.2b remaining)

Error of 2.2b against oracle of 0.0b and baseline of 2.2b

bsearch31.0ms

Steps

Iters	Range		Point
9	-2.2009494796599154e-299	8.22647317951487e-309	-6.174035256837851e-304
8	-2.339893276799551e-169	-4.3320711119446584e-172	-2.1281528084172094e-169

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	27
1	34	27

end0.0ms

sample573.0ms

Algorithm

intervals

Results

253.0ms	8000×	body	80	valid
61.0ms	2086×	body	80	invalid

Details

analyze644.0ms

sample19.0ms

simplify42.0ms

prune5.0ms

localize6.0ms

rewrite21.0ms

series29.0ms

simplify49.0ms

prune50.0ms

localize12.0ms

rewrite41.0ms

series86.0ms

simplify61.0ms

prune68.0ms

localize17.0ms

rewrite123.0ms

series121.0ms

simplify93.0ms

prune171.0ms

localize24.0ms

rewrite205.0ms

series93.0ms

simplify192.0ms

prune238.0ms

regimes324.0ms

bsearch31.0ms

simplify2.0ms

end0.0ms

sample573.0ms

Profiling