Details

sample36.0ms

Algorithm

intervals

Results

15.0ms	248×	body	80	valid
3.0ms	15×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	7×	body	1280	valid
0.0ms	4×	body	160	valid

simplify120.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	109	6
3	195	6
4	445	6
5	828	6
6	1434	6
7	2520	6
8	4830	6
9	5001	6

prune2.0ms

Filtered

1 candidates to 0 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: 16.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
1.4b	(- (+ x y) (/ (* (- z t) y) (- a t)))
10.9b	(/ (* (- z t) y) (- a t))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-l` `associate-/r*` `distribute-lft-out--`
4×	`flip3--` `associate-*l/` `flip--` `difference-of-squares`
3×	`associate-r`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 70

Calls

3 calls:

6.0ms	(* (- z t) y)
10.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.0ms	(/ (* (- z t) y) (- a t))

series199.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* (- z t) y)
107.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
62.0ms	(/ (* (- z t) y) (- a t))

simplify46.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	383	461
1	1704	422
2	5001	422

prune177.0ms

Filtered

79 candidates to 56 candidates (70.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	70	9	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	9	80

Merged error: 3.1b

Counts

80 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
4.2b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.0b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
30×	`associate-r`
27×	`cbrt-prod`
25×	`add-exp-log`
23×	`add-cube-cbrt`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
9×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `frac-times` `div-exp`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
5×	`associate-r/` `associate-l/`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 127

Calls

4 calls:

4.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
32.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series513.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- a t))
142.0ms	(cbrt (- a t))
95.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
134.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	785	1736
1	3321	1577
2	5001	1498

prune397.0ms

Filtered

139 candidates to 105 candidates (75.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	133	6	139
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	134	14	148

Merged error: 3.0b

Counts

148 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

6.3b	(cbrt (/ y (cbrt (- a t))))
6.3b	(cbrt (/ y (cbrt (- a t))))
6.3b	(cbrt (/ y (cbrt (- a t))))
7.5b	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (/ y (cbrt (- a t))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

135×	`cbrt-prod`
72×	`times-frac`
67×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`cbrt-div`
49×	`add-cube-cbrt`
34×	`frac-times`
30×	`frac-sub`
26×	`associate-*l/`
22×	`associate-*r/`
15×	`flip3-+` `flip-+`
9×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3` `div-inv`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 161

Calls

4 calls:

6.0ms	(cbrt (/ y (cbrt (- a t))))
7.0ms	(cbrt (/ y (cbrt (- a t))))
6.0ms	(cbrt (/ y (cbrt (- a t))))
10.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (/ y (cbrt (- a t))))))

series726.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt (/ y (cbrt (- a t))))
188.0ms	(cbrt (/ y (cbrt (- a t))))
188.0ms	(cbrt (/ y (cbrt (- a t))))
168.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (/ y (cbrt (- a t))))))

simplify92.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	807	3157
1	2859	2947
2	5001	2916

prune654.0ms

Filtered

173 candidates to 137 candidates (79.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	172	15	187

Merged error: 3.0b

Counts

187 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

5.9b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
5.9b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
5.9b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
7.5b	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

297×	`cbrt-div`
261×	`frac-times`
153×	`associate-*l/`
129×	`associate-*r/`
126×	`frac-sub`
63×	`flip3-+` `flip-+`
9×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
2×	`diff-log`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

4 → 176

Calls

4 calls:

19.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
22.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
18.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
19.0ms	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

280.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
291.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
283.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
168.0ms	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))

simplify163.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	1756	9997
1	4189	9460
2	5001	9279

prune468.0ms

Filtered

188 candidates to 95 candidates (50.5%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	188	15	203

Merged error: 3.0b

Counts

203 → 15

regimes360.0ms

Accuracy

24.9% (5.6b remaining)

Error of 9.6b against oracle of 4.0b and baseline of 11.5b

bsearch118.0ms

Steps

Iters	Range		Point
9	1.4238979729314793e-103	1.5553539010031847e-94	1.3163947765276547e-99
8	-3.1474851239653077e-05	-1.9767486436385896e-08	-2.0079036956703867e-08

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	22
1	30	22

end0.0ms

sample742.0ms

Algorithm

intervals

Results

286.0ms	7407×	body	80	valid
66.0ms	448×	body	640	valid
51.0ms	403×	body	320	valid
41.0ms	236×	body	1280	valid
21.0ms	288×	body	160	valid
3.0ms	12×	body	2560	valid

Details

sample36.0ms

simplify120.0ms

prune2.0ms

localize9.0ms

rewrite27.0ms

series199.0ms

simplify46.0ms

prune177.0ms

localize12.0ms

rewrite55.0ms

series513.0ms

simplify90.0ms

prune397.0ms

localize20.0ms

rewrite38.0ms

series726.0ms

simplify92.0ms

prune654.0ms

localize20.0ms

rewrite94.0ms

series1.0s

simplify163.0ms

prune468.0ms

regimes360.0ms

bsearch118.0ms

simplify3.0ms

end0.0ms

sample742.0ms

Profiling