Details

sample27.0ms

Algorithm

intervals

Results

9.0ms	226×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	10×	body	640	valid
1.0ms	5×	body	1280	valid
1.0ms	10×	body	160	valid

simplify120.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

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: 17.7b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.6b	(- (+ x y) (/ (* (- z t) y) (- a t)))
11.9b	(/ (* (- 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:

28.0ms	(* (- z t) y)
109.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
63.0ms	(/ (* (- z t) y) (- a t))

simplify47.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

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

prune194.0ms

Filtered

79 candidates to 56 candidates (70.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	10	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	10	80

Merged error: 4.2b

Counts

80 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
2.3b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.8b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite45.0ms

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:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
28.0ms	(* (/ (- 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)))))

series499.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (- a t))
143.0ms	(cbrt (- a t))
96.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
112.0ms	(- (+ 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	5002	1498

prune440.0ms

Filtered

139 candidates to 104 candidates (74.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	131	8	139
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	135	14	149

Merged error: 4.1b

Counts

149 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
2.3b	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
3.4b	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
35×	`add-cbrt-cube`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
15×	`cbrt-prod` `add-sqr-sqrt` `frac-times` `-un-lft-identity` `associate-r/`
14×	`associate-l` `frac-sub`
9×	`pow1` `add-cube-cbrt` `associate-*l/` `add-log-exp`
8×	`times-frac`
7×	`flip3-+` `flip-+`
6×	`cbrt-div`
4×	`flip3--` `flip--`
3×	`pow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `diff-log` `associate-/r/`
1×	`sub-neg` `associate-r` `associate--l+` `sum-log` `*-commutative` `div-inv`

Counts

4 → 120

Calls

4 calls:

3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))
36.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
7.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (- z t))
156.0ms	(cbrt (- z t))
101.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
114.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

simplify86.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	796	2499
1	3082	2071
2	5001	1925

prune342.0ms

Filtered

132 candidates to 77 candidates (58.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	134	12	146

Merged error: 4.1b

Counts

146 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt (- z t)) (cbrt (- z t))))
0.6b	(cbrt (cbrt (- z t)))
2.3b	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (* (cbrt (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (cbrt (- z t)))) (cbrt (- a t))) (/ y (cbrt (- a t)))))
4.3b	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (* (cbrt (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (cbrt (- z t)))) (cbrt (- a t))) (/ y (cbrt (- a t))))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-exp-log`
52×	`prod-exp` `cbrt-unprod`
51×	`add-cbrt-cube`
35×	`cbrt-undiv` `div-exp`
26×	`cbrt-div`
19×	`cbrt-prod` `frac-times`
17×	`associate-*r/`
14×	`associate-l` `frac-sub`
13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`associate-*l/`
9×	`pow1` `add-cube-cbrt` `flip3--` `flip--` `add-log-exp`
8×	`times-frac`
7×	`flip3-+` `flip-+`
3×	`pow-prod-down`
2×	`pow1/3` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `associate-r` `associate--l+` `sum-log` `*-commutative` `div-inv`

Counts

4 → 137

Calls

4 calls:

8.0ms	(cbrt (* (cbrt (- z t)) (cbrt (- z t))))
4.0ms	(cbrt (cbrt (- z t)))
31.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (* (cbrt (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (cbrt (- z t)))) (cbrt (- a t))) (/ y (cbrt (- a t)))))
7.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (* (cbrt (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (cbrt (- z t)))) (cbrt (- a t))) (/ y (cbrt (- a t))))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (* (cbrt (- z t)) (cbrt (- z t))))
148.0ms	(cbrt (cbrt (- z t)))
99.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (* (cbrt (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (cbrt (- z t)))) (cbrt (- a t))) (/ y (cbrt (- a t)))))
115.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (* (cbrt (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (cbrt (- z t)))) (cbrt (- a t))) (/ y (cbrt (- a t))))))

simplify115.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	1009	4100
1	4035	3321
2	5001	3102

prune383.0ms

Filtered

149 candidates to 78 candidates (52.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	148	13	161

Merged error: 4.1b

Counts

161 → 13

regimes319.0ms

Accuracy

19.5% (5.4b remaining)

Error of 9.6b against oracle of 4.2b and baseline of 10.9b

bsearch73.0ms

Steps

Iters	Range		Point
10	1.2853197318124835e-136	1.1263120929303989e-122	1.0947540558329952e-130
3	-1.6353355116055127e-108	-1.405023181230623e-108	-1.5633629083633597e-108

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	15
1	27	15

end0.0ms

sample742.0ms

Algorithm

intervals

Results

298.0ms	7356×	body	80	valid
69.0ms	474×	body	640	valid
43.0ms	398×	body	320	valid
41.0ms	225×	body	1280	valid
19.0ms	255×	body	160	valid
3.0ms	14×	body	2560	valid