Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	232×	body	80	valid
1.0ms	11×	body	1280	valid
1.0ms	17×	body	320	valid
1.0ms	11×	body	640	valid
0.0ms	8×	body	160	valid
0.0ms	1×	body	2560	valid

simplify117.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
1.6b	(- (+ x y) (/ (* (- z t) y) (- a t)))
12.3b	(/ (* (- z t) y) (- a t))

rewrite97.0ms

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:

22.0ms	(* (- z t) y)
48.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
25.0ms	(/ (* (- z t) y) (- a t))

series186.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* (- z t) y)
105.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
55.0ms	(/ (* (- z t) y) (- a t))

simplify45.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (10.0ms)

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

prune195.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.7b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
8.2b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite163.0ms

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))
4.0ms	(cbrt (- a t))
112.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
36.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (- a t))
135.0ms	(cbrt (- a t))
90.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
103.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	785	1736
1	3321	1577
2	5002	1498

prune475.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.7b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
13.4b	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite132.0ms

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--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 119

Calls

4 calls:

4.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
113.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
5.0ms	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (- a t))
137.0ms	(cbrt (- a t))
89.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
78.0ms	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	657	1524
1	2791	1373
2	5001	1294

prune453.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
0.6b	(cbrt (cbrt (- a t)))
1.6b	(* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
14.6b	(- y (* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

160×	`times-frac`
132×	`add-sqr-sqrt`
96×	`cbrt-div`
93×	`cbrt-prod`
80×	`associate-l`
69×	`*-un-lft-identity`
53×	`add-cube-cbrt`
42×	`associate-/r/`
39×	`flip3--` `associate-r` `flip--`
36×	`add-exp-log`
25×	`frac-times`
22×	`add-cbrt-cube`
20×	`unswap-sqr`
14×	`cbrt-undiv` `div-exp`
13×	`associate-r/` `associate-l/`
10×	`prod-exp` `cbrt-unprod`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `div-inv` `add-log-exp`
2×	`pow1/3`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 214

Calls

4 calls:

14.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
5.0ms	(cbrt (cbrt (- a t)))
189.0ms	(* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
5.0ms	(- y (* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
142.0ms	(cbrt (cbrt (- a t)))
92.0ms	(* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
81.0ms	(- y (* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1315	4473
1	5001	4247

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

regimes418.0ms

Accuracy

-3.9% (5.9b remaining)

Error of 9.9b against oracle of 4.0b and baseline of 9.7b

bsearch69.0ms

Steps

Iters	Range		Point
6	1.6651791319881276e+111	1.7999316342798602e+112	9.486373537355233e+111
7	-5.3995881599862944e+147	-5.687657779707553e+145	-4.9906133499449885e+147

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	33
1	36	33

end0.0ms

sample986.0ms

Algorithm

intervals

Results

456.0ms	7409×	body	80	valid
49.0ms	441×	body	640	valid
38.0ms	412×	body	320	valid
36.0ms	254×	body	1280	valid
14.0ms	240×	body	160	valid
2.0ms	13×	body	2560	valid