Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	237×	body	80	valid
2.0ms	18×	body	640	valid
2.0ms	13×	body	1280	valid
1.0ms	9×	body	320	valid
0.0ms	6×	body	160	valid
0.0ms	1×	body	2560	valid

simplify121.0ms

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: 17.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
1.7b	(- (+ x y) (/ (* (- z t) y) (- a t)))
10.5b	(/ (* (- z t) y) (- a t))

rewrite93.0ms

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:

21.0ms	(* (- z t) y)
48.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
22.0ms	(/ (* (- z t) y) (- a t))

series224.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* (- z t) y)
122.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
68.0ms	(/ (* (- 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

prune192.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
2.8b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
8.3b	(- (+ 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))
110.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
39.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series545.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (- a t))
150.0ms	(cbrt (- a t))
111.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
127.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (79.0ms)

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

prune471.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
2.8b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
16.0b	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite130.0ms

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))
111.0ms	(* (/ (- 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)))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (- a t))
153.0ms	(cbrt (- a t))
106.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
95.0ms	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify80.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (67.0ms)

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

prune441.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt y)
0.7b	(cbrt y)
0.8b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t))))))
19.8b	(- y (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
39×	`add-cbrt-cube`
36×	`cbrt-div`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
17×	`add-sqr-sqrt` `associate-l`
16×	`associate-/r/`
13×	`flip3--` `associate-r` `flip--`
11×	`*-un-lft-identity`
10×	`times-frac`
9×	`frac-times` `add-cube-cbrt`
6×	`pow1` `cbrt-prod` `add-log-exp`
5×	`associate-r/` `associate-l/`
4×	`unswap-sqr`
2×	`pow1/3` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 110

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
152.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t))))))
5.0ms	(- y (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

series813.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt y)
179.0ms	(cbrt y)
306.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t))))))
140.0ms	(- y (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

simplify107.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	817	2520
1	4048	1868
2	5001	1763

prune437.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.1b

regimes430.0ms

Accuracy

21.8% (5.2b remaining)

Error of 9.2b against oracle of 4.0b and baseline of 10.6b

bsearch57.0ms

Steps

Iters	Range		Point
4	7.2541173275628845e-214	1.4108458195748397e-213	1.344973671404873e-213
7	-2.8011562107228652e-223	-7.653750258453017e-225	-2.76601121203665e-223

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	43
1	40	43

end0.0ms

sample712.0ms

Algorithm

intervals

Results

235.0ms	7394×	body	80	valid
48.0ms	452×	body	640	valid
33.0ms	400×	body	320	valid
31.0ms	232×	body	1280	valid
13.0ms	244×	body	160	valid
3.0ms	16×	body	2560	valid