Details

sample32.0ms

Algorithm

intervals

Results

14.0ms	251×	body	80	valid
2.0ms	11×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	8×	body	160	valid

simplify123.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.3b	(- (+ x y) (/ (* (- z t) y) (- a t)))
11.7b	(/ (* (- z t) y) (- a t))

rewrite49.0ms

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:

10.0ms	(* (- z t) y)
28.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.0ms	(/ (* (- z t) y) (- a t))

series205.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* (- z t) y)
111.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
64.0ms	(/ (* (- z t) y) (- a t))

simplify51.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (12.0ms)

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

prune199.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
3.6b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.5b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite93.0ms

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:

2.0ms	(cbrt (- a t))
2.0ms	(cbrt (- a t))
64.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
18.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (- a t))
144.0ms	(cbrt (- a t))
97.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
111.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (74.0ms)

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

prune462.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
3.6b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
13.6b	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite75.0ms

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:

2.0ms	(cbrt (- a t))
2.0ms	(cbrt (- a t))
64.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
2.0ms	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (- a t))
146.0ms	(cbrt (- a t))
99.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
84.0ms	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (61.0ms)

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

prune442.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
2.8b	(- (+ x y) (* (- z t) (/ y (- a t))))
11.6b	(* (- z t) (/ y (- a t)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 107

Calls

3 calls:

5.0ms	(/ y (- a t))
19.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
23.0ms	(* (- z t) (/ y (- a t)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(/ y (- a t))
110.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
63.0ms	(* (- z t) (/ y (- a t)))

simplify66.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	559	844
1	2676	803
2	5001	803

prune298.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.6b

regimes242.0ms

Accuracy

31.5% (5.5b remaining)

Error of 9.2b against oracle of 3.7b and baseline of 11.7b

bsearch105.0ms

Steps

Iters	Range		Point
8	9.016362729330296e-116	2.274969720409758e-111	2.0545474487522696e-112
10	-8.18782140230201e-175	-4.635121056576664e-192	-8.04642291642522e-175

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	9
1	27	9

end0.0ms

sample907.0ms

Algorithm

intervals

Results

438.0ms	7413×	body	80	valid
73.0ms	436×	body	640	valid
54.0ms	405×	body	320	valid
49.0ms	234×	body	1280	valid
23.0ms	244×	body	160	valid
4.0ms	15×	body	2560	valid