Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	225×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	10×	body	1280	valid
1.0ms	12×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	2560	valid

simplify119.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
3.4b	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.8b	(/ (* (- z t) y) (- a t))

rewrite100.0ms

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)
52.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
23.0ms	(/ (* (- z t) y) (- a t))

series231.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* (- z t) y)
120.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
85.0ms	(/ (* (- 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

prune222.0ms

Pruning

13 alts after pruning (13 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))
2.5b	(* (/ (- 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)))))

rewrite172.0ms

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))
117.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
40.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (- a t))
142.0ms	(cbrt (- a t))
94.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
108.0ms	(- (+ 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

prune510.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
2.3b	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
5.1b	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

rewrite206.0ms

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:

4.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
148.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
44.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a t))
151.0ms	(cbrt (- a t))
95.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
109.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	774	2489
1	3059	2067
2	5001	1925

prune411.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
2.3b	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
7.0b	(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

rewrite167.0ms

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` `*-un-lft-identity`
14×	`associate-l`
9×	`pow1` `add-cube-cbrt`
8×	`times-frac`
6×	`cbrt-div` `add-log-exp`
5×	`frac-times` `associate-*r/`
4×	`flip3--` `flip--`
3×	`pow-prod-down` `associate-*l/` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `associate-/r/`
1×	`sub-neg` `diff-log` `associate-r` `*-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

5.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
147.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
6.0ms	(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- a t))
141.0ms	(cbrt (- a t))
100.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
76.0ms	(- y (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	599	1967
1	2327	1558
2	5002	1406

prune343.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.5b

regimes318.0ms

Accuracy

-16.1% (4.5b remaining)

Error of 8.5b against oracle of 4.0b and baseline of 7.9b

bsearch94.0ms

Steps

Iters	Range		Point
7	4.0021071348520306e-64	3.924939067665044e-62	4.716985687040972e-64
10	-2.1206772123425646e-94	-1.3515489369018799e-107	-1.660989681485316e-107

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	39
1	46	39
2	46	39

end0.0ms

sample767.0ms

Algorithm

intervals

Results

230.0ms	7332×	body	80	valid
56.0ms	477×	body	640	valid
33.0ms	250×	body	1280	valid
33.0ms	405×	body	320	valid
15.0ms	262×	body	160	valid
3.0ms	19×	body	2560	valid