Details

sample22.0ms

Algorithm

intervals

Results

7.0ms	66×	body	640	valid
4.0ms	134×	body	80	valid
2.0ms	29×	body	320	valid
2.0ms	12×	body	1280	valid
1.0ms	15×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.8b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.8b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
38.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
183.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1.0 (- x 1.0))
29.0ms	(/ 1.0 (+ x 1.0))
41.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
214.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5002	816

prune232.0ms

Filtered

126 candidates to 92 candidates (73.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(* (+ x 1.0) x)
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
18.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

48×	`associate-*l/`
16×	`frac-add`
15×	`add-sqr-sqrt` `flip3--` `*-un-lft-identity` `flip--`
14×	`flip3-+` `flip-+`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`frac-times`
11×	`associate-r`
9×	`add-cube-cbrt` `associate-l`
6×	`associate-*r/` `add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `sub-neg` `associate-+l+` `distribute-lft-in`
3×	`*-commutative`
2×	`distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `sum-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 105

Calls

4 calls:

17.0ms	(* (+ x 1.0) x)
17.0ms	(* (+ x 1.0) x)
24.0ms	(* (* (+ x 1.0) x) (- x 1.0))
10.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series180.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (+ x 1.0) x)
45.0ms	(* (+ x 1.0) x)
94.0ms	(* (* (+ x 1.0) x) (- x 1.0))
1.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify117.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	751	1323
1	4427	1240
2	5003	1240

prune320.0ms

Filtered

117 candidates to 82 candidates (70.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (pow (* (- (* x x) (* 1.0 1.0)) x) 1))
0.0b	(* (+ x 1.0) x)
0.0b	(* (- (* x x) (* 1.0 1.0)) x)
18.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

76×	`associate-*l/`
32×	`frac-add`
25×	`flip3--` `flip--`
22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`flip3-+` `flip-+`
18×	`add-cube-cbrt` `associate-/l/`
16×	`add-exp-log` `frac-times`
15×	`times-frac`
10×	`add-cbrt-cube`
8×	`pow1` `associate-r/` `associate-l*`
6×	`associate-r` `add-log-exp`
5×	`associate-/r*`
4×	`unpow-prod-down` `associate-+l+` `div-exp` `sqr-pow`
3×	`prod-exp` `associate-/l*`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `difference-of-squares`

Counts

4 → 129

Calls

4 calls:

25.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (pow (* (- (* x x) (* 1.0 1.0)) x) 1))
13.0ms	(* (+ x 1.0) x)
10.0ms	(* (- (* x x) (* 1.0 1.0)) x)
10.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series185.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (pow (* (- (* x x) (* 1.0 1.0)) x) 1))
45.0ms	(* (+ x 1.0) x)
74.0ms	(* (- (* x x) (* 1.0 1.0)) x)
1.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	928	2418
1	5001	2306

prune464.0ms

Filtered

141 candidates to 109 candidates (77.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3))))
0.1b	(/ 1 (pow x 5))
0.1b	(/ 1 (pow x 7))
0.3b	(/ 1 (pow x 3))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

88×	`*-un-lft-identity`
87×	`times-frac`
64×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down`
31×	`add-exp-log`
26×	`associate-/r*`
24×	`distribute-lft-out`
18×	`div-exp`
16×	`div-inv`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*` `add-log-exp`
4×	`pow1` `cube-mult` `unpow3` `frac-add`
3×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `sum-log` `inv-pow`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `associate-+r+`

Counts

4 → 208

Calls

4 calls:

176.0ms	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3))))
4.0ms	(/ 1 (pow x 5))
4.0ms	(/ 1 (pow x 7))
5.0ms	(/ 1 (pow x 3))

series188.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3))))
43.0ms	(/ 1 (pow x 5))
60.0ms	(/ 1 (pow x 7))
32.0ms	(/ 1 (pow x 3))

simplify76.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	586	1177
1	3298	983
2	5001	983

prune303.0ms

Filtered

220 candidates to 85 candidates (38.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 24.8b

bsearch119.0ms

Steps

Iters	Range		Point
8	48.29475874355119	356290.51007653365	485.7282925563347
10	-204248214.92732975	-1.534026600097144e-05	-127880528.28648625

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	25
1	53	25

end0.0ms

sample584.0ms

Algorithm

intervals

Results

198.0ms	1835×	body	640	valid
120.0ms	4217×	body	80	valid
75.0ms	949×	body	320	valid
73.0ms	551×	body	1280	valid
24.0ms	450×	body	160	valid