Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	55×	body	640	valid
4.0ms	130×	body	80	valid
3.0ms	34×	body	320	valid
2.0ms	18×	body	1280	valid
1.0ms	19×	body	160	valid

simplify18.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.1b

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))
3.3b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite244.0ms

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:

6.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
39.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
189.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (- x 1.0))
28.0ms	(/ 1.0 (+ x 1.0))
42.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
215.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (38.0ms)

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

prune247.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0)))
0.0b	(- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x))
3.3b	(+ (- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

105×	`times-frac`
83×	`*-un-lft-identity`
76×	`add-sqr-sqrt`
44×	`add-cube-cbrt`
33×	`associate-/r*`
26×	`cbrt-prod`
18×	`add-exp-log`
14×	`distribute-lft-out`
12×	`add-cbrt-cube` `difference-of-squares`
11×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`distribute-lft-out--`
4×	`pow1` `div-inv` `associate-/l*`
3×	`flip3--` `frac-add` `associate-/r/` `flip--`
2×	`sub-neg` `associate-+l+` `frac-2neg` `diff-log` `prod-exp` `clear-num` `sum-log` `frac-sub` `cbrt-unprod`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

4 → 155

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
13.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0)))
70.0ms	(- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x))
330.0ms	(+ (- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1.0 (- x 1.0))
60.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0)))
70.0ms	(- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x))
247.0ms	(+ (- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	772	1816
1	3266	1731
2	5001	1693

prune366.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) (cbrt 1.0)) x)
0.0b	(- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0))
0.1b	(* (* (/ (+ x 1.0) (cbrt 1.0)) x) (- x 1.0))
19.0b	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
29×	`associate-l`
26×	`times-frac`
23×	`associate-*l/`
21×	`add-cube-cbrt`
18×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`cbrt-prod`
11×	`pow1`
9×	`flip3--` `flip--`
8×	`associate-r` `frac-add` `add-log-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`frac-times` `distribute-lft-out`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-*r/` `pow-prod-down`
3×	`unswap-sqr`
2×	`cbrt-undiv` `div-exp` `*-commutative`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

19.0ms	(* (/ (+ x 1.0) (cbrt 1.0)) x)
12.0ms	(- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0))
30.0ms	(* (* (/ (+ x 1.0) (cbrt 1.0)) x) (- x 1.0))
24.0ms	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0))

series814.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (/ (+ x 1.0) (cbrt 1.0)) x)
289.0ms	(- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0))
178.0ms	(* (* (/ (+ x 1.0) (cbrt 1.0)) x) (- x 1.0))
228.0ms	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	725	1713
1	3546	1583
2	5002	1581

prune382.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0))
0.0b	(* (/ (+ x 1.0) (cbrt 1.0)) x)
0.0b	(- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0))
19.0b	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
31×	`associate-l`
26×	`times-frac`
22×	`add-cube-cbrt`
21×	`associate-*l/`
13×	`cbrt-prod` `flip3--` `flip--`
11×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`pow1` `frac-times` `associate-r` `frac-add` `add-log-exp`
6×	`distribute-lft-out`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-*r/` `unswap-sqr`
3×	`prod-exp` `cbrt-unprod`
2×	`pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `diff-log` `div-exp` `sum-log` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 115

Calls

4 calls:

55.0ms	(* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0))
19.0ms	(* (/ (+ x 1.0) (cbrt 1.0)) x)
12.0ms	(- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0))
22.0ms	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0))

series838.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0))
120.0ms	(* (/ (+ x 1.0) (cbrt 1.0)) x)
280.0ms	(- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0))
222.0ms	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0))

simplify97.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	663	2035
1	2984	1927
2	5003	1927

prune481.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes33.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 9.7b

bsearch126.0ms

Steps

Iters	Range		Point
10	4.555257425893614e-05	47183757994.54101	461.0848391068729
9	-13600.963204601821	-0.00047371797307045637	-3491.6129493700505

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	33
1	52	33

end0.0ms

sample628.0ms

Algorithm

intervals

Results

215.0ms	1926×	body	640	valid
126.0ms	4057×	body	80	valid
85.0ms	604×	body	1280	valid
79.0ms	944×	body	320	valid
26.0ms	471×	body	160	valid