Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	59×	body	640	valid
4.0ms	133×	body	80	valid
3.0ms	36×	body	320	valid
2.0ms	15×	body	1280	valid
1.0ms	13×	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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

707×	`*-un-lft-identity`
691×	`times-frac`
514×	`add-sqr-sqrt`
482×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
91×	`distribute-lft-out`
64×	`div-inv`
56×	`associate-/r/`
28×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
10×	`fma-def` `add-log-exp`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `flip3--` `frac-add` `flip--` `log1p-expm1-u` `associate-/l*`
2×	`sub-neg` `diff-log` `sum-log` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `clear-num`

Counts

3 → 583

Calls

3 calls:

10.0ms	(/ 1.0 (- x 1.0))
71.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
302.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series264.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ 1.0 (- x 1.0))
41.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
197.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify153.0ms

Algorithm

egg-herbie

Counts

592 → 592

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1108	10776
1	3407	8118
2	5001	7502

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
0.2b	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
2.2b	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
17.0b	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

1572×	`*-un-lft-identity`
1497×	`times-frac`
1096×	`add-sqr-sqrt`
985×	`add-cube-cbrt`
937×	`prod-diff`
472×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
172×	`distribute-lft-out`
150×	`frac-sub`
129×	`div-inv`
117×	`associate-/r/`
101×	`distribute-lft-out--`
94×	`frac-times`
64×	`flip3--` `flip--`
52×	`flip3-+` `associate-r/` `associate-l/` `flip-+`
51×	`difference-of-squares`
47×	`associate-/l/`
41×	`swap-sqr`
31×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
18×	`pow1`
11×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `sub-neg` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`frac-2neg` `fma-neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 1298

Calls

4 calls:

52.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
352.0ms	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
215.0ms	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
758.0ms	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

series948.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
62.0ms	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
209.0ms	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
642.0ms	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

simplify352.0ms

Algorithm

egg-herbie

Counts

1310 → 1310

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2992	36267
1	5001	33666

prune3.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite453.0ms

Algorithm

rewrite-expression-head

Rules

707×	`*-un-lft-identity`
691×	`times-frac`
514×	`add-sqr-sqrt`
482×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
91×	`distribute-lft-out`
64×	`div-inv`
56×	`associate-/r/`
28×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
10×	`fma-def` `add-log-exp`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `flip3--` `frac-add` `flip--` `log1p-expm1-u` `associate-/l*`
2×	`sub-neg` `diff-log` `sum-log` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `clear-num`

Counts

3 → 583

Calls

3 calls:

10.0ms	(/ 1.0 (- x 1.0))
75.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
313.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series272.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ 1.0 (- x 1.0))
43.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
203.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify155.0ms

Algorithm

egg-herbie

Counts

592 → 592

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	1108	10776
1	3407	8118
2	5001	7502

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ 1.0 (- x 1.0)))
0.3b	(cbrt (/ 1.0 (- x 1.0)))
0.3b	(cbrt (/ 1.0 (- x 1.0)))
18.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

rewrite348.0ms

Algorithm

rewrite-expression-head

Rules

371×	`times-frac`
369×	`*-un-lft-identity`
292×	`add-sqr-sqrt`
262×	`add-cube-cbrt`
236×	`associate-+l+`
234×	`prod-diff`
63×	`cbrt-prod`
40×	`distribute-lft-out`
39×	`cbrt-div`
34×	`div-inv`
32×	`associate-/r/`
21×	`frac-add`
15×	`frac-times` `associate-*l/`
14×	`flip3-+` `flip-+`
13×	`difference-of-squares`
12×	`distribute-lft-out--`
10×	`flip3--` `fma-def` `flip--`
9×	`associate-*r/` `add-log-exp`
7×	`frac-sub`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
2×	`sum-log`
1×	`+-commutative` `associate-+l-` `sub-neg` `diff-log`

Counts

4 → 378

Calls

4 calls:

5.0ms	(cbrt (/ 1.0 (- x 1.0)))
5.0ms	(cbrt (/ 1.0 (- x 1.0)))
6.0ms	(cbrt (/ 1.0 (- x 1.0)))
297.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

series613.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (/ 1.0 (- x 1.0)))
120.0ms	(cbrt (/ 1.0 (- x 1.0)))
122.0ms	(cbrt (/ 1.0 (- x 1.0)))
243.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

390 → 390

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	876	7948
1	2989	4845
2	5001	3800

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes35.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 25.8b

bsearch96.0ms

Steps

Iters	Range		Point
8	3.618674152218468	3974.013529084827	100.99693679484112
9	-28256763.0897718	-0.23317146499959118	-111.60844155440536

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	26
1	47	26
2	47	26

end0.0ms

sample639.0ms

Algorithm

intervals

Results

200.0ms	1840×	body	640	valid
119.0ms	4166×	body	80	valid
88.0ms	600×	body	1280	valid
77.0ms	927×	body	320	valid
28.0ms	468×	body	160	valid