Details

sample32.0ms

Algorithm

intervals

Results

15.0ms	81×	body	1280	valid
4.0ms	42×	body	640	valid
3.0ms	158×	body	80	valid
3.0ms	40×	body	320	valid
1.0ms	9×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize4.0ms

Local error

Found 1 expressions with local error:

2.5b	(- (exp x) 1.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

4.0ms

(- (exp x) 1.0)

series14.0ms

Counts

1 → 3

Calls

1 calls:

14.0ms

(- (exp x) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	81	72
1	185	67
2	499	66
3	1399	66
4	5001	66

prune38.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x 1/6) 1/2)
0.0b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)
1.6b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-r` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`associate-r/` `-commutative` `cbrt-unprod` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 89

Calls

4 calls:

4.0ms	(+ (* x 1/6) 1/2)
8.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
3.0ms	(* x 1/6)
10.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

series158.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* x 1/6) 1/2)
66.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
14.0ms	(* x 1/6)
48.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	384	622
1	2008	564
2	5002	564

prune194.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
13.1b	(cbrt (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
13.1b	(cbrt (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
13.1b	(cbrt (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`

Counts

4 → 50

Calls

4 calls:

1.0ms	(cbrt x)
7.0ms	(cbrt (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
7.0ms	(cbrt (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
7.0ms	(cbrt (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))

series363.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt x)
63.0ms	(cbrt (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
61.0ms	(cbrt (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
61.0ms	(cbrt (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))

simplify97.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	197	690
1	628	648
2	2899	640
3	5001	640

prune255.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (sqrt (exp x)) (sqrt 1.0))
0.0b	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
2.5b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

6.0ms	(+ (sqrt (exp x)) (sqrt 1.0))
15.0ms	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
6.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series167.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (sqrt (exp x)) (sqrt 1.0))
96.0ms	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
40.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	248	720
1	1094	623
2	5002	599

prune144.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.7b

bsearch31.0ms

Steps

Iters	Range		Point
9	-0.0004106978961831668	-2.2963680336716634e-10	-0.00019657375756151034

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	18
1	29	18

end0.0ms

sample872.0ms

Algorithm

intervals

Results

380.0ms	2227×	body	1280	valid
178.0ms	1711×	body	640	valid
102.0ms	5519×	body	80	valid
60.0ms	818×	body	320	valid
17.0ms	392×	body	160	valid