Details

sample48.0ms

Algorithm

intervals

Results

17.0ms	66×	body	1280	valid
12.0ms	53×	body	640	valid
6.0ms	181×	body	80	valid
5.0ms	39×	body	320	valid
1.0ms	11×	body	160	valid

simplify7.0ms

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: 40.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.0b	(- (exp x) 1.0)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

11.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series59.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify75.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	329
1	625	311
2	2739	309
3	5001	309

prune113.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
0.2b	(* 1/6 (pow x 2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log` `add-log-exp`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp` `sum-log`
2×	`pow1` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 40

Calls

2 calls:

8.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
6.0ms	(* 1/6 (pow x 2))

series49.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
29.0ms	(* 1/6 (pow x 2))

simplify35.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	201	222
1	825	201
2	5001	198

prune82.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/6 (pow x 2))
0.2b	(* 1/6 (pow x 2))
9.8b	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
13.6b	(/ (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`add-exp-log` `associate-r`
15×	`times-frac`
10×	`add-cbrt-cube`
8×	`unpow-prod-down` `unswap-sqr`
6×	`associate-l` `prod-exp` `add-log-exp`
5×	`sum-cubes` `distribute-lft-out` `associate-/l*`
4×	`pow1` `unpow2` `sqr-pow`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 106

Calls

4 calls:

6.0ms	(* 1/6 (pow x 2))
6.0ms	(* 1/6 (pow x 2))
20.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
89.0ms	(/ (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 1/6 (pow x 2))
26.0ms	(* 1/6 (pow x 2))
52.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
81.0ms	(/ (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	406	1692
1	2139	1561
2	5002	1555

prune349.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

9.0b	(/ (sqrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2))))))
9.8b	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
9.8b	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
11.9b	(/ (sqrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (* (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2))))) (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
56×	`times-frac`
45×	`sqrt-prod`
40×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`cbrt-prod`
16×	`associate-/l*`
14×	`cbrt-div`
11×	`add-exp-log` `flip3-+` `sum-cubes` `flip-+` `distribute-lft-out`
10×	`associate-/r/`
8×	`add-cbrt-cube` `add-log-exp`
7×	`associate-/r*`
4×	`pow1` `frac-times` `sqrt-div` `associate-/l/`
3×	`cbrt-undiv` `div-exp`
2×	`+-commutative` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `sum-log` `div-inv`
1×	`prod-exp` `cbrt-unprod`

Counts

4 → 145

Calls

4 calls:

89.0ms	(/ (sqrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2))))))
19.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
20.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
123.0ms	(/ (sqrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (* (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2))))) (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (sqrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2))))))
53.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
52.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
143.0ms	(/ (sqrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (* (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2))))) (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))))

simplify124.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	680	5550
1	2565	5235
2	5002	5204

prune692.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.0b

bsearch47.0ms

Steps

Iters	Range		Point
8	-1.3862719480695398	-4.2961337728369966e-05	-0.0004040655084722963

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	33
1	51	33

end0.0ms

sample1.4s

Algorithm

intervals

Results

605.0ms	2380×	body	1280	valid
287.0ms	1623×	body	640	valid
185.0ms	5461×	body	80	valid
100.0ms	848×	body	320	valid
32.0ms	404×	body	160	valid