Details

sample89.0ms

Algorithm

intervals

Results

39.0ms	71×	body	1280	valid
19.0ms	56×	body	640	valid
8.0ms	20×	body	2560	valid
7.0ms	64×	body	80	valid
5.0ms	23×	body	320	valid
3.0ms	22×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ x (sqrt (+ (* x x) 1.0)))
4.7b	(log (+ x (sqrt (+ (* x x) 1.0))))
12.8b	(sqrt (+ (* x x) 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

Calls

3 calls:

8.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series277.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(+ x (sqrt (+ (* x x) 1.0)))
171.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms	(sqrt (+ (* x x) 1.0))

simplify139.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (134.0ms)

Iter	Nodes	Cost
0	309	393
1	1027	364
2	4764	348
3	5002	347

prune146.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
182×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
118×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 286

Calls

2 calls:

116.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
74.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series298.0ms

Counts

2 → 6

Calls

2 calls:

155.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
143.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify120.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	854	2089
1	4642	1654
2	5001	1654

prune434.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- 1/36) (pow (/ x (sqrt 1.0)) 6))
0.1b	(* (pow (/ x (sqrt 1.0)) 3) 1/6)
13.8b	(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
36.0b	(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
69×	`times-frac`
60×	`associate-l`
57×	`add-cube-cbrt` `*-un-lft-identity`
50×	`unpow-prod-down`
30×	`sqrt-prod`
29×	`associate-r`
25×	`cube-prod`
22×	`add-exp-log`
13×	`unswap-sqr`
10×	`add-cbrt-cube`
8×	`prod-exp`
6×	`add-log-exp`
4×	`pow1` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `div-inv` `sqr-pow`
3×	`cube-div` `distribute-lft-neg-in` `distribute-rgt-neg-in` `div-exp` `associate-l/` `associate-/r` `associate-/l*`
2×	`pow-to-exp` `associate-+r+` `frac-add` `*-commutative` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `distribute-lft-neg-out` `distribute-rgt-in` `cube-mult` `neg-mul-1` `frac-2neg` `distribute-lft-in` `unpow3` `clear-num` `sum-log`

Counts

4 → 176

Calls

4 calls:

26.0ms	(* (- 1/36) (pow (/ x (sqrt 1.0)) 6))
28.0ms	(* (pow (/ x (sqrt 1.0)) 3) 1/6)
13.0ms	(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
134.0ms	(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))

series1.1s

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (- 1/36) (pow (/ x (sqrt 1.0)) 6))
141.0ms	(* (pow (/ x (sqrt 1.0)) 3) 1/6)
305.0ms	(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
511.0ms	(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))

simplify136.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	853	2672
1	4339	2417
2	5001	2417

prune556.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

18.8b	(cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))
18.8b	(cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))
18.8b	(cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))
28.7b	(* (/ 1 (* (cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6))) (cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6))))) (/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

56×	`cbrt-div`
49×	`add-exp-log`
43×	`add-sqr-sqrt`
33×	`times-frac` `associate-*l/`
31×	`associate-l`
28×	`cube-div` `flip3-+` `frac-add` `associate-/r/` `flip-+`
26×	`associate-r`
25×	`*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`cbrt-prod`
20×	`prod-exp`
18×	`add-cbrt-cube`
17×	`frac-times`
15×	`div-exp`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1`
5×	`associate-*r/`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow1/3`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 143

Calls

4 calls:

47.0ms	(cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))
47.0ms	(cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))
45.0ms	(cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))
1.0s	(* (/ 1 (* (cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6))) (cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6))))) (/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))))

series2.0s

Counts

4 → 12

Calls

4 calls:

470.0ms	(cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))
531.0ms	(cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))
472.0ms	(cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))
524.0ms	(* (/ 1 (* (cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6))) (cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6))))) (/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (cbrt (+ (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	919	7786
1	5001	6961

prune822.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes45.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.6b

bsearch102.0ms

Steps

Iters	Range		Point
9	0.00035723662727133143	33.11368705657117	0.8876369628249866
10	-29.541817090935037	-6.322351620237733e-11	-1.0202654642914022

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	2347×	body	1280	valid
537.0ms	1579×	body	640	valid
309.0ms	781×	body	2560	valid
176.0ms	793×	body	320	valid
140.0ms	2075×	body	80	valid
60.0ms	425×	body	160	valid