Details

sample28.0ms

Algorithm

intervals

Results

12.0ms	74×	body	1280	valid
4.0ms	40×	body	640	valid
3.0ms	154×	body	80	valid
2.0ms	28×	body	320	valid
1.0ms	19×	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: 38.3b

localize4.0ms

Local error

Found 1 expressions with local error:

4.5b	(- (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)

simplify53.0ms

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	5002	66

prune40.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))
0.4b	(* x 1/6)
3.7b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

rewrite36.0ms

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:

3.0ms	(+ (* x 1/6) 1/2)
13.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
3.0ms	(* x 1/6)
16.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

series159.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* x 1/6) 1/2)
66.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
13.0ms	(* x 1/6)
49.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

simplify68.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (12.0ms)

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

prune193.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
0.0b	(pow (exp x) 3)
4.5b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

158×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
38×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`add-exp-log`
5×	`pow1` `difference-cubes`
4×	`pow-pow`
3×	`pow-unpow` `exp-prod` `associate-/r*`
2×	`associate-+l+` `flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `rem-cube-cbrt`

Counts

4 → 193

Calls

4 calls:

11.0ms	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
67.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
2.0ms	(pow (exp x) 3)
20.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series186.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
91.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
27.0ms	(pow (exp x) 3)
36.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify105.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	596	3033
1	2606	2958
2	5002	2879

prune412.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (exp (+ x x)) (exp x)) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
0.0b	(* (exp (+ x x)) (exp x))
0.0b	(/ (/ (- (* (exp (+ x x)) (exp x)) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))) x)
4.5b	(- (* (exp (+ x x)) (exp x)) (pow 1.0 3))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
80×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
69×	`add-cube-cbrt`
22×	`associate-/l*`
20×	`exp-sum`
18×	`exp-prod` `pow3`
17×	`difference-cubes`
13×	`add-cbrt-cube`
11×	`add-exp-log`
10×	`associate-/r/`
7×	`pow1`
6×	`associate-/r*` `pow-prod-up` `div-inv` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down`
3×	`distribute-rgt-out` `div-sub` `associate-r` `associate-/l/` `distribute-lft-out`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `unswap-sqr`
1×	`sub-neg` `distribute-lft1-in` `pow-plus` `count-2` `diff-log` `distribute-rgt1-in` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 171

Calls

4 calls:

119.0ms	(/ (- (* (exp (+ x x)) (exp x)) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
40.0ms	(* (exp (+ x x)) (exp x))
135.0ms	(/ (/ (- (* (exp (+ x x)) (exp x)) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))) x)
34.0ms	(- (* (exp (+ x x)) (exp x)) (pow 1.0 3))

series278.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (- (* (exp (+ x x)) (exp x)) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
20.0ms	(* (exp (+ x x)) (exp x))
134.0ms	(/ (/ (- (* (exp (+ x x)) (exp x)) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))) x)
35.0ms	(- (* (exp (+ x x)) (exp x)) (pow 1.0 3))

simplify102.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	791	3403
1	3706	3190
2	5001	3165

prune518.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes26.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.1b

bsearch38.0ms

Steps

Iters	Range		Point
10	-4.508778152722845	-1.8057709034692785e-13	-8.833420281998711e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms

sample875.0ms

Algorithm

intervals

Results

390.0ms	2295×	body	1280	valid
178.0ms	1673×	body	640	valid
99.0ms	5388×	body	80	valid
56.0ms	807×	body	320	valid
19.0ms	436×	body	160	valid