Details

Time bar (total: 3.5s)

sample36.0ms

Algorithm
intervals
Results
12.0ms64×body1280valid
8.0ms59×body640valid
6.0ms180×body80valid
3.0ms28×body320valid
1.0ms12×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0103
1133
2153
3153

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- (exp x) 1.0) x)
3.3b
(- (exp x) 1.0)

rewrite19.0ms

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:
13.0ms
(/ (- (exp x) 1.0) x)
4.0ms
(- (exp x) 1.0)

series54.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(/ (- (exp x) 1.0) x)
15.0ms
(- (exp x) 1.0)

simplify73.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0222329
1625311
22739309
35001309

prune108.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

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))

series44.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
25.0ms
(* 1/6 (pow x 2))

simplify37.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0201222
1825201
25001198

prune78.0ms

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
(+ 1.0 (exp x))
0.0b
(* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x)
0.0b
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x))
3.3b
(- (pow (exp x) 3) (pow 1.0 3))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
82×add-sqr-sqrt
48×difference-of-squares
40×*-un-lft-identity
36×unpow-prod-down cube-prod
25×times-frac associate-/l*
24×sqr-pow
15×distribute-lft-out--
11×add-exp-log add-cbrt-cube
8×add-cube-cbrt add-log-exp
6×pow1
4×associate-*l/
3×difference-cubes flip3-+ associate-*r* associate-*l* flip-+
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ flip-- cbrt-unprod associate-/l/
1×+-commutative sub-neg frac-2neg diff-log div-sub pow-prod-down clear-num associate-/r* sum-log *-commutative div-inv distribute-lft-out unswap-sqr
Counts
4 → 136
Calls
4 calls:
3.0ms
(+ 1.0 (exp x))
43.0ms
(* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x)
57.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x))
20.0ms
(- (pow (exp x) 3) (pow 1.0 3))

series243.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+ 1.0 (exp x))
67.0ms
(* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x)
130.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x))
39.0ms
(- (pow (exp x) 3) (pow 1.0 3))

simplify70.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
05321729
123351593
250021593

prune330.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* 1.0 (* (sqrt (+ 1.0 (exp x))) (sqrt (+ 1.0 (exp x))))) (exp (+ x x))) x)
0.0b
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (+ (* 1.0 (* (sqrt (+ 1.0 (exp x))) (sqrt (+ 1.0 (exp x))))) (exp (+ x x))) x))
0.6b
(* (sqrt (+ 1.0 (exp x))) (sqrt (+ 1.0 (exp x))))
3.3b
(- (pow (exp x) 3) (pow 1.0 3))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
102×add-sqr-sqrt
60×*-un-lft-identity
48×difference-of-squares
36×unpow-prod-down cube-prod
26×sqrt-prod
25×times-frac associate-/l*
24×sqr-pow
21×pow1
16×add-cube-cbrt
15×distribute-lft-out--
13×add-exp-log add-cbrt-cube
12×sqrt-div
11×swap-sqr
10×associate-*r* associate-*l*
8×sqrt-pow1 flip3-+ pow1/2 flip-+
6×associate-*l/ distribute-lft-out add-log-exp
5×pow-prod-up unswap-sqr
4×frac-times pow-prod-down
3×difference-cubes prod-exp pow-sqr cbrt-unprod
2×cbrt-undiv flip3-- associate-*r/ div-exp associate-/r/ *-commutative flip-- associate-/l/
1×pow2 sub-neg frac-2neg pow-plus sqrt-unprod diff-log div-sub clear-num associate-/r* rem-square-sqrt div-inv
Counts
4 → 186
Calls
4 calls:
130.0ms
(* (+ (* 1.0 (* (sqrt (+ 1.0 (exp x))) (sqrt (+ 1.0 (exp x))))) (exp (+ x x))) x)
86.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (+ (* 1.0 (* (sqrt (+ 1.0 (exp x))) (sqrt (+ 1.0 (exp x))))) (exp (+ x x))) x))
23.0ms
(* (sqrt (+ 1.0 (exp x))) (sqrt (+ 1.0 (exp x))))
20.0ms
(- (pow (exp x) 3) (pow 1.0 3))

series255.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (+ (* 1.0 (* (sqrt (+ 1.0 (exp x))) (sqrt (+ 1.0 (exp x))))) (exp (+ x x))) x)
136.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (+ (* 1.0 (* (sqrt (+ 1.0 (exp x))) (sqrt (+ 1.0 (exp x))))) (exp (+ x x))) x))
8.0ms
(* (sqrt (+ 1.0 (exp x))) (sqrt (+ 1.0 (exp x))))
41.0ms
(- (pow (exp x) 3) (pow 1.0 3))

simplify99.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
06132576
129502031
250011983

prune467.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes20.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.6b

bsearch44.0ms

Steps
ItersRangePoint
9
-0.00029412782026305056
-4.163765984402517e-10
-0.00012037718021432156

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03822
13822

end0.0ms

sample1.0s

Algorithm
intervals
Results
425.0ms2253×body1280valid
212.0ms1663×body640valid
174.0ms5472×body80valid
69.0ms819×body320valid
24.0ms401×body160valid