Details

Time bar (total: 2.4s)

sample31.0ms

Algorithm
intervals
Results
12.0ms76×body1280valid
6.0ms60×body640valid
3.0ms169×body80valid
2.0ms27×body320valid
1.0ms14×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0103
1133
2153
3153

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 42.4b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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:
6.0ms
(/ (- (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)

simplify74.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0222329
1625311
22739309
35001309

prune112.0ms

Filtered
58 candidates to 43 candidates (74.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New55358
Fresh000
Picked101
Done000
Total56359

Merged error: 0.0b

Counts
59 → 3

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))

rewrite14.0ms

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:
7.0ms
(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
5.0ms
(* 1/6 (pow x 2))

series46.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
24.0ms
(* 1/6 (pow x 2))

simplify34.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0201222
1825201
25001198

prune77.0ms

Filtered
46 candidates to 29 candidates (63.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New46046
Fresh022
Picked011
Done000
Total46349

Merged error: 0.0b

Counts
49 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
0.1b
(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b
(* x 1/6)
2.8b
(/ (+ (* (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×distribute-rgt-in associate-+l+ distribute-lft-in associate-*r/ *-commutative cbrt-unprod associate-/l/ unpow2 sqr-pow
1×cbrt-undiv +-commutative pow-to-exp frac-2neg div-exp pow-prod-down pow-exp clear-num sum-log div-inv
Counts
4 → 91
Calls
4 calls:
8.0ms
(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
11.0ms
(* (pow x 2) (+ (* x 1/6) 1/2))
4.0ms
(* x 1/6)
10.0ms
(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

series148.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
63.0ms
(* (pow x 2) (+ (* x 1/6) 1/2))
13.0ms
(* x 1/6)
44.0ms
(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

simplify65.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0390685
12030628
25002628

prune185.0ms

Filtered
103 candidates to 71 candidates (68.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1021103
Fresh011
Picked101
Done011
Total1033106

Merged error: 0.0b

Counts
106 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x) 3)
0.3b
(* x 1/6)
2.8b
(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)
5.0b
(cbrt (pow (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x) 3))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
45×times-frac
44×add-cube-cbrt *-un-lft-identity
32×cbrt-prod
26×unpow-prod-down cube-prod
11×add-exp-log add-cbrt-cube
7×pow1
5×div-inv
4×add-log-exp
3×pow-unpow associate-*r* associate-*l* associate-/r* associate-/l*
2×cbrt-undiv cube-div cube-mult unpow3 div-exp pow-exp associate-/l/ rem-cube-cbrt sqr-pow
1×pow-to-exp cbrt-div pow-pow frac-2neg flip3-+ pow1/3 pow-prod-down prod-exp clear-num *-commutative rem-cbrt-cube cbrt-unprod flip-+ unswap-sqr
Counts
4 → 135
Calls
4 calls:
10.0ms
(pow (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x) 3)
4.0ms
(* x 1/6)
10.0ms
(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)
9.0ms
(cbrt (pow (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x) 3))

series176.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(pow (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x) 3)
13.0ms
(* x 1/6)
43.0ms
(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)
59.0ms
(cbrt (pow (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x) 3))

simplify79.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
05021507
125121405
250011393

prune256.0ms

Filtered
147 candidates to 81 candidates (55.1%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1470147
Fresh011
Picked011
Done011
Total1473150

Merged error: 0.0b

Counts
150 → 3

regimes19.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 20.6b

bsearch31.0ms

Steps
ItersRangePoint
10
-85019.06990604498
-4.503960361653909e-11
-0.00018041726414346648

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02814
12814

end0.0ms

sample849.0ms

Algorithm
intervals
Results
382.0ms2309×body1280valid
165.0ms1633×body640valid
91.0ms5284×body80valid
61.0ms849×body320valid
20.0ms471×body160valid