Details

Time bar (total: 3.4s)

sample47.0ms

Algorithm
intervals
Results
22.0ms97×body1280valid
6.0ms179×body80valid
6.0ms39×body640valid
3.0ms26×body320valid
1.0ms14×body160valid

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0113
1183
2263
3483
41103
53183
616233
750013

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize5.0ms

Local error

Found 1 expressions with local error:

3.4b
(- (exp (* a x)) 1.0)

rewrite4.0ms

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 (* a x)) 1.0)

series33.0ms

Counts
1 → 3
Calls
1 calls:
33.0ms
(- (exp (* a x)) 1.0)

simplify44.0ms

Algorithm
egg-herbie
Counts
17 → 17
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
0103100
130092
2105590
3500190

prune50.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.7b

localize17.0ms

Local error

Found 4 expressions with local error:

2.2b
(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.9b
(* (* 1/2 (pow a 2)) x)
11.3b
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
18.4b
(* (pow a 3) (pow x 3))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
28×add-exp-log
18×associate-*r*
17×prod-exp unswap-sqr
16×associate-*l*
14×unpow-prod-down cube-prod
13×add-cube-cbrt *-un-lft-identity add-cbrt-cube
10×sqr-pow
8×pow1
7×pow-to-exp pow-exp
6×add-log-exp
5×cbrt-unprod
3×pow-prod-down *-commutative
2×distribute-rgt-in cube-mult associate-+l+ distribute-lft-in flip3-+ unpow3 associate-*r/ flip-+
1×+-commutative sum-log
Counts
4 → 113
Calls
4 calls:
7.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
9.0ms
(* (* 1/2 (pow a 2)) x)
6.0ms
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
12.0ms
(* (pow a 3) (pow x 3))

series234.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
20.0ms
(* (* 1/2 (pow a 2)) x)
93.0ms
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
63.0ms
(* (pow a 3) (pow x 3))

simplify101.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0471797
12758738
25001738

prune289.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* a x) 3)
2.2b
(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.9b
(* (* 1/2 (pow a 2)) x)
11.3b
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
14×add-cbrt-cube
11×pow1
10×add-sqr-sqrt
9×prod-exp
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* add-log-exp
5×cbrt-unprod
4×associate-*l*
3×pow-unpow pow-prod-down pow-exp
2×distribute-rgt-in pow-to-exp associate-+l+ pow-pow distribute-lft-in flip3-+ associate-*r/ *-commutative flip-+ rem-cube-cbrt
1×+-commutative cube-mult unpow-prod-down unpow3 cube-prod sum-log unswap-sqr sqr-pow
Counts
4 → 76
Calls
4 calls:
2.0ms
(pow (* a x) 3)
9.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
9.0ms
(* (* 1/2 (pow a 2)) x)
5.0ms
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(pow (* a x) 3)
56.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
20.0ms
(* (* 1/2 (pow a 2)) x)
92.0ms
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify76.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0376530
12297478
25001478

prune191.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* a x) 2)
0.2b
(pow (* a x) 3)
3.8b
(+ (* a x) (* 1/2 (pow (* a x) 2)))
11.3b
(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
10×pow1 add-exp-log
7×add-cbrt-cube
6×add-sqr-sqrt add-cube-cbrt pow-unpow *-un-lft-identity
4×pow-pow pow-exp sum-log
2×+-commutative pow-to-exp unpow-prod-down flip3-+ pow-prod-down prod-exp flip-+ rem-cube-cbrt sqr-pow
1×cube-mult associate-+l+ unpow3 cube-prod cbrt-unprod unpow2
Counts
4 → 64
Calls
4 calls:
2.0ms
(pow (* a x) 2)
2.0ms
(pow (* a x) 3)
3.0ms
(+ (* a x) (* 1/2 (pow (* a x) 2)))
12.0ms
(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(pow (* a x) 2)
47.0ms
(pow (* a x) 3)
58.0ms
(+ (* a x) (* 1/2 (pow (* a x) 2)))
96.0ms
(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

simplify61.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0285425
11624392
25001392

prune142.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes146.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 21.4b

bsearch22.0ms

Steps
ItersRangePoint
7
-0.0012728124422975138
-2.6109793238642456e-05
-0.00019732286240242323

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02615
12615

end0.0ms

sample1.3s

Algorithm
intervals
Results
601.0ms2716×body1280valid
202.0ms1317×body640valid
193.0ms5473×body80valid
78.0ms738×body320valid
29.0ms392×body160valid