Details

Time bar (total: 7.0s)

sample119.0ms

Algorithm
intervals
Results
100.0ms657×body80valid

simplify92.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×unpow-prod-down pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out sqr-pow
Counts
4 → 79
Calls
4 calls:
23.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* (* a a) (+ 1.0 a))
100.0ms
(pow (+ (* a a) (* b b)) 2.0)
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify66.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0504702
12520622
25002622

prune258.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(cbrt (+ 1.0 a))
0.1b
(cbrt (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×pow1 add-exp-log add-sqr-sqrt
9×add-cube-cbrt add-cbrt-cube
8×cbrt-prod
4×cbrt-div add-log-exp
3×unpow-prod-down pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow1/3 associate-*r/ flip-+ distribute-lft-out
1×pow-to-exp flip3-- pow-pow associate-*l* pow-exp *-commutative flip-- unswap-sqr sqr-pow
Counts
4 → 70
Calls
4 calls:
2.0ms
(cbrt (+ 1.0 a))
2.0ms
(cbrt (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(cbrt (+ 1.0 a))
88.0ms
(cbrt (+ 1.0 a))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0404539
11616487
25001483

prune501.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
6.3b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.3b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-div associate-*r/ add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 80
Calls
4 calls:
11.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
11.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
29.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
27.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series440.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
169.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
169.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify48.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03331082
11424980
25002978

prune318.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.2b
(* (pow a 2) (pow b 2))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
27×add-sqr-sqrt
16×unswap-sqr
15×add-log-exp
14×unpow-prod-down *-un-lft-identity
12×pow-to-exp pow-exp
11×associate-*l* add-cbrt-cube
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
3×diff-log
2×pow-prod-down *-commutative distribute-lft-out--
1×+-commutative sub-neg flip3-- flip3-+ associate--l+ flip-- flip-+ distribute-lft-out difference-of-squares
Counts
4 → 105
Calls
4 calls:
136.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
6.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
13.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

series174.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
54.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
34.0ms
(* 2 (* (pow a 2) (pow b 2)))
31.0ms
(* (pow a 2) (pow b 2))

simplify54.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0382781
11594689
25001676

prune234.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes127.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03122
13122

end0.0ms

sample3.4s

Algorithm
intervals
Results
3.1s20396×body80valid