Details

Time bar (total: 5.6s)

sample63.0ms

Algorithm
intervals
Results
39.0ms713×body80valid

simplify95.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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

rewrite129.0ms

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:
54.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
31.0ms
(* (* a a) (+ 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms
(* (* a a) (+ 1.0 a))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify71.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
0504702
12520622
25002622

prune272.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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)))
11.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
11.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite180.0ms

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:
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
28.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
59.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
61.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series432.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
163.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
172.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify56.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03331080
11424980
25002978

prune336.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
11.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
11.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
11.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-sqr-sqrt
9×add-exp-log sqrt-prod add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 70
Calls
4 calls:
28.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
57.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
57.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
61.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series762.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
375.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
165.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
171.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify55.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03331266
114241182
250021179

prune348.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.4b
(* (pow a 2) (pow b 2))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
28×prod-exp
24×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×associate-*l*
10×add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt *-un-lft-identity
5×pow1 add-log-exp
4×cbrt-unprod
2×pow-prod-down *-commutative
1×+-commutative flip3-+ sum-log flip-+
Counts
3 → 87
Calls
3 calls:
13.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
26.0ms
(* 2 (* (pow a 2) (pow b 2)))
17.0ms
(* (pow a 2) (pow b 2))

series115.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
36.0ms
(* 2 (* (pow a 2) (pow b 2)))
30.0ms
(* (pow a 2) (pow b 2))

simplify55.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0297518
11270445
25001432

prune186.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes107.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03250
13250

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s20279×body80valid