Details

Time bar (total: 6.1s)

sample53.0ms

Algorithm
intervals
Results
32.0ms623×body80valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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)
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out
Counts
4 → 100
Calls
4 calls:
62.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
32.0ms
(* (* a a) (+ 1.0 a))
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
28.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
49.0ms
(* (* a a) (+ 1.0 a))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify73.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
0564828
12826724
25001715

prune341.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.1b
(* (* a a) (+ 1.0 a))
0.2b
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
16×pow1 add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt associate-*r*
7×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
6×prod-diff
5×associate-*l*
4×expm1-log1p-u flip3-+ frac-add flip-+ log1p-expm1-u add-log-exp
3×flip3-- *-commutative flip-- unswap-sqr
2×sub-neg
1×fma-udef distribute-lft-out
Counts
4 → 97
Calls
4 calls:
81.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
32.0ms
(* (* a a) (+ 1.0 a))
0.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
28.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
53.0ms
(* (* a a) (+ 1.0 a))
124.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify106.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06661047
13763904
25001897

prune366.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
8.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity prod-diff
10×distribute-rgt-in distribute-lft-in
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u sub-neg sqrt-div associate-*r/ log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 100
Calls
4 calls:
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
28.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
63.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
67.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series460.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
180.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
176.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03881304
116741186
250021176

prune385.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
9.0b
(cbrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.0b
(cbrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.0b
(cbrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 72
Calls
4 calls:
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(cbrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
1.0ms
(cbrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
1.0ms
(cbrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series873.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
268.0ms
(cbrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
277.0ms
(cbrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
270.0ms
(cbrt (fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify51.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03771702
114951526
250011476

prune406.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes153.0ms

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
02932
12932

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s20611×body80valid