Details

Time bar (total: 5.0s)

sample48.0ms

Algorithm
intervals
Results
31.0ms624×body80valid

simplify50.0ms

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

localize15.0ms

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)
1.1b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite65.0ms

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:
28.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
15.0ms
(* (* a a) (+ 1.0 a))
7.0ms
(pow (+ (* a a) (* b b)) 2.0)
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
48.0ms
(* (* a a) (+ 1.0 a))
100.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify73.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0564828
12826724
25001715

prune314.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.1b
(* (* b b) (- 1.0 (* 3.0 a)))
12.2b
(sqrt (pow (+ (* a a) (* b b)) 2.0))
12.2b
(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×sqrt-prod
13×add-cube-cbrt *-un-lft-identity
11×unpow-prod-down
10×pow1 add-exp-log
9×add-cbrt-cube
6×rem-sqrt-square prod-diff
5×distribute-rgt-in distribute-lft-in sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg sqrt-pow1 pow1/2 associate-*r/
1×pow-to-exp flip3-- pow-pow associate-*l* pow-exp *-commutative flip-- unswap-sqr
Counts
4 → 94
Calls
4 calls:
5.0ms
(pow (+ (* a a) (* b b)) 2.0)
14.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
8.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
7.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

series433.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(pow (+ (* a a) (* b b)) 2.0)
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
139.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
145.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0343691
11458621
25002611

prune380.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (* b b) (- 1.0 (* 3.0 a)))
11.5b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
11.5b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
11.5b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite60.0ms

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×cbrt-div prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 78
Calls
4 calls:
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
15.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
15.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
15.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series600.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
181.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
190.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
177.0ms
(cbrt (+ (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
90 → 90
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04011582
116891442
250021408

prune380.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2 (pow a 2))
0.0b
(- (fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
0.1b
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
1.4b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
9×add-exp-log prod-diff
8×associate-*r*
6×add-cbrt-cube add-log-exp
4×pow1 expm1-log1p-u unpow-prod-down log1p-expm1-u unswap-sqr
3×fma-neg associate-*l* prod-exp fma-udef
2×unpow2 sqr-pow
1×pow-to-exp sub-neg flip3-- diff-log pow-exp associate--l+ *-commutative flip-- cbrt-unprod distribute-lft-out-- difference-of-squares
Counts
4 → 78
Calls
4 calls:
10.0ms
(* 2 (pow a 2))
3.0ms
(- (fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
0.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
0.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series217.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* 2 (pow a 2))
64.0ms
(- (fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
63.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
66.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify48.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0276764
11144636
25001628

prune250.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes99.0ms

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
02721
12721

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s20551×body80valid