Details

Time bar (total: 5.1s)

sample50.0ms

Algorithm
intervals
Results
33.0ms624×body80valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
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)
1.1b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite59.0ms

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:
27.0ms
(+ (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)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(+ (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))
99.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify69.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
0564828
12826724
25001715

prune313.0ms

Filtered
112 candidates to 80 candidates (71.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 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))))))
1.1b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-exp-log add-cbrt-cube
12×distribute-rgt-in add-sqr-sqrt *-un-lft-identity distribute-lft-in associate-*r/ prod-diff
10×add-cube-cbrt associate-+r+
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u sub-neg flip3-+ frac-add flip-+ log1p-expm1-u
3×flip3-- flip--
2×associate-+l+ associate-*l* *-commutative unswap-sqr
1×+-commutative fma-def sum-log fma-udef distribute-lft-out
Counts
4 → 99
Calls
4 calls:
12.0ms
(+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))
14.0ms
(* (* 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))))))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))
49.0ms
(* (* a a) (+ 1.0 a))
113.0ms
(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))))))
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify92.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
06561046
13391904
25002895

prune340.0ms

Filtered
111 candidates to 77 candidates (69.4%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (* b b) (- 1.0 (* 3.0 a)))
11.5b
(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)))))))
11.5b
(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)))))))
11.5b
(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)))))))

rewrite16.0ms

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:
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
0.0ms
(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)))))))
0.0ms
(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)))))))

series833.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
264.0ms
(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)))))))
260.0ms
(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)))))))
258.0ms
(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)))))))

simplify52.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03771702
114951526
250011476

prune399.0ms

Filtered
84 candidates to 68 candidates (81.0%)
Pruning

5 alts after pruning (3 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))

rewrite15.0ms

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:
6.0ms
(* 2 (pow a 2))
6.0ms
(- (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))

series224.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 2 (pow a 2))
65.0ms
(- (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)))
70.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify45.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0276764
11144636
25001628

prune272.0ms

Filtered
90 candidates to 61 candidates (67.8%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes72.0ms

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
02821
12821

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s20551×body80valid