Details

Time bar (total: 5.0s)

sample53.0ms

Algorithm
intervals
Results
36.0ms624×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

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

rewrite63.0ms

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:
30.0ms
(+ (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)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
54.0ms
(* (* a a) (+ 1.0 a))
100.0ms
(pow (+ (* a a) (* b b)) 2.0)
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify74.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0564828
12826724
25001715

prune334.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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)))

rewrite45.0ms

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:
15.0ms
(+ (* (* 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)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))
47.0ms
(* (* a a) (+ 1.0 a))
123.0ms
(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))))))
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify98.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
06561046
13391904
25002895

prune363.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

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:
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
17.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
14.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
14.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series609.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
185.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
185.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
186.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04011582
116891442
250021408

prune405.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

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))

rewrite12.0ms

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))
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))

series228.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* 2 (pow a 2))
61.0ms
(- (fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
64.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
74.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify50.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0276764
11144636
25001628

prune267.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes93.0ms

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