Details

Time bar (total: 6.2s)

sample89.0ms

Algorithm
intervals
Results
71.0ms639×body80valid

simplify82.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05314
117313
253212
3168112
4427812
5500112

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.5b
(* (* b b) (+ 3.0 a))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
18×prod-diff
15×pow1 add-exp-log
14×add-cbrt-cube
13×distribute-rgt-in distribute-lft-in
9×associate-*r*
7×fma-def
6×unpow-prod-down 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 distribute-lft-out-- difference-of-squares
Counts
4 → 114
Calls
4 calls:
29.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
15.0ms
(* (* a a) (- 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
14.0ms
(* (* b b) (+ 3.0 a))

series309.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
58.0ms
(* (* a a) (- 1.0 a))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))

simplify91.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
0646990
13454779
25001776

prune340.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 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) (+ 3.0 a)))))
1.5b
(* (* b b) (+ 3.0 a))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
36×prod-diff
34×add-sqr-sqrt *-un-lft-identity
30×add-cube-cbrt
24×distribute-rgt-in distribute-lft-in
22×associate-+l+
14×pow1 add-exp-log add-cbrt-cube
12×associate-*r/
9×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-+r+ associate-*l* *-commutative unswap-sqr
1×+-commutative fma-def sum-log fma-udef distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 125
Calls
4 calls:
13.0ms
(+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))
15.0ms
(* (* 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) (+ 3.0 a)))))
13.0ms
(* (* b b) (+ 3.0 a))

series253.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))
55.0ms
(* (* a a) (- 1.0 a))
115.0ms
(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) (+ 3.0 a)))))
33.0ms
(* (* b b) (+ 3.0 a))

simplify108.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07051308
138611011
250011006

prune431.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (* b b) (+ 3.0 a))
21.8b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.8b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.8b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
13×*-un-lft-identity
12×add-sqr-sqrt
11×add-cube-cbrt
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod sqr-pow
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ associate-*l* *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 77
Calls
4 calls:
13.0ms
(* (* b b) (+ 3.0 a))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series504.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (* b b) (+ 3.0 a))
153.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
158.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
150.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0270642
11138585
25001579

prune373.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 2 (pow a 2))
0.1b
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
1.8b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×add-exp-log associate-*r*
6×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down unswap-sqr
3×pow1 expm1-log1p-u associate-*l* prod-exp log1p-expm1-u add-log-exp
2×fma-udef unpow2 sqr-pow
1×pow-to-exp pow-exp *-commutative cbrt-unprod
Counts
3 → 49
Calls
3 calls:
6.0ms
(* 2 (pow a 2))
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))

series163.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(* 2 (pow a 2))
65.0ms
(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))

simplify183.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 3 (178.0ms)

IterNodesCost
0175315
1770276
24508274
35001270

prune185.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes103.0ms

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
02620
12620

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.3s20597×body80valid