Details

Time bar (total: 20.6s)

sample73.0ms

Algorithm
intervals
Results
47.0ms659×body80valid

simplify3.7s

Counts
1 → 1
Iterations
IterNodes
done5000
42195
3588
2179
155
019

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite150.0ms

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×associate-+r+ sub-neg flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×pow-to-exp +-commutative sum-log pow-pow flip3-- pow-exp flip-- distribute-lft-out
Counts
4 → 100
Calls
4 calls:
80.0ms
(+ (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))
8.0ms
(pow (+ (* a a) (* b b)) 2.0)
24.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
57.0ms
(* (* a a) (+ 1.0 a))
140.0ms
(pow (+ (* a a) (* b b)) 2.0)
93.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.6s

Counts
112 → 112
Iterations
IterNodes
done5000
24499
1620
0201

prune680.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 3.0 a))
0.1b
(* (* a a) (+ 1.0 a))
0.1b
(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))))))
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-cbrt-cube add-exp-log
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×prod-diff
7×associate-*r*
6×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×sub-neg fma-neg
2×flip3-- associate-*l* *-commutative flip-- unswap-sqr
1×flip3-+ diff-log flip-+ fma-udef distribute-lft-out
Counts
4 → 89
Calls
4 calls:
14.0ms
(- 1.0 (* 3.0 a))
41.0ms
(* (* 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))))))
26.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- 1.0 (* 3.0 a))
67.0ms
(* (* a a) (+ 1.0 a))
165.0ms
(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))))))
74.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.1s

Counts
101 → 101
Iterations
IterNodes
done5000
23574
1480
0159

prune573.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (fma b b (* a a)) (* (/ 2.0 2) 2))
0.3b
(pow (fma b b (* a a)) (* (/ 2.0 2) 2))
8.1b
(sqrt (fma 4.0 (fma (* (- 1.0 (* 3.0 a)) b) b (* (* a a) (+ 1.0 a))) (pow (fma b b (* a a)) (* (/ 2.0 2) 2))))
8.1b
(sqrt (fma 4.0 (fma (* (- 1.0 (* 3.0 a)) b) b (* (* a a) (+ 1.0 a))) (pow (fma b b (* a a)) (* (/ 2.0 2) 2))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cube-cbrt
6×unpow-prod-down add-exp-log sqrt-prod
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-to-exp rem-sqrt-square pow-unpow pow-pow sqrt-pow1 pow1/2 pow-exp sqr-pow
Counts
4 → 64
Calls
4 calls:
2.0ms
(pow (fma b b (* a a)) (* (/ 2.0 2) 2))
4.0ms
(pow (fma b b (* a a)) (* (/ 2.0 2) 2))
2.0ms
(sqrt (fma 4.0 (fma (* (- 1.0 (* 3.0 a)) b) b (* (* a a) (+ 1.0 a))) (pow (fma b b (* a a)) (* (/ 2.0 2) 2))))
3.0ms
(sqrt (fma 4.0 (fma (* (- 1.0 (* 3.0 a)) b) b (* (* a a) (+ 1.0 a))) (pow (fma b b (* a a)) (* (/ 2.0 2) 2))))

series873.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(pow (fma b b (* a a)) (* (/ 2.0 2) 2))
132.0ms
(pow (fma b b (* a a)) (* (/ 2.0 2) 2))
278.0ms
(sqrt (fma 4.0 (fma (* (- 1.0 (* 3.0 a)) b) b (* (* a a) (+ 1.0 a))) (pow (fma b b (* a a)) (* (/ 2.0 2) 2))))
321.0ms
(sqrt (fma 4.0 (fma (* (- 1.0 (* 3.0 a)) b) b (* (* a a) (+ 1.0 a))) (pow (fma b b (* a a)) (* (/ 2.0 2) 2))))

simplify554.0ms

Counts
76 → 76
Iterations
IterNodes
done5001
2915
1237
099

prune689.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize107.0ms

Local error

Found 4 expressions with local error:

8.1b
(sqrt (fma 4.0 (fma (* (- 1.0 (* 3.0 a)) b) b (* (* a a) (+ 1.0 a))) (* (pow (* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a)))) 2.0) (pow (cbrt (fma b b (* a a))) 2.0))))
8.7b
(cbrt (fma b b (* a a)))
8.7b
(cbrt (fma b b (* a a)))
8.7b
(cbrt (fma b b (* a a)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
2.0ms
(sqrt (fma 4.0 (fma (* (- 1.0 (* 3.0 a)) b) b (* (* a a) (+ 1.0 a))) (* (pow (* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a)))) 2.0) (pow (cbrt (fma b b (* a a))) 2.0))))
1.0ms
(cbrt (fma b b (* a a)))
1.0ms
(cbrt (fma b b (* a a)))
2.0ms
(cbrt (fma b b (* a a)))

series824.0ms

Counts
4 → 12
Calls
4 calls:
354.0ms
(sqrt (fma 4.0 (fma (* (- 1.0 (* 3.0 a)) b) b (* (* a a) (+ 1.0 a))) (* (pow (* (cbrt (fma b b (* a a))) (cbrt (fma b b (* a a)))) 2.0) (pow (cbrt (fma b b (* a a))) 2.0))))
137.0ms
(cbrt (fma b b (* a a)))
180.0ms
(cbrt (fma b b (* a a)))
154.0ms
(cbrt (fma b b (* a a)))

simplify1.7s

Counts
66 → 66
Iterations
IterNodes
done5000
33108
2647
1204
096

prune864.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes287.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done28
128
021

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.1s20551×body80valid