Details

Time bar (total: 6.4s)

sample61.0ms

Algorithm
intervals
Results
35.0ms708×body80valid

simplify82.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
05314
117313
253212
3168112
4427812
5500112
done500112

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

rewrite148.0ms

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:
64.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
36.0ms
(* (* a a) (- 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
35.0ms
(* (* b b) (+ 3.0 a))

series315.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
57.0ms
(* (* a a) (- 1.0 a))
109.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))

simplify85.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
0646990
13454779
25001776
done5001776

prune328.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(* (* b b) (+ 3.0 a))
15.9b
(sqrt (pow (+ (* a a) (* b b)) 2.0))
15.9b
(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×sqrt-prod
13×*-un-lft-identity
11×add-cube-cbrt unpow-prod-down
10×pow1 add-exp-log
9×add-cbrt-cube
6×rem-sqrt-square
5×sqr-pow
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×pow-unpow pow-prod-down prod-exp cbrt-unprod
2×sqrt-pow1 pow1/2 associate-*r/
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in flip3-+ associate-*l* pow-exp *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 87
Calls
4 calls:
11.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (+ 3.0 a))
16.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
20.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

series435.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(pow (+ (* a a) (* b b)) 2.0)
33.0ms
(* (* b b) (+ 3.0 a))
149.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
147.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify41.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0299564
11364514
25002509
done5002509

prune389.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(* (* b b) (+ 3.0 a))
15.9b
(sqrt (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0)))
15.9b
(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×pow1 *-un-lft-identity
10×add-exp-log
9×add-cube-cbrt add-cbrt-cube
8×sqrt-prod
7×unpow-prod-down
6×sqrt-pow1
4×expm1-log1p-u rem-sqrt-square associate-*r* pow-prod-down log1p-expm1-u add-log-exp
3×pow-unpow prod-exp cbrt-unprod sqr-pow
2×pow1/2 associate-*r/
1×pow2 distribute-rgt-in pow-to-exp pow-pow distribute-lft-in flip3-+ associate-*l* pow-exp pow-sqr *-commutative pow-prod-up flip-+ distribute-lft-out unswap-sqr
Counts
4 → 83
Calls
4 calls:
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
30.0ms
(* (* b b) (+ 3.0 a))
7.0ms
(sqrt (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0)))
20.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

series463.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))
171.0ms
(sqrt (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0)))
151.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify44.0ms

Counts
95 → 95
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0323491
11422450
25001449
done5001449

prune433.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
8.5b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.5b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.5b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite350.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
251.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
31.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
34.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
31.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series790.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
189.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
190.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
194.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify63.0ms

Counts
107 → 107
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03553170
112762937
250022705
done50022705

prune437.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes195.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02921
12921
done2921

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.0s20783×body80valid