Details

Time bar (total: 10.1s)

sample51.0ms

Algorithm
intervals
Results
34.0ms622×body80valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01829
15327
215326
341426
4104726
5267426
done500026

prune11.0ms

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)
1.4b
(* (* 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)))))
16.0ms
(* (* a a) (- 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
14.0ms
(* (* b b) (+ 3.0 a))

series291.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
52.0ms
(* (* a a) (- 1.0 a))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)
33.0ms
(* (* b b) (+ 3.0 a))

simplify1.7s

Counts
126 → 126
Iterations

Useful iterations: 2 (242.0ms)

IterNodesCost
02352118
16461782
231711527
done50011527

prune338.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
0.1b
(* (* a a) (- (* 1.0 1.0) (* a a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.4b
(* (* b b) (+ 3.0 a))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
23×add-cbrt-cube
16×*-un-lft-identity
15×pow1
12×add-sqr-sqrt
10×add-cube-cbrt
9×prod-exp cbrt-unprod
8×associate-*r*
6×associate-*r/ pow-prod-down
4×distribute-rgt-in expm1-log1p-u distribute-lft-in times-frac associate-/r* log1p-expm1-u add-log-exp
3×cbrt-undiv unpow-prod-down pow-unpow div-exp distribute-lft-out
2×sub-neg flip3-- flip3-+ associate-*l* prod-diff associate-/r/ *-commutative flip-- flip-+ associate-/l/ unswap-sqr
1×pow-to-exp pow-pow frac-2neg pow-exp clear-num div-inv associate-/l* difference-of-squares sqr-pow
Counts
4 → 106
Calls
4 calls:
15.0ms
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
15.0ms
(* (* a a) (- (* 1.0 1.0) (* a a)))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)
14.0ms
(* (* b b) (+ 3.0 a))

series335.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
81.0ms
(* (* a a) (- (* 1.0 1.0) (* a a)))
103.0ms
(pow (+ (* a a) (* b b)) 2.0)
36.0ms
(* (* b b) (+ 3.0 a))

simplify1.3s

Counts
118 → 118
Iterations

Useful iterations: 2 (221.0ms)

IterNodesCost
02051760
16041626
230411371
done50011371

prune374.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (* b b) (+ 3.0 a))
22.2b
(cbrt (* (* b b) (+ 3.0 a)))
22.2b
(cbrt (* (* b b) (+ 3.0 a)))
22.2b
(cbrt (* (* b b) (+ 3.0 a)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-cbrt-cube
8×associate-*r/
7×*-un-lft-identity
6×add-sqr-sqrt cbrt-div
5×add-cube-cbrt
4×expm1-log1p-u flip3-+ associate-*r* flip-+ log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3 pow-prod-down prod-exp cbrt-unprod
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 65
Calls
4 calls:
13.0ms
(* (* b b) (+ 3.0 a))
8.0ms
(cbrt (* (* b b) (+ 3.0 a)))
8.0ms
(cbrt (* (* b b) (+ 3.0 a)))
8.0ms
(cbrt (* (* b b) (+ 3.0 a)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* b b) (+ 3.0 a))
128.0ms
(cbrt (* (* b b) (+ 3.0 a)))
122.0ms
(cbrt (* (* b b) (+ 3.0 a)))
123.0ms
(cbrt (* (* b b) (+ 3.0 a)))

simplify483.0ms

Counts
77 → 77
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
01261306
13371242
212861125
done50001125

prune368.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (* b b) (+ 3.0 a))
17.9b
(cbrt (pow (fma a a (* b b)) 2.0))
17.9b
(cbrt (pow (fma a a (* b b)) 2.0))
17.9b
(cbrt (pow (fma a a (* b b)) 2.0))

rewrite19.0ms

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))
1.0ms
(cbrt (pow (fma a a (* b b)) 2.0))
1.0ms
(cbrt (pow (fma a a (* b b)) 2.0))
1.0ms
(cbrt (pow (fma a a (* b b)) 2.0))

series689.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* b b) (+ 3.0 a))
157.0ms
(cbrt (pow (fma a a (* b b)) 2.0))
151.0ms
(cbrt (pow (fma a a (* b b)) 2.0))
349.0ms
(cbrt (pow (fma a a (* b b)) 2.0))

simplify511.0ms

Counts
89 → 89
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
01091189
12641158
210191035
done50001035

prune381.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes90.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02456
13356
done3356

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s20276×body80valid