Details

Time bar (total: 12.6s)

sample28.0ms

Algorithm
intervals
Results
7.0ms256×pre80true
6.0ms256×body80valid

simplify64.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
1187
2417
3767
41137
51177
done1177

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 1 expressions with local error:

0.1b
(* a (+ (+ b c) d))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
5×add-sqr-sqrt associate-*r*
3×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt distribute-lft-out
2×associate-*r/
1×distribute-rgt-in expm1-log1p-u distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ log1p-expm1-u add-log-exp unswap-sqr
Counts
1 → 26
Calls
1 calls:
98.0ms
(* a (+ (+ b c) d))

series43.0ms

Counts
1 → 3
Calls
1 calls:
43.0ms
(* a (+ (+ b c) d))

simplify560.0ms

Counts
29 → 29
Iterations

Useful iterations: done (558.0ms)

IterNodesCost
054271
1170258
2764230
done5000228

prune133.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (+ b c) d))
0.0b
(sqrt (+ (+ b c) d))
0.2b
(* a (sqrt (+ (+ b c) d)))
0.3b
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))

rewrite310.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
21×add-sqr-sqrt sqrt-prod
18×sqrt-div
16×associate-*r*
13×pow1
12×distribute-lft-out
11×add-cbrt-cube add-exp-log add-cube-cbrt
10×associate-*r/
9×flip3-+ flip-+
4×expm1-log1p-u frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative hypot-def unswap-sqr
Counts
4 → 101
Calls
4 calls:
36.0ms
(sqrt (+ (+ b c) d))
32.0ms
(sqrt (+ (+ b c) d))
97.0ms
(* a (sqrt (+ (+ b c) d)))
142.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (+ (+ b c) d))
67.0ms
(sqrt (+ (+ b c) d))
95.0ms
(* a (sqrt (+ (+ b c) d)))
99.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))

simplify1.0s

Counts
113 → 113
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01411627
13801299
218041198
done50011165

prune439.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (+ b c) (+ b c)) (* d d))
0.0b
(* (+ b c) (+ b c))
0.5b
(* a (- (* (+ b c) (+ b c)) (* d d)))
7.6b
(/ (* a (- (* (+ b c) (+ b c)) (* d d))) (- (+ b c) d))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
20×add-sqr-sqrt
13×pow1 add-cbrt-cube add-exp-log
12×add-cube-cbrt
9×distribute-rgt-in distribute-lft-in
8×associate-*r* distribute-lft-out
7×associate-*l*
6×associate-/r* flip3-+ times-frac swap-sqr associate--l+ associate-*r/ flip-+ add-log-exp
4×expm1-log1p-u frac-times flip3-- log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares
3×sub-neg prod-diff prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down associate-*l/ associate-/r/ *-commutative unswap-sqr associate-/l/
1×pow2 clear-num frac-2neg pow-plus fma-neg diff-log pow-sqr pow-prod-up div-inv associate-/l*
Counts
4 → 127
Calls
4 calls:
19.0ms
(- (* (+ b c) (+ b c)) (* d d))
39.0ms
(* (+ b c) (+ b c))
80.0ms
(* a (- (* (+ b c) (+ b c)) (* d d)))
83.0ms
(/ (* a (- (* (+ b c) (+ b c)) (* d d))) (- (+ b c) d))

series504.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (* (+ b c) (+ b c)) (* d d))
29.0ms
(* (+ b c) (+ b c))
196.0ms
(* a (- (* (+ b c) (+ b c)) (* d d)))
200.0ms
(/ (* a (- (* (+ b c) (+ b c)) (* d d))) (- (+ b c) d))

simplify2.5s

Counts
139 → 139
Iterations

Useful iterations: 2 (918.0ms)

IterNodesCost
02002349
16362212
246051921
done50001921

prune712.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (+ b c) (+ b c) (* d (- d (+ b c))))
0.0b
(* d (- d (+ b c)))
0.6b
(* (+ (pow (+ b c) 3) (pow d 3)) a)
18.0b
(/ (* (+ (pow (+ b c) 3) (pow d 3)) a) (fma (+ b c) (+ b c) (* d (- d (+ b c)))))

rewrite407.0ms

Algorithm
rewrite-expression-head
Rules
63×*-un-lft-identity
30×add-sqr-sqrt
24×prod-diff add-cube-cbrt
20×distribute-lft-out
16×associate-*l*
14×distribute-rgt-in distribute-lft-in
13×add-cbrt-cube add-exp-log
9×associate-*r*
8×pow1 unpow-prod-down cube-prod
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv sub-neg flip3-+ div-exp pow-prod-down associate-*r/ *-commutative flip-+ distribute-lft-out-- unswap-sqr associate-/l/
1×clear-num frac-2neg flip3-- sum-cubes fma-udef div-inv flip-- associate-/l* difference-of-squares
Counts
4 → 120
Calls
4 calls:
0.0ms
(fma (+ b c) (+ b c) (* d (- d (+ b c))))
53.0ms
(* d (- d (+ b c)))
264.0ms
(* (+ (pow (+ b c) 3) (pow d 3)) a)
85.0ms
(/ (* (+ (pow (+ b c) 3) (pow d 3)) a) (fma (+ b c) (+ b c) (* d (- d (+ b c)))))

series555.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(fma (+ b c) (+ b c) (* d (- d (+ b c))))
33.0ms
(* d (- d (+ b c)))
256.0ms
(* (+ (pow (+ b c) 3) (pow d 3)) a)
166.0ms
(/ (* (+ (pow (+ b c) 3) (pow d 3)) a) (fma (+ b c) (+ b c) (* d (- d (+ b c)))))

simplify2.2s

Counts
132 → 132
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02072822
15312472
231382026
done50001989

prune754.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes471.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
1107
done107

end0.0ms

sample1.1s

Algorithm
intervals
Results
364.0ms8000×body80valid
335.0ms8000×pre80true