Details

Time bar (total: 15.0s)

sample51.0ms

Algorithm
intervals
Results
12.0ms256×pre80true
11.0ms256×body80valid

simplify69.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
1187
2397
3667
4857
5897
done897

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite65.0ms

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 distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ add-log-exp unswap-sqr
Counts
1 → 24
Calls
1 calls:
64.0ms
(* a (+ (+ b c) d))

series39.0ms

Counts
1 → 3
Calls
1 calls:
39.0ms
(* a (+ (+ b c) d))

simplify612.0ms

Counts
27 → 27
Iterations

Useful iterations: done (610.0ms)

IterNodesCost
052255
1165244
2727214
done5000212

prune139.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize25.0ms

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)))

rewrite342.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
21×sqrt-prod
18×sqrt-div
17×add-sqr-sqrt
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×frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative unswap-sqr
Counts
4 → 91
Calls
4 calls:
42.0ms
(sqrt (+ (+ b c) d))
25.0ms
(sqrt (+ (+ b c) d))
79.0ms
(* a (sqrt (+ (+ b c) d)))
191.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(sqrt (+ (+ b c) d))
71.0ms
(sqrt (+ (+ b c) d))
105.0ms
(* a (sqrt (+ (+ b c) d)))
111.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))

simplify981.0ms

Counts
103 → 103
Iterations

Useful iterations: done (976.0ms)

IterNodesCost
01351549
13611243
217671149
done50001125

prune454.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* a (sqrt (+ (+ b c) d)))
0.2b
(* a (sqrt (+ (+ b c) d)))
0.3b
(* (* (sqrt (* a (sqrt (+ (+ b c) d)))) (sqrt (* a (sqrt (+ (+ b c) d))))) (sqrt (+ (+ b c) d)))
0.5b
(* (sqrt (* a (sqrt (+ (+ b c) d)))) (sqrt (* a (sqrt (+ (+ b c) d)))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
118×sqrt-div
78×pow1
62×associate-*r/
40×sqrt-pow1
39×pow-prod-down
35×flip3-+ flip-+
32×frac-times
31×*-un-lft-identity
28×add-sqr-sqrt associate-*r*
22×sqrt-prod
16×associate-*l/ add-cube-cbrt
15×add-cbrt-cube add-exp-log
13×pow1/2
11×associate-*l*
10×pow-prod-up
9×distribute-lft-out
7×unswap-sqr
6×prod-exp pow-sqr cbrt-unprod
4×swap-sqr *-commutative add-log-exp
3×sqrt-unprod
1×pow2 rem-square-sqrt pow-plus
Counts
4 → 166
Calls
4 calls:
83.0ms
(* a (sqrt (+ (+ b c) d)))
106.0ms
(* a (sqrt (+ (+ b c) d)))
785.0ms
(* (* (sqrt (* a (sqrt (+ (+ b c) d)))) (sqrt (* a (sqrt (+ (+ b c) d))))) (sqrt (+ (+ b c) d)))
196.0ms
(* (sqrt (* a (sqrt (+ (+ b c) d)))) (sqrt (* a (sqrt (+ (+ b c) d)))))

series590.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* a (sqrt (+ (+ b c) d)))
121.0ms
(* a (sqrt (+ (+ b c) d)))
236.0ms
(* (* (sqrt (* a (sqrt (+ (+ b c) d)))) (sqrt (* a (sqrt (+ (+ b c) d))))) (sqrt (+ (+ b c) d)))
118.0ms
(* (sqrt (* a (sqrt (+ (+ b c) d)))) (sqrt (* a (sqrt (+ (+ b c) d)))))

simplify2.5s

Counts
178 → 178
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02184334
16033340
233932802
done50012741

prune912.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sqrt (+ (+ d b) c)) a) (sqrt (+ (pow (+ b c) 3) (pow d 3))))
7.6b
(/ (* (* (sqrt (+ (+ d b) c)) a) (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))))
7.6b
(sqrt (+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d))))
14.6b
(sqrt (+ (pow (+ b c) 3) (pow d 3)))

rewrite620.0ms

Algorithm
rewrite-expression-head
Rules
62×sqrt-div
56×*-un-lft-identity
39×flip3-+ flip-+
35×sqrt-prod
32×frac-add
26×distribute-lft-out
24×frac-times associate-*l/
18×add-cbrt-cube add-exp-log associate-/r/
16×unpow-prod-down flip3-- cube-prod associate-*r* flip--
14×add-sqr-sqrt
12×associate-*r/ add-cube-cbrt
11×pow1
8×associate-/l/
6×associate-/r* times-frac prod-exp cbrt-unprod
4×add-log-exp
3×cbrt-undiv div-exp pow-prod-down
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-cubes
1×clear-num frac-2neg associate-*l* *-commutative div-inv associate-/l*
Counts
4 → 150
Calls
4 calls:
226.0ms
(* (* (sqrt (+ (+ d b) c)) a) (sqrt (+ (pow (+ b c) 3) (pow d 3))))
210.0ms
(/ (* (* (sqrt (+ (+ d b) c)) a) (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))))
39.0ms
(sqrt (+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d))))
137.0ms
(sqrt (+ (pow (+ b c) 3) (pow d 3)))

series2.2s

Counts
4 → 12
Calls
4 calls:
452.0ms
(* (* (sqrt (+ (+ d b) c)) a) (sqrt (+ (pow (+ b c) 3) (pow d 3))))
1.3s
(/ (* (* (sqrt (+ (+ d b) c)) a) (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))))
122.0ms
(sqrt (+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d))))
376.0ms
(sqrt (+ (pow (+ b c) 3) (pow d 3)))

simplify576.0ms

Counts
162 → 162
Iterations

Useful iterations: done (567.0ms)

IterNodesCost
03796911
112075926
done50015498

prune1.5s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes485.0ms

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

sample1.2s

Algorithm
intervals
Results
374.0ms8000×pre80true
359.0ms8000×body80valid