Details

Time bar (total: 12.2s)

sample58.0ms

Algorithm
intervals
Results
24.0ms510×body80valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01113
11913
25013
316013
444313
5144213
done500013

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* z z) t)
0.0b
(- (* x x) (* (* y 4.0) (- (* z z) t)))
4.5b
(* (* y 4.0) (- (* z z) t))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-exp-log add-cbrt-cube
7×add-log-exp
6×add-sqr-sqrt sub-neg
4×distribute-rgt-in add-cube-cbrt *-un-lft-identity distribute-lft-in associate-*r* associate--r+
3×flip3-- pow-prod-down prod-exp flip-- cbrt-unprod
2×diff-log associate-*r/ difference-of-squares
1×associate-*l* *-commutative
Counts
3 → 54
Calls
3 calls:
9.0ms
(- (* z z) t)
14.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
38.0ms
(* (* y 4.0) (- (* z z) t))

series172.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(- (* z z) t)
83.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
64.0ms
(* (* y 4.0) (- (* z z) t))

simplify1.1s

Counts
63 → 63
Iterations

Useful iterations: 2 (260.0ms)

IterNodesCost
0103843
1327802
21901696
done5001696

prune194.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.5b

localize21.0ms

Local error

Found 4 expressions with local error:

1.3b
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
1.3b
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
4.5b
(* (* y 4.0) (- (* z z) t))
4.5b
(* (* y 4.0) (- (* z z) t))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r*
6×pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×distribute-rgt-in sub-neg flip3-- distribute-lft-in sqrt-div associate-*r/ flip-- add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative difference-of-squares
Counts
4 → 80
Calls
4 calls:
13.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
13.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
54.0ms
(* (* y 4.0) (- (* z z) t))
53.0ms
(* (* y 4.0) (- (* z z) t))

series553.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
192.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
81.0ms
(* (* y 4.0) (- (* z z) t))
79.0ms
(* (* y 4.0) (- (* z z) t))

simplify985.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (222.0ms)

IterNodesCost
01011438
12851296
215831168
done50011168

prune300.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x x) (/ (* (- (pow z 4) (* t t)) (* y 4.0)) (+ (* z z) t)))
1.5b
(- (pow z 4) (* t t))
9.4b
(* (- (pow z 4) (* t t)) (* y 4.0))
19.9b
(/ (* (- (pow z 4) (* t t)) (* y 4.0)) (+ (* z z) t))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
9×pow1
8×add-log-exp
7×add-cube-cbrt *-un-lft-identity difference-of-squares
6×associate-*l* prod-exp cbrt-unprod
4×flip3-- associate-*l/ flip--
3×cbrt-undiv times-frac div-exp pow-prod-down associate-/r*
2×sub-neg unpow-prod-down diff-log associate-/r/ associate-/l/ sqr-pow
1×frac-2neg flip3-+ associate-*r* clear-num *-commutative flip-+ div-inv associate-/l*
Counts
4 → 78
Calls
4 calls:
33.0ms
(- (* x x) (/ (* (- (pow z 4) (* t t)) (* y 4.0)) (+ (* z z) t)))
16.0ms
(- (pow z 4) (* t t))
54.0ms
(* (- (pow z 4) (* t t)) (* y 4.0))
59.0ms
(/ (* (- (pow z 4) (* t t)) (* y 4.0)) (+ (* z z) t))

series425.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(- (* x x) (/ (* (- (pow z 4) (* t t)) (* y 4.0)) (+ (* z z) t)))
47.0ms
(- (pow z 4) (* t t))
86.0ms
(* (- (pow z 4) (* t t)) (* y 4.0))
100.0ms
(/ (* (- (pow z 4) (* t t)) (* y 4.0)) (+ (* z z) t))

simplify2.0s

Counts
90 → 90
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01611805
15101694
235971446
done50021429

prune336.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x x) (/ (* (+ (pow z (/ 4 2)) t) (* (- (* z z) t) (* y 4.0))) (+ (* z z) t)))
0.1b
(* (+ (pow z (/ 4 2)) t) (* (- (* z z) t) (* y 4.0)))
4.5b
(* (- (* z z) t) (* y 4.0))
19.9b
(/ (* (+ (pow z (/ 4 2)) t) (* (- (* z z) t) (* y 4.0))) (+ (* z z) t))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
18×pow1 associate-*l/
15×prod-exp cbrt-unprod
10×add-sqr-sqrt *-un-lft-identity
9×pow-prod-down
8×frac-times add-cube-cbrt flip3-- associate-*l* flip-- associate-/l/
7×flip3-+ flip-+
6×add-log-exp
4×cbrt-undiv associate-*r/ div-exp
3×times-frac associate-/r*
2×associate-*r* associate-/r/ *-commutative difference-of-squares
1×sub-neg frac-2neg diff-log clear-num div-inv distribute-lft-out associate-/l*
Counts
4 → 99
Calls
4 calls:
50.0ms
(- (* x x) (/ (* (+ (pow z (/ 4 2)) t) (* (- (* z z) t) (* y 4.0))) (+ (* z z) t)))
187.0ms
(* (+ (pow z (/ 4 2)) t) (* (- (* z z) t) (* y 4.0)))
53.0ms
(* (- (* z z) t) (* y 4.0))
107.0ms
(/ (* (+ (pow z (/ 4 2)) t) (* (- (* z z) t) (* y 4.0))) (+ (* z z) t))

series361.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (* x x) (/ (* (+ (pow z (/ 4 2)) t) (* (- (* z z) t) (* y 4.0))) (+ (* z z) t)))
116.0ms
(* (+ (pow z (/ 4 2)) t) (* (- (* z z) t) (* y 4.0)))
77.0ms
(* (- (* z z) t) (* y 4.0))
86.0ms
(/ (* (+ (pow z (/ 4 2)) t) (* (- (* z z) t) (* y 4.0))) (+ (* z z) t))

simplify321.0ms

Counts
111 → 111
Iterations

Useful iterations: done (317.0ms)

IterNodesCost
01892969
16182275
done50001905

prune489.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 2.5b

regimes555.0ms

Accuracy

83.7% (0.5b remaining)

Error of 3.3b against oracle of 2.8b and baseline of 5.9b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02036
12536
done2536

end0.0ms

sample2.3s

Algorithm
intervals
Results
913.0ms15656×body80valid