Details

Time bar (total: 7.5s)

sample34.0ms

Algorithm
intervals
Results
18.0ms513×body80valid

simplify17.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
12415
24215
35415
done5415

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ (* x x) (* y y)) (/ (* z z) (* t t)))
21.9b
(/ (* x x) (* y y))
23.4b
(/ (* z z) (* t t))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log add-cbrt-cube
8×cbrt-undiv div-exp prod-exp cbrt-unprod
5×*-un-lft-identity add-log-exp
3×pow1 add-sqr-sqrt add-cube-cbrt
2×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
1×+-commutative flip3-+ frac-add sum-log flip-+ distribute-lft-out
Counts
3 → 55
Calls
3 calls:
9.0ms
(+ (/ (* x x) (* y y)) (/ (* z z) (* t t)))
5.0ms
(/ (* x x) (* y y))
5.0ms
(/ (* z z) (* t t))

series145.0ms

Counts
3 → 9
Calls
3 calls:
93.0ms
(+ (/ (* x x) (* y y)) (/ (* z z) (* t t)))
26.0ms
(/ (* x x) (* y y))
26.0ms
(/ (* z z) (* t t))

simplify701.0ms

Counts
64 → 64
Iterations

Useful iterations: 2 (145.0ms)

IterNodesCost
0113909
1356856
21537664
done5000664

prune152.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (fabs (/ x y)) (fabs (/ x y))) (/ (* z z) (* t t)))
0.3b
(* (fabs (/ x y)) (fabs (/ x y)))
23.4b
(/ (* z z) (* t t))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log add-cbrt-cube
10×pow1
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
5×prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv div-exp
3×swap-sqr associate-*r* associate-*l*
1×+-commutative pow2 frac-2neg flip3-+ times-frac pow-plus pow-prod-down clear-num associate-/r* sum-log pow-sqr *-commutative pow-prod-up flip-+ div-inv associate-/l* unswap-sqr
Counts
3 → 57
Calls
3 calls:
4.0ms
(+ (* (fabs (/ x y)) (fabs (/ x y))) (/ (* z z) (* t t)))
3.0ms
(* (fabs (/ x y)) (fabs (/ x y)))
5.0ms
(/ (* z z) (* t t))

series105.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(+ (* (fabs (/ x y)) (fabs (/ x y))) (/ (* z z) (* t t)))
7.0ms
(* (fabs (/ x y)) (fabs (/ x y)))
30.0ms
(/ (* z z) (* t t))

simplify726.0ms

Counts
66 → 66
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
095963
1253760
21011619
done5000619

prune165.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (fabs (/ x y)) (fabs (/ x y))) (* (fabs (/ z t)) (fabs (/ z t))))
0.3b
(* (fabs (/ x y)) (fabs (/ x y)))
0.3b
(* (fabs (/ z t)) (fabs (/ z t)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
15×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
6×swap-sqr associate-*r* associate-*l*
5×add-log-exp
2×pow2 pow-plus pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
1×+-commutative flip3-+ sum-log flip-+
Counts
3 → 61
Calls
3 calls:
2.0ms
(+ (* (fabs (/ x y)) (fabs (/ x y))) (* (fabs (/ z t)) (fabs (/ z t))))
3.0ms
(* (fabs (/ x y)) (fabs (/ x y)))
3.0ms
(* (fabs (/ z t)) (fabs (/ z t)))

series39.0ms

Counts
3 → 9
Calls
3 calls:
20.0ms
(+ (* (fabs (/ x y)) (fabs (/ x y))) (* (fabs (/ z t)) (fabs (/ z t))))
11.0ms
(* (fabs (/ x y)) (fabs (/ x y)))
8.0ms
(* (fabs (/ z t)) (fabs (/ z t)))

simplify1.8s

Counts
70 → 70
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
0781054
1175702
2636611
33000587
done5000587

prune181.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (fabs (/ z t)) 2)
0.5b
(* (sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2))) (sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2))))
5.5b
(sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2)))
5.5b
(sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
40×sqrt-prod
30×add-sqr-sqrt
22×pow1
16×add-cube-cbrt sqrt-div
15×unpow-prod-down
14×distribute-lft-out
12×swap-sqr
10×sqrt-pow1 pow1/2
8×flip3-+ associate-*r* associate-*l* flip-+
7×add-exp-log
6×add-cbrt-cube
5×pow-prod-up
4×frac-times add-log-exp unswap-sqr
3×pow-unpow pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 pow-to-exp pow-pow pow-plus sqrt-unprod pow-exp prod-exp rem-square-sqrt *-commutative cbrt-unprod unpow2 sqr-pow
Counts
4 → 117
Calls
4 calls:
1.0ms
(pow (fabs (/ z t)) 2)
66.0ms
(* (sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2))) (sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2))))
14.0ms
(sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2)))
15.0ms
(sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2)))

series111.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(pow (fabs (/ z t)) 2)
20.0ms
(* (sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2))) (sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2))))
40.0ms
(sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2)))
44.0ms
(sqrt (+ (pow (fabs (/ z t)) 2) (pow (fabs (/ x y)) 2)))

simplify1.4s

Counts
129 → 129
Iterations

Useful iterations: 3 (634.0ms)

IterNodesCost
01143549
12042361
25772191
321402086
done50002086

prune280.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes503.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01423
11623
done1623

end0.0ms

sample914.0ms

Algorithm
intervals
Results
543.0ms15465×body80valid