Details

Time bar (total: 10.8s)

sample37.0ms

Algorithm
intervals
Results
19.0ms513×body80valid

simplify29.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01115
12415
24414
35814
46014
done6014

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b
(fma (/ x y) (/ x y) (/ (* z z) (* t t)))
23.4b
(/ (* z z) (* t t))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
4×cbrt-undiv div-exp prod-exp cbrt-unprod
2×pow1 add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity log1p-expm1-u add-log-exp
1×frac-2neg times-frac clear-num associate-/r* fma-udef div-inv associate-/l*
Counts
2 → 33
Calls
2 calls:
0.0ms
(fma (/ x y) (/ x y) (/ (* z z) (* t t)))
5.0ms
(/ (* z z) (* t t))

series152.0ms

Counts
2 → 6
Calls
2 calls:
118.0ms
(fma (/ x y) (/ x y) (/ (* z z) (* t t)))
33.0ms
(/ (* z z) (* t t))

simplify3.2s

Counts
39 → 39
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
066517
1169509
2631379
34787364
done5000364

prune128.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (/ x y) (/ z t))
0.0b
(hypot (/ x y) (/ z t))
0.5b
(* (hypot (/ x y) (/ z t)) (hypot (/ x y) (/ z t)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×hypot-udef
5×add-exp-log add-cbrt-cube
3×expm1-log1p-u swap-sqr associate-*r* associate-*l* log1p-expm1-u add-log-exp
1×pow2 pow-plus sqrt-unprod pow-prod-down prod-exp rem-square-sqrt pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
Counts
3 → 49
Calls
3 calls:
0.0ms
(hypot (/ x y) (/ z t))
0.0ms
(hypot (/ x y) (/ z t))
4.0ms
(* (hypot (/ x y) (/ z t)) (hypot (/ x y) (/ z t)))

series313.0ms

Counts
3 → 9
Calls
3 calls:
86.0ms
(hypot (/ x y) (/ z t))
87.0ms
(hypot (/ x y) (/ z t))
140.0ms
(* (hypot (/ x y) (/ z t)) (hypot (/ x y) (/ z t)))

simplify1.5s

Counts
58 → 58
Iterations

Useful iterations: 3 (148.0ms)

IterNodesCost
050831
1103748
2263629
31035547
done5000547

prune197.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (hypot (/ x y) (/ z t)) (* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t)))))
0.5b
(* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t))))
1.4b
(sqrt (hypot (/ x y) (/ z t)))
1.4b
(sqrt (hypot (/ x y) (/ z t)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
38×pow1
31×add-sqr-sqrt
24×sqrt-prod
16×sqrt-pow1 pow1/2
15×add-cube-cbrt *-un-lft-identity pow-prod-up
11×add-exp-log add-cbrt-cube
9×swap-sqr associate-*l*
7×associate-*r*
6×pow-prod-down
5×pow-sqr unswap-sqr
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×sqrt-unprod
2×rem-sqrt-square *-commutative
1×pow2 hypot-udef pow-plus rem-square-sqrt
Counts
4 → 110
Calls
4 calls:
19.0ms
(* (hypot (/ x y) (/ z t)) (* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t)))))
7.0ms
(* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t))))
1.0ms
(sqrt (hypot (/ x y) (/ z t)))
1.0ms
(sqrt (hypot (/ x y) (/ z t)))

series401.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(* (hypot (/ x y) (/ z t)) (* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t)))))
88.0ms
(* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t))))
85.0ms
(sqrt (hypot (/ x y) (/ z t)))
84.0ms
(sqrt (hypot (/ x y) (/ z t)))

simplify1.4s

Counts
122 → 122
Iterations

Useful iterations: 3 (388.0ms)

IterNodesCost
0992276
12031398
24681154
316641100
done50001100

prune295.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (hypot (/ x y) (/ z t)) (* (sqrt (sqrt (hypot (/ x y) (/ z t)))) (pow (sqrt (sqrt (hypot (/ x y) (/ z t)))) 3)))
0.6b
(pow (sqrt (sqrt (hypot (/ x y) (/ z t)))) 3)
1.4b
(sqrt (hypot (/ x y) (/ z t)))
1.4b
(sqrt (hypot (/ x y) (/ z t)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-prod
16×add-sqr-sqrt
15×add-exp-log
14×add-cube-cbrt *-un-lft-identity
11×pow1
10×add-cbrt-cube
9×unpow-prod-down cube-prod
7×prod-exp
6×sqrt-pow1
5×pow-pow
4×expm1-log1p-u pow1/2 log1p-expm1-u add-log-exp
3×pow-unpow associate-*l* cbrt-unprod
2×pow-to-exp rem-sqrt-square pow-exp
1×cube-mult unpow3 associate-*r* pow-prod-down *-commutative sqrt-pow2 rem-cube-cbrt sqr-pow
Counts
4 → 93
Calls
4 calls:
24.0ms
(* (hypot (/ x y) (/ z t)) (* (sqrt (sqrt (hypot (/ x y) (/ z t)))) (pow (sqrt (sqrt (hypot (/ x y) (/ z t)))) 3)))
3.0ms
(pow (sqrt (sqrt (hypot (/ x y) (/ z t)))) 3)
1.0ms
(sqrt (hypot (/ x y) (/ z t)))
1.0ms
(sqrt (hypot (/ x y) (/ z t)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(* (hypot (/ x y) (/ z t)) (* (sqrt (sqrt (hypot (/ x y) (/ z t)))) (pow (sqrt (sqrt (hypot (/ x y) (/ z t)))) 3)))
151.0ms
(pow (sqrt (sqrt (hypot (/ x y) (/ z t)))) 3)
80.0ms
(sqrt (hypot (/ x y) (/ z t)))
80.0ms
(sqrt (hypot (/ x y) (/ z t)))

simplify844.0ms

Counts
105 → 105
Iterations

Useful iterations: done (841.0ms)

IterNodesCost
01371973
13291651
29191261
done50001260

prune287.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.0b

regimes520.0ms

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
01025
11125
done1125

end0.0ms

sample972.0ms

Algorithm
intervals
Results
572.0ms15465×body80valid