Details

Time bar (total: 10.2s)

sample17.0ms

Algorithm
intervals
Results
7.0ms274×body80valid

simplify48.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0911
12111
23611
35711
48511
510011
done10011

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.0b

localize8.0ms

Local error

Found 2 expressions with local error:

3.7b
(* y (+ 1.0 (* z z)))
5.2b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×flip3-+ associate-/r/ flip-+ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 70
Calls
2 calls:
7.0ms
(* y (+ 1.0 (* z z)))
10.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series110.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(* y (+ 1.0 (* z z)))
56.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify599.0ms

Counts
76 → 76
Iterations

Useful iterations: 2 (131.0ms)

IterNodesCost
01561062
14101035
21854887
done5000887

prune172.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize14.0ms

Local error

Found 2 expressions with local error:

2.4b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (+ 1.0 (* z z))))
3.4b
(/ (/ (cbrt 1.0) x) (+ 1.0 (* z z)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
275×times-frac
167×add-sqr-sqrt
141×add-cube-cbrt *-un-lft-identity
72×associate-*r*
65×cbrt-prod
43×add-exp-log
33×add-cbrt-cube
22×associate-/l*
18×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
10×div-inv
8×unswap-sqr
7×associate-*l*
4×pow1 associate-/r/
3×associate-/r*
2×flip3-+ flip-+ add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
2 → 225
Calls
2 calls:
46.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (+ 1.0 (* z z))))
10.0ms
(/ (/ (cbrt 1.0) x) (+ 1.0 (* z z)))

series249.0ms

Counts
2 → 6
Calls
2 calls:
135.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (+ 1.0 (* z z))))
114.0ms
(/ (/ (cbrt 1.0) x) (+ 1.0 (* z z)))

simplify413.0ms

Counts
231 → 231
Iterations

Useful iterations: done (405.0ms)

IterNodesCost
03765294
112045066
done50005026

prune662.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
2.4b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (+ 1.0 (* z z)))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite462.0ms

Algorithm
rewrite-expression-head
Rules
2612×times-frac
1290×add-sqr-sqrt
1160×add-cube-cbrt *-un-lft-identity
911×sqrt-prod
834×associate-*r*
395×cbrt-prod
63×add-exp-log
52×div-inv
51×add-cbrt-cube
30×unswap-sqr
29×cbrt-undiv div-exp
22×associate-/l*
20×sqrt-div
16×prod-exp associate-/r/ cbrt-unprod
10×flip3-+ flip-+
8×pow1
7×associate-*l*
6×associate-/r*
4×add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 1114
Calls
4 calls:
12.0ms
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
314.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
2.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
132.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
46.0ms
(sqrt (+ 1.0 (* z z)))
43.0ms
(sqrt (+ 1.0 (* z z)))

simplify417.0ms

Counts
1126 → 1126
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
0157435082
done500035082

prune3.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))) (/ 1 (sqrt (+ 1.0 (* z z)))))
2.5b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (+ 1.0 (* z z)))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
238×add-exp-log
194×add-sqr-sqrt
162×associate-*r*
144×add-cube-cbrt *-un-lft-identity
117×add-cbrt-cube
100×prod-exp
95×div-exp
87×sqrt-prod
58×cbrt-prod
56×cbrt-unprod
55×cbrt-undiv
14×unswap-sqr
13×pow1
10×rec-exp 1-exp
9×div-inv
8×sqrt-div associate-*l*
6×frac-times associate-*l/
4×flip3-+ associate-*r/ pow-prod-down associate-/r/ flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative
1×un-div-inv
Counts
4 → 322
Calls
4 calls:
104.0ms
(* (* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))) (/ 1 (sqrt (+ 1.0 (* z z)))))
82.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))) (/ 1 (sqrt (+ 1.0 (* z z)))))
138.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
43.0ms
(sqrt (+ 1.0 (* z z)))
49.0ms
(sqrt (+ 1.0 (* z z)))

simplify616.0ms

Counts
334 → 334
Iterations

Useful iterations: done (601.0ms)

IterNodesCost
05519553
119378518
done50017964

prune835.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.1b

regimes248.0ms

Accuracy

0% (1.3b remaining)

Error of 6.0b against oracle of 4.8b and baseline of 6.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01628
12228
done2228

end0.0ms

sample423.0ms

Algorithm
intervals
Results
241.0ms8683×body80valid