Details

Time bar (total: 18.6s)

sample69.0ms

Algorithm
intervals
Results
15.0ms50×body640valid
13.0ms59×body1280valid
12.0ms282×body80nan
6.0ms123×body80valid
2.0ms18×body320valid
1.0ms6×body160valid

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
1.5b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ hypot-def flip--
Counts
2 → 89
Calls
2 calls:
11.0ms
(sqrt (+ x 1.0))
90.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series147.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(sqrt (+ x 1.0))
104.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.0s

Counts
95 → 95
Iterations
IterNodes
done5001
21076
1322
0139

prune284.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
33×distribute-lft-out
32×sqrt-prod
24×times-frac
21×add-sqr-sqrt
18×add-cube-cbrt
7×fma-def
6×associate-/r*
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
3×expm1-log1p-u log1p-expm1-u
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp hypot-def div-inv
Counts
3 → 94
Calls
3 calls:
11.0ms
(sqrt (+ x 1.0))
30.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
62.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series381.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(sqrt (+ x 1.0))
102.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
225.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.5s

Counts
103 → 103
Iterations
IterNodes
done5000
22060
1439
0173

prune500.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite370.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
708×sqrt-prod
594×times-frac
280×distribute-lft-out
270×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-cbrt-cube add-exp-log
8×hypot-def
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 461
Calls
4 calls:
38.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
56.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
74.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
165.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.2s

Counts
4 → 12
Calls
4 calls:
217.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
231.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
528.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
192.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify3.4s

Counts
473 → 473
Iterations
IterNodes
done5000
24313
11103
0448

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (cbrt (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (/ 1.0 (cbrt (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.3b
(cbrt (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite492.0ms

Algorithm
rewrite-expression-head
Rules
348×times-frac
335×*-un-lft-identity
265×sqrt-prod
152×add-sqr-sqrt
146×add-cube-cbrt
108×distribute-lft-out
96×cbrt-div
90×associate-/r/
80×sqrt-div
79×flip3-+ flip-+
52×frac-times
35×cbrt-prod
27×associate-/l*
26×associate-*l/ associate-*r/
13×associate-/r* add-exp-log
12×div-inv
11×add-cbrt-cube
10×pow1
9×associate-*l*
6×associate-*r*
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 cube-unmult pow-prod-up unswap-sqr
1×distribute-rgt-in distribute-lft-in pow1/3 pow-prod-down prod-exp *-commutative rem-cbrt-cube cbrt-unprod associate-/l/
Counts
4 → 374
Calls
4 calls:
19.0ms
(/ 1.0 (cbrt (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x)))))
280.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x)))
90.0ms
(/ (/ 1.0 (cbrt (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
67.0ms
(cbrt (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.2s

Counts
4 → 12
Calls
4 calls:
429.0ms
(/ 1.0 (cbrt (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x)))))
366.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x)))
189.0ms
(/ (/ 1.0 (cbrt (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
241.0ms
(cbrt (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify2.5s

Counts
386 → 386
Iterations
IterNodes
done5000
11459
0567

prune2.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes56.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done13
213
112
09

end0.0ms

sample1.5s

Algorithm
intervals
Results
409.0ms7994×body80nan
397.0ms1720×body1280valid
201.0ms4065×body80valid
172.0ms1278×body640valid
58.0ms628×body320valid
19.0ms309×body160valid