Details

Time bar (total: 21.8s)

sample103.0ms

Algorithm
intervals
Results
31.0ms259×body80nan
23.0ms59×body640valid
17.0ms36×body1280valid
13.0ms137×body80valid
5.0ms17×body320valid
1.0ms7×body160valid

simplify13.0ms

Counts
1 → 1
Iterations
IterNodes
done17
217
113
08

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize32.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (sqrt (+ x 1)))
0.2b
(/ 1 (sqrt x))
2.6b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
1063×times-frac
897×*-un-lft-identity
782×add-sqr-sqrt
712×add-cube-cbrt
594×prod-diff
576×sqrt-prod
73×distribute-lft-out
56×div-inv
46×sqrt-div associate-/r/
25×difference-of-squares
23×flip3-+ flip-+
22×fma-neg
13×associate-/r* distribute-lft-out--
11×add-exp-log
7×pow1 add-cbrt-cube
6×pow-flip associate-/l*
5×add-log-exp
4×div-exp
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp inv-pow
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
3 → 772
Calls
3 calls:
11.0ms
(/ 1 (sqrt (+ x 1)))
11.0ms
(/ 1 (sqrt x))
74.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series173.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(/ 1 (sqrt (+ x 1)))
38.0ms
(/ 1 (sqrt x))
96.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.3s

Counts
781 → 781
Iterations
IterNodes
done2000
22000
11420
0643

prune9.4s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (sqrt x))
0.5b
(* (cbrt (sqrt x)) (cbrt (sqrt x)))
28.9b
(fma (/ 1 (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ 1 (cbrt (sqrt x))) (- (* (/ 1 (cbrt (sqrt (+ x 1)))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
30.8b
(fma (- (/ 1 (cbrt (sqrt (+ x 1))))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ 1 (cbrt (sqrt (+ x 1)))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
46×cbrt-prod
40×add-sqr-sqrt
23×sqrt-prod
18×*-un-lft-identity add-cube-cbrt
11×pow1 swap-sqr
9×associate-*r* associate-*l* unswap-sqr
7×pow1/3
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up fma-udef
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 98
Calls
4 calls:
1.0ms
(cbrt (sqrt x))
10.0ms
(* (cbrt (sqrt x)) (cbrt (sqrt x)))
0.0ms
(fma (/ 1 (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ 1 (cbrt (sqrt x))) (- (* (/ 1 (cbrt (sqrt (+ x 1)))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
0.0ms
(fma (- (/ 1 (cbrt (sqrt (+ x 1))))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ 1 (cbrt (sqrt (+ x 1)))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))

series764.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(cbrt (sqrt x))
177.0ms
(* (cbrt (sqrt x)) (cbrt (sqrt x)))
192.0ms
(fma (/ 1 (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ 1 (cbrt (sqrt x))) (- (* (/ 1 (cbrt (sqrt (+ x 1)))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
219.0ms
(fma (- (/ 1 (cbrt (sqrt (+ x 1))))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ 1 (cbrt (sqrt (+ x 1)))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))

simplify822.0ms

Counts
110 → 110
Iterations
IterNodes
done2003
32003
21231
1430
0176

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ 1 (sqrt (+ x 1)))
11.0b
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
231×*-un-lft-identity
203×add-sqr-sqrt
189×prod-diff
180×times-frac
172×add-cube-cbrt
106×sqrt-prod
89×unpow-prod-down
33×sqr-pow
25×distribute-lft-out
16×sqrt-div associate-/r/
15×difference-of-squares
9×div-inv
8×flip3-+ flip-+
7×associate-/r* fma-neg
6×add-exp-log
4×pow1 add-cbrt-cube add-log-exp
3×pow-flip associate-/l*
2×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u distribute-lft-out--
1×cbrt-undiv rec-exp clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log 1-exp flip-- inv-pow
Counts
2 → 282
Calls
2 calls:
13.0ms
(/ 1 (sqrt (+ x 1)))
22.0ms
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series95.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ 1 (sqrt (+ x 1)))
58.0ms
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify903.0ms

Counts
288 → 288
Iterations
IterNodes
done2004
32004
21821
1921
0388

prune2.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 18.0b

localize20.0ms

Local error

Found 1 expressions with local error:

2.6b
(- (pow x -1/2) (pow (+ x 1) -1/2))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
65×unpow-prod-down
56×prod-diff
54×*-un-lft-identity
45×add-sqr-sqrt
33×add-cube-cbrt
22×sqr-pow
9×difference-of-squares
8×distribute-lft-out
7×fma-neg
3×distribute-lft-out-- add-log-exp
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u flip--
Counts
1 → 90
Calls
1 calls:
31.0ms
(- (pow x -1/2) (pow (+ x 1) -1/2))

series141.0ms

Counts
1 → 3
Calls
1 calls:
141.0ms
(- (pow x -1/2) (pow (+ x 1) -1/2))

simplify849.0ms

Counts
93 → 93
Iterations
IterNodes
done2003
32003
21016
1414
0188

prune575.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

regimes33.0ms

Accuracy

97.2% (0.5b remaining)

Error of 1.5b against oracle of 0.9b and baseline of 19.7b

bsearch53.0ms

Steps
ItersRangePoint
10
1.8230705747381016e-09
318690.85562629136
11789.29797293433

simplify4.0ms

Iterations
IterNodes
done30
130
025

end0.0ms

sample2.3s

Algorithm
intervals
Results
642.0ms1147×body1280valid
522.0ms8060×body80nan
461.0ms1830×body640valid
340.0ms4063×body80valid
130.0ms649×body320valid
36.0ms311×body160valid