Details

Time bar (total: 33.2s)

sample100.0ms

Algorithm
intervals
Results
21.0ms62×body640valid
20.0ms41×body1280valid
20.0ms262×body80nan
18.0ms125×body80valid
5.0ms18×body320valid
2.0ms10×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
315
215
111
08

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1))
0.1b
(/ 1 (sqrt (+ x 1)))
0.3b
(/ 1 (sqrt x))
2.9b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
1063×times-frac
902×*-un-lft-identity
788×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
580×sqrt-prod
74×distribute-lft-out
56×div-inv
48×sqrt-div
46×associate-/r/
25×difference-of-squares
24×flip3-+ flip-+
22×fma-neg
13×associate-/r* distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube
6×pow-flip associate-/l* add-log-exp
4×expm1-log1p-u div-exp log1p-expm1-u
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp hypot-def inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 789
Calls
4 calls:
9.0ms
(sqrt (+ x 1))
16.0ms
(/ 1 (sqrt (+ x 1)))
9.0ms
(/ 1 (sqrt x))
66.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series194.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1))
32.0ms
(/ 1 (sqrt (+ x 1)))
52.0ms
(/ 1 (sqrt x))
75.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify2.9s

Counts
801 → 801
Iterations
IterNodes
22380
11410
0647

prune9.2s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 19.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (sqrt x) 1)
0.1b
(/ 1 (hypot (sqrt x) 1))
0.3b
(/ 1 (sqrt x))
2.9b
(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
505×times-frac
406×add-sqr-sqrt
386×*-un-lft-identity
365×add-cube-cbrt
286×prod-diff
144×sqrt-prod
42×div-inv
22×fma-neg
15×difference-of-squares
12×add-exp-log
9×associate-/r*
8×add-cbrt-cube
7×pow1 distribute-lft-out--
6×associate-/l* add-log-exp
4×expm1-log1p-u div-exp log1p-expm1-u pow-flip
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp inv-pow
1×hypot-udef sub-neg sqrt-pow1 flip3-- pow1/2 diff-log frac-sub flip--
Counts
4 → 435
Calls
4 calls:
0.0ms
(hypot (sqrt x) 1)
7.0ms
(/ 1 (hypot (sqrt x) 1))
9.0ms
(/ 1 (sqrt x))
34.0ms
(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
231.0ms
(hypot (sqrt x) 1)
365.0ms
(/ 1 (hypot (sqrt x) 1))
50.0ms
(/ 1 (sqrt x))
452.0ms
(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

simplify2.2s

Counts
447 → 447
Iterations
IterNodes
22258
11125
0491

prune4.9s

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 19.3b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1))
0.1b
(/ 1 (sqrt (+ x 1)))
10.6b
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
236×*-un-lft-identity
209×add-sqr-sqrt
189×prod-diff
180×times-frac
174×add-cube-cbrt
110×sqrt-prod
89×unpow-prod-down
33×sqr-pow
26×distribute-lft-out
18×sqrt-div
16×associate-/r/
15×difference-of-squares
9×flip3-+ flip-+ div-inv
7×associate-/r* fma-neg add-exp-log
6×pow1
5×add-cbrt-cube add-log-exp
3×expm1-log1p-u log1p-expm1-u pow-flip associate-/l*
2×sqrt-pow1 pow1/2 div-exp hypot-def distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp clear-num sub-neg frac-2neg flip3-- diff-log 1-exp flip-- inv-pow
Counts
3 → 300
Calls
3 calls:
4.0ms
(sqrt (+ x 1))
8.0ms
(/ 1 (sqrt (+ x 1)))
25.0ms
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series167.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(sqrt (+ x 1))
45.0ms
(/ 1 (sqrt (+ x 1)))
86.0ms
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify3.4s

Counts
309 → 309
Iterations
IterNodes
33577
21684
1927
0398

prune3.3s

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 19.3b

localize94.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
31.4b
(fma (pow (* (cbrt x) (cbrt x)) -1/2) (pow (cbrt x) -1/2) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
34.0b
(fma (- (/ 1 (sqrt (cbrt (+ x 1))))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
2×pow1/3 fma-udef
Counts
4 → 46
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
0.0ms
(fma (pow (* (cbrt x) (cbrt x)) -1/2) (pow (cbrt x) -1/2) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
0.0ms
(fma (- (/ 1 (sqrt (cbrt (+ x 1))))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
302.0ms
(cbrt x)
250.0ms
(cbrt x)
179.0ms
(fma (pow (* (cbrt x) (cbrt x)) -1/2) (pow (cbrt x) -1/2) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
286.0ms
(fma (- (/ 1 (sqrt (cbrt (+ x 1))))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))

simplify792.0ms

Counts
58 → 58
Iterations
IterNodes
32030
2690
1263
0111

prune836.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 19.3b

regimes175.0ms

Accuracy

0% (0.7b remaining)

Error of 19.7b against oracle of 19.0b and baseline of 19.7b

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
17
07

end0.0ms

sample2.5s

Algorithm
intervals
Results
821.0ms1855×body640valid
505.0ms8145×body80nan
473.0ms1139×body1280valid
351.0ms4102×body80valid
132.0ms592×body320valid
42.0ms312×body160valid