Details

Time bar (total: 27.5s)

sample52.0ms

Algorithm
intervals
Results
13.0ms49×body1280valid
13.0ms59×body640valid
7.0ms116×body80valid
3.0ms22×body320valid
1.0ms10×body160valid

simplify478.0ms

Counts
1 → 1
Iterations
IterNodes
done353
14353
13349
12343
11332
10222
996
875
758
639
527
421
319
216
112
07

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
3.0b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite440.0ms

Algorithm
rewrite-expression-head
Rules
981×*-un-lft-identity
736×times-frac
585×add-sqr-sqrt
468×prod-diff
419×add-cube-cbrt
189×distribute-lft-out
94×associate-/r/
90×distribute-lft-out--
81×difference-of-squares
47×div-inv
29×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
9×associate-/r*
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 596
Calls
3 calls:
29.0ms
(/ x (+ x 1.0))
41.0ms
(/ (+ x 1.0) (- x 1.0))
249.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series363.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(/ x (+ x 1.0))
71.0ms
(/ (+ x 1.0) (- x 1.0))
237.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify4.2s

Counts
605 → 605
Iterations
IterNodes
done5004
23313
11253
0523

prune3.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ 3.0 x) (/ 1 (* x x)) (/ 3.0 x))
0.5b
(/ 1 (* x x))
0.5b
(/ 1 (* x x))
6.3b
(fma (/ 1 (* x x)) 1.0 (fma (/ 3.0 x) (/ 1 (* x x)) (/ 3.0 x)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
20×pow1
14×add-cbrt-cube
12×pow-flip
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity div-exp
6×times-frac prod-exp associate-/l*
4×cbrt-undiv expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
2×pow2 frac-2neg pow-plus pow-prod-down clear-num associate-/r* pow-sqr pow-prod-up cbrt-unprod fma-udef div-inv inv-pow
Counts
4 → 88
Calls
4 calls:
1.0ms
(fma (/ 3.0 x) (/ 1 (* x x)) (/ 3.0 x))
37.0ms
(/ 1 (* x x))
28.0ms
(/ 1 (* x x))
1.0ms
(fma (/ 1 (* x x)) 1.0 (fma (/ 3.0 x) (/ 1 (* x x)) (/ 3.0 x)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(fma (/ 3.0 x) (/ 1 (* x x)) (/ 3.0 x))
27.0ms
(/ 1 (* x x))
29.0ms
(/ 1 (* x x))
66.0ms
(fma (/ 1 (* x x)) 1.0 (fma (/ 3.0 x) (/ 1 (* x x)) (/ 3.0 x)))

simplify4.3s

Counts
100 → 100
Iterations
IterNodes
done5008
31966
2502
1187
087

prune600.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* x x))
0.5b
(/ 1 (* x x))
1.8b
(log (exp (/ 1 (* x x))))
6.3b
(fma (/ 1 (* x x)) 1.0 (fma (/ 3.0 x) (log (exp (/ 1 (* x x)))) (/ 3.0 x)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
21×pow1
14×add-cbrt-cube
12×pow-flip
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
8×div-exp log-pow
7×exp-prod
6×prod-exp associate-/l*
4×cbrt-undiv expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×log-prod div-inv
2×pow2 frac-2neg pow-plus pow-prod-down clear-num associate-/r* pow-sqr pow-prod-up cbrt-unprod inv-pow
1×rem-log-exp fma-udef
Counts
4 → 99
Calls
4 calls:
24.0ms
(/ 1 (* x x))
24.0ms
(/ 1 (* x x))
21.0ms
(log (exp (/ 1 (* x x))))
1.0ms
(fma (/ 1 (* x x)) 1.0 (fma (/ 3.0 x) (log (exp (/ 1 (* x x)))) (/ 3.0 x)))

series190.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ 1 (* x x))
37.0ms
(/ 1 (* x x))
31.0ms
(log (exp (/ 1 (* x x))))
87.0ms
(fma (/ 1 (* x x)) 1.0 (fma (/ 3.0 x) (log (exp (/ 1 (* x x)))) (/ 3.0 x)))

simplify5.2s

Counts
111 → 111
Iterations
IterNodes
done5006
43421
31043
2436
1211
0105

prune814.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize86.0ms

Local error

Found 4 expressions with local error:

13.3b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
13.3b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
33.8b
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))
36.9b
(fma (- (+ x 1.0)) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))) (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
32×times-frac
24×add-sqr-sqrt add-cube-cbrt
10×distribute-lft-out difference-of-squares
8×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ fma-udef div-inv
Counts
4 → 104
Calls
4 calls:
71.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
48.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
0.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))
0.0ms
(fma (- (+ x 1.0)) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))) (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
99.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
366.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))
536.0ms
(fma (- (+ x 1.0)) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))) (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))))

simplify2.1s

Counts
116 → 116
Iterations
IterNodes
done5001
21068
1306
0127

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes125.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.5b

bsearch181.0ms

Steps
ItersRangePoint
8
87.84726908649233
263824.51516633737
8811.972647140785
10
-75476531921.81544
-1.440408271564231
-12705.479066605956

simplify23.0ms

Iterations
IterNodes
done49
249
145
030

end1.0ms

sample2.4s

Algorithm
intervals
Results
793.0ms648×body320valid
601.0ms1728×body1280valid
443.0ms1243×body640valid
326.0ms4053×body80valid
34.0ms328×body160valid