Details

Time bar (total: 22.1s)

sample268.0ms

Algorithm
intervals
Results
87.0ms57×body10240exit
50.0ms55×body1280valid
44.0ms326×body80valid
35.0ms60×body640valid
8.0ms20×body320valid
2.0ms8×body160valid

simplify604.0ms

Counts
1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize81.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
2.4b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite306.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
32×flip3-- flip--
30×flip3-+ flip-+
23×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
15×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-lft-out--
1×sub-neg times-frac diff-log distribute-lft-out
Counts
4 → 173
Calls
4 calls:
53.0ms
(* (- 1.0 eps) x)
78.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
89.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
69.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series490.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (- 1.0 eps) x)
84.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
89.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
284.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify2.3s

Counts
185 → 185

prune646.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (/ 3002399751580331.0 4503599627370496.0) (pow x 3))
5.0b
(- (+ (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
15×add-exp-log
13×times-frac associate-*l*
12×add-cube-cbrt *-un-lft-identity associate-*r*
8×unswap-sqr
7×add-cbrt-cube add-log-exp
6×prod-exp
5×unpow-prod-down cube-prod
3×div-exp sqr-pow
2×pow1 pow-to-exp diff-log pow-exp cbrt-unprod
1×cbrt-undiv cube-mult sub-neg flip3-- unpow3 associate-*l/ associate--l+ sum-log *-commutative flip-- div-inv
Counts
2 → 64
Calls
2 calls:
48.0ms
(* (/ 3002399751580331.0 4503599627370496.0) (pow x 3))
118.0ms
(- (+ (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series127.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(* (/ 3002399751580331.0 4503599627370496.0) (pow x 3))
79.0ms
(- (+ (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify937.0ms

Counts
70 → 70

prune257.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

5.0b
(- (+ (* (* (cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3))) (cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))) (cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
40.1b
(cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))
40.1b
(cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))
40.1b
(cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))

rewrite432.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cbrt-prod cbrt-div pow1/3 associate-*l/
2×diff-log
1×sub-neg flip3-- associate--l+ sum-log flip--
Counts
4 → 44
Calls
4 calls:
396.0ms
(- (+ (* (* (cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3))) (cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))) (cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
17.0ms
(cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))
9.0ms
(cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))
9.0ms
(cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(- (+ (* (* (cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3))) (cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))) (cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
47.0ms
(cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))
51.0ms
(cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))
47.0ms
(cbrt (* (/ 3002399751580331.0 4503599627370496.0) (pow x 3)))

simplify1.5s

Counts
56 → 56

prune328.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 1 expressions with local error:

0.1b
(* (pow x 2) (- (* x (/ 3002399751580331.0 4503599627370496.0)) 1.0))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×associate-*l*
6×add-exp-log
4×add-cube-cbrt unpow-prod-down *-un-lft-identity unswap-sqr
3×associate-*r* prod-exp add-cbrt-cube
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ unpow2 sqr-pow
1×pow1 pow-to-exp flip3-- pow-exp *-commutative flip-- cbrt-unprod add-log-exp
Counts
1 → 33
Calls
1 calls:
59.0ms
(* (pow x 2) (- (* x (/ 3002399751580331.0 4503599627370496.0)) 1.0))

series154.0ms

Counts
1 → 3
Calls
1 calls:
154.0ms
(* (pow x 2) (- (* x (/ 3002399751580331.0 4503599627370496.0)) 1.0))

simplify3.0s

Counts
36 → 36

prune112.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes75.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.3b

bsearch249.0ms

Steps
ItersRangePoint
9
0.3311692926351245
51141.47312026252
84.47417936124704

simplify874.0ms

end0.0ms

sample8.9s

Algorithm
intervals
Results
2.4s1313×body640valid
2.0s1828×body10240exit
1.7s1778×body1280valid
1.7s9885×body80valid
305.0ms632×body320valid
67.0ms297×body160valid