Details

Time bar (total: 10.3s)

sample131.0ms

Algorithm
intervals
Results
43.0ms51×body1280valid
26.0ms49×body10240exit
23.0ms294×body80valid
11.0ms33×body640valid
4.0ms19×body320valid
2.0ms13×body160valid

simplify31.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (* (+ 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)))
3.6b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite403.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
106×times-frac
90×add-sqr-sqrt
34×add-cube-cbrt
26×distribute-lft-out--
17×difference-of-squares
10×distribute-lft-out associate-/l* add-log-exp
8×add-cbrt-cube
6×add-exp-log associate-/r*
4×pow1 div-inv associate-/l/
3×div-sub
2×cbrt-undiv flip3-- exp-to-pow frac-2neg div-exp clear-num flip--
1×sub-neg exp-prod distribute-rgt-out-- flip3-+ diff-log sum-log frac-sub flip-+ rem-exp-log sub-div associate--r-
Counts
4 → 127
Calls
4 calls:
6.0ms
(exp (* (+ 1.0 eps) x))
41.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
47.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
300.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series318.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(exp (* (+ 1.0 eps) x))
49.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
49.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
199.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify53.0ms

Counts
139 → 139

prune450.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
0.1b
(* 0.33333333333333337 (pow x 3))
7.2b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp unswap-sqr
7×add-cbrt-cube
6×associate-*l* prod-exp
4×cube-prod sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×cube-mult sub-neg flip3-- unpow3 associate--l+ sum-log flip--
Counts
3 → 72
Calls
3 calls:
12.0ms
(* 0.5 (pow x 2))
13.0ms
(* 0.33333333333333337 (pow x 3))
59.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series109.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(* 0.5 (pow x 2))
40.0ms
(* 0.33333333333333337 (pow x 3))
41.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify42.0ms

Counts
81 → 81

prune189.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (pow x 2))
0.0b
(- 1.0 (* 0.5 (pow x 2)))
0.1b
(* 0.33333333333333337 (pow x 3))
7.2b
(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* 0.5 (pow x 2))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×associate-*r*
14×add-exp-log
11×add-cube-cbrt *-un-lft-identity add-log-exp
8×unpow-prod-down add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×pow1 cube-prod sqr-pow
2×pow-to-exp sub-neg associate-+r+ diff-log pow-exp sum-log *-commutative cbrt-unprod unpow2
1×+-commutative cube-mult associate-+r- flip3-- flip3-+ unpow3 flip-- flip-+
Counts
4 → 85
Calls
4 calls:
12.0ms
(* 0.5 (pow x 2))
5.0ms
(- 1.0 (* 0.5 (pow x 2)))
13.0ms
(* 0.33333333333333337 (pow x 3))
16.0ms
(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* 0.5 (pow x 2))))

series175.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* 0.5 (pow x 2))
63.0ms
(- 1.0 (* 0.5 (pow x 2)))
39.0ms
(* 0.33333333333333337 (pow x 3))
45.0ms
(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* 0.5 (pow x 2))))

simplify46.0ms

Counts
97 → 97

prune229.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize23.0ms

Local error

Found 4 expressions with local error:

7.2b
(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* (* (cbrt (* 0.5 (pow x 2))) (cbrt (* 0.5 (pow x 2)))) (cbrt (* 0.5 (pow x 2))))))
33.5b
(cbrt (* 0.5 (pow x 2)))
33.5b
(cbrt (* 0.5 (pow x 2)))
33.5b
(cbrt (* 0.5 (pow x 2)))

rewrite32.0ms

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 pow1/3
2×associate-+r+ sum-log
1×+-commutative associate-+r- sub-neg flip3-+ diff-log flip-+
Counts
4 → 42
Calls
4 calls:
16.0ms
(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* (* (cbrt (* 0.5 (pow x 2))) (cbrt (* 0.5 (pow x 2)))) (cbrt (* 0.5 (pow x 2))))))
5.0ms
(cbrt (* 0.5 (pow x 2)))
5.0ms
(cbrt (* 0.5 (pow x 2)))
5.0ms
(cbrt (* 0.5 (pow x 2)))

series796.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* (* (cbrt (* 0.5 (pow x 2))) (cbrt (* 0.5 (pow x 2)))) (cbrt (* 0.5 (pow x 2))))))
235.0ms
(cbrt (* 0.5 (pow x 2)))
241.0ms
(cbrt (* 0.5 (pow x 2)))
246.0ms
(cbrt (* 0.5 (pow x 2)))

simplify99.0ms

Counts
54 → 54

prune155.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

regimes119.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.8b

bsearch108.0ms

Steps
ItersRangePoint
5
1.494961173861339
5.509787273302661
1.8185133940036449

simplify1.0ms

end0.0ms

sample6.6s

Algorithm
intervals
Results
2.2s1731×body1280valid
1.8s1919×body10240exit
1.2s10032×body80valid
630.0ms1320×body640valid
169.0ms588×body320valid
56.0ms335×body160valid