Details

Time bar (total: 24.9s)

sample199.0ms

Algorithm
intervals
Results
66.0ms349×body80valid
44.0ms74×body10240exit
32.0ms55×body1280valid
13.0ms37×body640valid
8.0ms24×body320valid
1.0ms7×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5000
42266
3377
2122
146
019

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps)))
0.0b
(exp (* x (+ eps 1.0)))
0.0b
(exp (* (- eps 1.0) x))
5.1b
(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
12×add-log-exp
8×add-sqr-sqrt *-un-lft-identity
6×pow1 add-cbrt-cube add-cube-cbrt
5×add-exp-log
4×associate-*r* associate-*r/
3×distribute-rgt-in distribute-lft-in flip3-+ exp-to-pow associate-*l* flip-+
2×associate-+r+ exp-prod exp-sum frac-add rem-exp-log
1×+-commutative sum-log diff-log div-sub pow-prod-down prod-exp *-commutative associate-+l- cbrt-unprod distribute-lft-out unswap-sqr
Counts
4 → 62
Calls
4 calls:
59.0ms
(* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps)))
8.0ms
(exp (* x (+ eps 1.0)))
7.0ms
(exp (* (- eps 1.0) x))
103.0ms
(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

series464.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps)))
13.0ms
(exp (* x (+ eps 1.0)))
26.0ms
(exp (* (- eps 1.0) x))
355.0ms
(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

simplify1.6s

Counts
74 → 74
Iterations
IterNodes
done5001
22201
1429
0152

prune571.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17))
0.7b
(* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)
0.7b
(/ (* x x) (/ eps x))
2.6b
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
34×add-sqr-sqrt add-cbrt-cube add-exp-log
27×*-un-lft-identity add-cube-cbrt
18×associate-*l*
13×associate-/r*
12×cbrt-undiv div-exp
11×add-log-exp
9×prod-exp cbrt-unprod
6×pow1
5×div-inv
4×diff-log
3×sub-neg associate-*r* unswap-sqr
2×flip3-- associate--l+ associate-/r/ flip--
1×associate--l- clear-num frac-2neg pow-prod-down associate-*l/ *-commutative associate-/l*
Counts
4 → 118
Calls
4 calls:
4.0ms
(- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17))
43.0ms
(* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)
21.0ms
(/ (* x x) (/ eps x))
49.0ms
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))

series196.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17))
37.0ms
(* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)
32.0ms
(/ (* x x) (/ eps x))
76.0ms
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))

simplify2.8s

Counts
130 → 130
Iterations
IterNodes
done5001
24712
1638
0207

prune669.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.3b

localize108.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))
8.7b
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))
8.7b
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))
8.7b
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-log-exp
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-div
4×pow1 flip3-- add-cbrt-cube add-exp-log flip--
3×pow1/3 diff-log
2×sub-neg associate--l+
1×associate--l-
Counts
4 → 55
Calls
4 calls:
32.0ms
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))
26.0ms
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))
15.0ms
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))
15.0ms
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))

series1.9s

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))
598.0ms
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))
587.0ms
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))
655.0ms
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))

simplify1.3s

Counts
67 → 67
Iterations
IterNodes
done5001
2828
1225
090

prune524.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 4.2b

localize83.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))
2.6b
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))
8.7b
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))
8.7b
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
14×add-log-exp
6×cbrt-prod add-sqr-sqrt *-un-lft-identity diff-log add-cube-cbrt
4×pow1 cbrt-div sub-neg flip3-- add-cbrt-cube associate--l+ add-exp-log flip--
2×associate--l- pow1/3
Counts
4 → 58
Calls
4 calls:
49.0ms
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))
52.0ms
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))
32.0ms
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))
20.0ms
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))

series1.3s

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))
83.0ms
(- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x)))
601.0ms
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))
565.0ms
(cbrt (- (- 2.0 (* (/ (* x x) (/ eps x)) 2.7755575615628914e-17)) (* 1.0 (* x x))))

simplify1.3s

Counts
70 → 70
Iterations
IterNodes
done5001
2828
1225
090

prune488.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.2b

regimes165.0ms

Accuracy

92.5% (1.3b remaining)

Error of 5.9b against oracle of 4.6b and baseline of 21.9b

bsearch235.0ms

Steps
ItersRangePoint
10
1.9673231826388637e-10
9645967.64350026
3.434809865163426e-10

simplify12.0ms

Iterations
IterNodes
done37
137
030

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.6s1879×body10240exit
2.1s1738×body1280valid
1.4s9945×body80valid
645.0ms1248×body640valid
275.0ms638×body320valid
71.0ms327×body160valid