Details

Time bar (total: 17.5s)

sample222.0ms

Algorithm
intervals
Results
62.0ms319×body80valid
52.0ms59×body10240exit
43.0ms51×body1280valid
17.0ms35×body640valid
10.0ms26×body320valid
2.0ms10×body160valid

simplify684.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b
(exp (* (+ 1.0 eps) x))
0.0b
(exp (* (- 1.0 eps) x))
1.7b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite625.0ms

Algorithm
rewrite-expression-head
Rules
101×*-un-lft-identity
94×times-frac
81×add-sqr-sqrt
26×distribute-lft-out--
25×add-cube-cbrt
17×difference-of-squares
14×add-log-exp
6×add-cbrt-cube distribute-lft-out associate-/l*
5×add-exp-log
4×pow1 exp-to-pow
3×div-sub associate-/r* div-inv
2×exp-prod flip3-- diff-log flip-- rem-exp-log associate-/l/
1×cbrt-undiv sub-neg distribute-rgt-out-- frac-2neg div-exp clear-num sum-log frac-sub sub-div associate--r-
Counts
4 → 105
Calls
4 calls:
93.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
13.0ms
(exp (* (+ 1.0 eps) x))
18.0ms
(exp (* (- 1.0 eps) x))
495.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series393.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
21.0ms
(exp (* (+ 1.0 eps) x))
23.0ms
(exp (* (- 1.0 eps) x))
272.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify776.0ms

Counts
117 → 117

prune539.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×associate-*l*
7×add-exp-log
5×add-cube-cbrt *-un-lft-identity
4×distribute-rgt-in sub-neg unpow-prod-down associate-+r+ distribute-lft-in add-cbrt-cube add-log-exp unswap-sqr
3×associate-*r* prod-exp
2×pow1 associate-*r/ unpow2 sqr-pow
1×+-commutative pow-to-exp flip3-- flip3-+ pow-exp sum-log *-commutative flip-- cbrt-unprod flip-+
Counts
2 → 48
Calls
2 calls:
10.0ms
(+ 1.0 (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
65.0ms
(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

series180.0ms

Counts
2 → 6
Calls
2 calls:
64.0ms
(+ 1.0 (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
116.0ms
(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

simplify567.0ms

Counts
54 → 54

prune181.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (pow x 3) 0.33333333333333337) 1.0)
0.1b
(* (pow x 3) 0.33333333333333337)
7.8b
(+ (+ (* (pow x 3) 0.33333333333333337) 1.0) (* (pow x 2) (- 0.5)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×associate-*l*
10×add-log-exp
8×add-exp-log
7×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down cube-prod sum-log unswap-sqr
3×pow1 associate-*r* prod-exp
2×+-commutative flip3-+ distribute-rgt-neg-out flip-+ sqr-pow
1×cube-mult pow-to-exp associate-+l+ unpow3 unsub-neg pow-exp *-commutative cbrt-unprod
Counts
3 → 57
Calls
3 calls:
17.0ms
(+ (* (pow x 3) 0.33333333333333337) 1.0)
31.0ms
(* (pow x 3) 0.33333333333333337)
78.0ms
(+ (+ (* (pow x 3) 0.33333333333333337) 1.0) (* (pow x 2) (- 0.5)))

series269.0ms

Counts
3 → 9
Calls
3 calls:
148.0ms
(+ (* (pow x 3) 0.33333333333333337) 1.0)
56.0ms
(* (pow x 3) 0.33333333333333337)
65.0ms
(+ (+ (* (pow x 3) 0.33333333333333337) 1.0) (* (pow x 2) (- 0.5)))

simplify844.0ms

Counts
66 → 66

prune236.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (+ (* (pow x 3) 0.33333333333333337) 1.0) 3)
0.1b
(* (pow x 3) 0.33333333333333337)
4.3b
(cbrt (pow (+ (* (pow x 3) 0.33333333333333337) 1.0) 3))
7.8b
(+ (cbrt (pow (+ (* (pow x 3) 0.33333333333333337) 1.0) 3)) (* (pow x 2) (- 0.5)))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×cbrt-prod associate-*l*
10×add-exp-log unpow-prod-down cube-prod
7×add-cbrt-cube
6×add-log-exp
5×pow1
4×cube-div unswap-sqr sqr-pow
3×cube-mult pow-unpow flip3-+ unpow3 associate-*r* prod-exp flip-+
2×pow-to-exp cbrt-div pow-exp distribute-rgt-neg-out
1×+-commutative pow-pow pow1/3 unsub-neg sum-log *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 92
Calls
4 calls:
25.0ms
(pow (+ (* (pow x 3) 0.33333333333333337) 1.0) 3)
15.0ms
(* (pow x 3) 0.33333333333333337)
23.0ms
(cbrt (pow (+ (* (pow x 3) 0.33333333333333337) 1.0) 3))
146.0ms
(+ (cbrt (pow (+ (* (pow x 3) 0.33333333333333337) 1.0) 3)) (* (pow x 2) (- 0.5)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(pow (+ (* (pow x 3) 0.33333333333333337) 1.0) 3)
58.0ms
(* (pow x 3) 0.33333333333333337)
106.0ms
(cbrt (pow (+ (* (pow x 3) 0.33333333333333337) 1.0) 3))
56.0ms
(+ (cbrt (pow (+ (* (pow x 3) 0.33333333333333337) 1.0) 3)) (* (pow x 2) (- 0.5)))

simplify1.3s

Counts
104 → 104

prune384.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

regimes120.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.9b

bsearch232.0ms

Steps
ItersRangePoint
9
0.8658429469844214
6055834.380950506
359.42303284477396

simplify659.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
2.5s1953×body10240exit
2.4s1698×body1280valid
1.2s9998×body80valid
1.1s1250×body640valid
361.0ms657×body320valid
160.0ms353×body160valid