Details

Time bar (total: 30.3s)

sample225.0ms

Algorithm
intervals
Results
79.0ms78×body2560valid
56.0ms64×body10240exit
55.0ms110×body1280valid
9.0ms37×body640valid
5.0ms320×pre80true
2.0ms12×body320valid
1.0ms16×body80valid
0.0ms3×body160valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01724
14024
210124
325824
476024
5373824
done500024

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.0b
(- (exp (* a eps)) 1.0)
3.5b
(- (exp (* b eps)) 1.0)
5.6b
(- (exp (* (+ a b) eps)) 1.0)

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
49×*-un-lft-identity
45×prod-diff
39×add-cube-cbrt
11×distribute-rgt-in distribute-lft-in
10×add-log-exp
9×flip3-- fma-neg flip--
6×pow1 add-exp-log add-cbrt-cube
5×sub-neg associate-*r* associate-*l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u frac-times log1p-expm1-u
3×diff-log
2×associate-*r/ associate-*l/
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 138
Calls
4 calls:
75.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
14.0ms
(- (exp (* a eps)) 1.0)
17.0ms
(- (exp (* b eps)) 1.0)
16.0ms
(- (exp (* (+ a b) eps)) 1.0)

series175.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
34.0ms
(- (exp (* a eps)) 1.0)
33.0ms
(- (exp (* b eps)) 1.0)
53.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify768.0ms

Counts
150 → 150
Iterations

Useful iterations: done (763.0ms)

IterNodesCost
02213064
14882615
214942203
done50012038

prune439.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 49.7b

localize27.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma (* 1/6 (pow b 3)) (pow eps 3) (* b (+ eps (* (* 1/2 (pow eps 2)) b))))))
5.6b
(- (exp (* (+ a b) eps)) 1.0)
7.6b
(* (* 1/2 (pow eps 2)) b)
16.0b
(fma (* 1/6 (pow b 3)) (pow eps 3) (* b (+ eps (* (* 1/2 (pow eps 2)) b))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
21×add-cbrt-cube
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
11×prod-exp
9×prod-diff
7×cbrt-unprod
6×pow1 add-log-exp
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×flip3-- fma-neg associate-*r* flip--
2×associate-*r/ associate-*l/ associate-/r/ associate-/l/
1×pow-to-exp sub-neg frac-2neg times-frac diff-log associate-*l* pow-prod-down pow-exp clear-num associate-/r* *-commutative fma-udef div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 86
Calls
4 calls:
48.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma (* 1/6 (pow b 3)) (pow eps 3) (* b (+ eps (* (* 1/2 (pow eps 2)) b))))))
16.0ms
(- (exp (* (+ a b) eps)) 1.0)
24.0ms
(* (* 1/2 (pow eps 2)) b)
0.0ms
(fma (* 1/6 (pow b 3)) (pow eps 3) (* b (+ eps (* (* 1/2 (pow eps 2)) b))))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.5s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma (* 1/6 (pow b 3)) (pow eps 3) (* b (+ eps (* (* 1/2 (pow eps 2)) b))))))
52.0ms
(- (exp (* (+ a b) eps)) 1.0)
22.0ms
(* (* 1/2 (pow eps 2)) b)
106.0ms
(fma (* 1/6 (pow b 3)) (pow eps 3) (* b (+ eps (* (* 1/2 (pow eps 2)) b))))

simplify1.3s

Counts
98 → 98
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02242896
16142742
226092166
done50022121

prune441.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (/ 1 b) (/ 1 a))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
15×times-frac
13×fma-def
10×add-sqr-sqrt add-cube-cbrt
7×distribute-lft-out
5×div-inv
3×add-log-exp
1×pow1 add-exp-log +-commutative expm1-log1p-u flip3-+ frac-add sum-log add-cbrt-cube flip-+ log1p-expm1-u
Counts
1 → 34
Calls
1 calls:
28.0ms
(+ (/ 1 b) (/ 1 a))

series12.0ms

Counts
1 → 3
Calls
1 calls:
12.0ms
(+ (/ 1 b) (/ 1 a))

simplify2.9s

Counts
37 → 37
Iterations

Useful iterations: 3 (116.0ms)

IterNodesCost
042245
1108231
2251211
3523210
41465210
53712210
done5000210

prune75.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 b) b)
0.1b
(/ (/ 1 a) a)
4.7b
(- (/ (/ 1 b) b) (/ (/ 1 a) a))
29.1b
(/ (- (/ (/ 1 b) b) (/ (/ 1 a) a)) (- (/ 1 b) (/ 1 a)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
8712×times-frac
5874×add-sqr-sqrt
4654×*-un-lft-identity
3306×add-cube-cbrt
1849×prod-diff
858×difference-of-squares
801×div-inv
427×distribute-lft-out--
62×associate-/l*
43×fma-neg
25×associate-/r*
24×add-exp-log
16×add-cbrt-cube
13×div-exp
10×pow1
7×cbrt-undiv
6×add-log-exp
5×associate-/l/
4×expm1-log1p-u log1p-expm1-u pow-div
3×flip3-- frac-2neg clear-num associate-/r/ frac-sub flip--
2×rec-exp pow-flip 1-exp inv-pow
1×sub-neg diff-log div-sub
Counts
4 → 2852
Calls
4 calls:
12.0ms
(/ (/ 1 b) b)
12.0ms
(/ (/ 1 a) a)
167.0ms
(- (/ (/ 1 b) b) (/ (/ 1 a) a))
524.0ms
(/ (- (/ (/ 1 b) b) (/ (/ 1 a) a)) (- (/ 1 b) (/ 1 a)))

series102.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ (/ 1 b) b)
16.0ms
(/ (/ 1 a) a)
26.0ms
(- (/ (/ 1 b) b) (/ (/ 1 a) a))
38.0ms
(/ (- (/ (/ 1 b) b) (/ (/ 1 a) a)) (- (/ 1 b) (/ 1 a)))

simplify976.0ms

Counts
2864 → 2864
Iterations

Useful iterations: done (789.0ms)

IterNodesCost
03090158692
done5001156928

prune10.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

0% (3.2b remaining)

Error of 3.3b against oracle of 0.1b and baseline of 3.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
done97

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.5s2604×body2560valid
1.7s1927×body10240exit
1.7s3389×body1280valid
313.0ms1100×body640valid
165.0ms9929×pre80true
62.0ms349×body320valid
23.0ms437×body80valid
17.0ms123×body160valid