Details

Time bar (total: 19.5s)

sample230.0ms

Algorithm
intervals
Results
79.0ms78×body2560valid
58.0ms110×body1280valid
54.0ms64×body10240exit
12.0ms37×body640valid
5.0ms320×pre80true
2.0ms12×body320valid
1.0ms16×body80valid
0.0ms3×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01724
14024
210124
324524
469224
5330124
done500124

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize22.0ms

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)

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
10×add-log-exp
9×flip3-- flip--
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×sub-neg associate-*r* associate-*l* distribute-lft-out-- difference-of-squares
4×frac-times
3×diff-log
2×distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 76
Calls
4 calls:
70.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
12.0ms
(- (exp (* a eps)) 1.0)
12.0ms
(- (exp (* b eps)) 1.0)
13.0ms
(- (exp (* (+ a b) eps)) 1.0)

series181.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
41.0ms
(- (exp (* a eps)) 1.0)
34.0ms
(- (exp (* b eps)) 1.0)
52.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify697.0ms

Counts
88 → 88
Iterations

Useful iterations: done (694.0ms)

IterNodesCost
01431364
13451326
212311196
done50001190

prune325.0ms

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) (+ (* b (+ eps (* (* 1/2 (pow eps 2)) b))) (* 1/6 (* (pow eps 3) (pow b 3))))))
5.6b
(- (exp (* (+ a b) eps)) 1.0)
7.6b
(* (* 1/2 (pow eps 2)) b)
16.7b
(* (pow eps 3) (pow b 3))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
37×add-sqr-sqrt
23×add-cbrt-cube
20×prod-exp
16×unswap-sqr
15×associate-*r*
14×unpow-prod-down cube-prod
13×*-un-lft-identity associate-*l*
11×add-cube-cbrt
10×sqr-pow
8×associate-/r/ cbrt-unprod
7×pow-to-exp pow-exp
6×pow1 add-log-exp
5×flip3-- flip--
4×cbrt-undiv frac-times associate-*r/ div-exp
3×flip3-+ flip-+
2×cube-mult unpow3 pow-prod-down associate-*l/ *-commutative associate-/l/
1×sub-neg frac-2neg times-frac diff-log clear-num associate-/r* div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 123
Calls
4 calls:
69.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* b (+ eps (* (* 1/2 (pow eps 2)) b))) (* 1/6 (* (pow eps 3) (pow b 3))))))
13.0ms
(- (exp (* (+ a b) eps)) 1.0)
24.0ms
(* (* 1/2 (pow eps 2)) b)
21.0ms
(* (pow eps 3) (pow b 3))

series1.6s

Counts
4 → 12
Calls
4 calls:
1.5s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* b (+ eps (* (* 1/2 (pow eps 2)) b))) (* 1/6 (* (pow eps 3) (pow b 3))))))
53.0ms
(- (exp (* (+ a b) eps)) 1.0)
23.0ms
(* (* 1/2 (pow eps 2)) b)
69.0ms
(* (pow eps 3) (pow b 3))

simplify1.7s

Counts
135 → 135
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02593228
17903046
240482568
done50012567

prune540.0ms

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))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
7×distribute-lft-out
6×times-frac
4×div-inv
3×add-sqr-sqrt add-cube-cbrt add-log-exp
1×pow1 add-exp-log +-commutative flip3-+ frac-add sum-log add-cbrt-cube flip-+
Counts
1 → 19
Calls
1 calls:
24.0ms
(+ (/ 1 b) (/ 1 a))

series11.0ms

Counts
1 → 3
Calls
1 calls:
11.0ms
(+ (/ 1 b) (/ 1 a))

simplify2.6s

Counts
22 → 22
Iterations

Useful iterations: 3 (104.0ms)

IterNodesCost
040229
1102216
2233196
3459194
41153194
52581194
done5000194

prune42.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

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)))

rewrite503.0ms

Algorithm
rewrite-expression-head
Rules
1000×times-frac
788×add-sqr-sqrt
695×*-un-lft-identity
200×difference-of-squares
160×div-inv
148×add-cube-cbrt
111×distribute-lft-out
64×distribute-lft-out--
62×associate-/l*
24×add-exp-log
16×add-cbrt-cube
13×div-exp
12×associate-/r*
10×pow1
7×cbrt-undiv
6×add-log-exp
5×associate-/l/
4×pow-div
3×frac-2neg clear-num associate-/r/
2×rec-exp flip3-- pow-flip 1-exp frac-sub flip-- inv-pow
1×sub-neg flip3-+ diff-log div-sub frac-add flip-+
Counts
4 → 471
Calls
4 calls:
11.0ms
(/ (/ 1 b) b)
12.0ms
(/ (/ 1 a) a)
103.0ms
(- (/ (/ 1 b) b) (/ (/ 1 a) a))
330.0ms
(/ (- (/ (/ 1 b) b) (/ (/ 1 a) a)) (+ (/ 1 b) (/ -1 a)))

series104.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (/ 1 b) b)
17.0ms
(/ (/ 1 a) a)
26.0ms
(- (/ (/ 1 b) b) (/ (/ 1 a) a))
40.0ms
(/ (- (/ (/ 1 b) b) (/ (/ 1 a) a)) (+ (/ 1 b) (/ -1 a)))

simplify1.4s

Counts
483 → 483
Iterations

Useful iterations: done (1.4s)

IterNodesCost
062012512
1133211498
2235310052
done50008511

prune557.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes54.0ms

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

sample7.0s

Algorithm
intervals
Results
2.5s2604×body2560valid
1.8s1927×body10240exit
1.7s3389×body1280valid
305.0ms1100×body640valid
156.0ms9929×pre80true
63.0ms349×body320valid
23.0ms437×body80valid
14.0ms123×body160valid