Details

Time bar (total: 28.0s)

sample365.0ms

Algorithm
intervals
Results
120.0ms86×body2560valid
82.0ms110×body1280valid
71.0ms57×body10240exit
48.0ms33×body640valid
8.0ms313×pre80true
4.0ms13×body320valid
1.0ms10×body80valid
1.0ms4×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
14024
210124
324524
469924
5358324
done500224

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.6b
(- (exp (* b eps)) 1.0)
3.7b
(- (exp (* a eps)) 1.0)
6.2b
(- (exp (* (+ a b) eps)) 1.0)

rewrite197.0ms

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:
127.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
27.0ms
(- (exp (* b eps)) 1.0)
21.0ms
(- (exp (* a eps)) 1.0)
18.0ms
(- (exp (* (+ a b) eps)) 1.0)

series218.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
34.0ms
(- (exp (* b eps)) 1.0)
45.0ms
(- (exp (* a eps)) 1.0)
79.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify694.0ms

Counts
88 → 88
Iterations

Useful iterations: done (692.0ms)

IterNodesCost
01431364
13551326
216351198
done50011196

prune754.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 52.4b

localize108.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
6.2b
(- (exp (* (+ a b) eps)) 1.0)
14.7b
(* (pow a 2) (pow eps 2))
15.7b
(* (pow a 3) (pow eps 3))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
40×add-exp-log
32×unswap-sqr
28×unpow-prod-down
22×prod-exp
20×associate-*r* associate-*l* add-cbrt-cube sqr-pow
16×*-un-lft-identity
14×add-cube-cbrt cube-prod
12×pow-to-exp pow-exp
10×unpow2
8×associate-/r/
6×cbrt-unprod add-log-exp
5×flip3-- flip--
4×pow1 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 → 155
Calls
4 calls:
134.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
19.0ms
(- (exp (* (+ a b) eps)) 1.0)
24.0ms
(* (pow a 2) (pow eps 2))
41.0ms
(* (pow a 3) (pow eps 3))

series1.5s

Counts
4 → 12
Calls
4 calls:
1.2s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
87.0ms
(- (exp (* (+ a b) eps)) 1.0)
68.0ms
(* (pow a 2) (pow eps 2))
111.0ms
(* (pow a 3) (pow eps 3))

simplify517.0ms

Counts
167 → 167
Iterations

Useful iterations: done (509.0ms)

IterNodesCost
02903699
18553487
done50002879

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite48.0ms

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:
47.0ms
(+ (/ 1 b) (/ 1 a))

series12.0ms

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

simplify1.0s

Counts
22 → 22
Iterations

Useful iterations: 3 (241.0ms)

IterNodesCost
040229
1102216
2360196
31364194
done5001194

prune92.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
0.5b
(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b
(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b
(cbrt (+ (/ 1 b) (/ 1 a)))

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
139×*-un-lft-identity
114×cbrt-prod
81×distribute-lft-out
60×div-inv
42×times-frac
37×add-sqr-sqrt
33×cbrt-div swap-sqr
29×add-cube-cbrt
13×associate-*r* associate-*l*
11×pow1 flip3-+ frac-add flip-+
9×frac-times pow1/3
6×add-exp-log
4×add-cbrt-cube add-log-exp unswap-sqr
3×associate-*r/ associate-*l/
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 159
Calls
4 calls:
265.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
25.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
19.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
44.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))

series550.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
128.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
133.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
116.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))

simplify1.1s

Counts
171 → 171
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01783472
14293024
217232832
done50012573

prune687.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes180.0ms

Accuracy

0% (2.9b remaining)

Error of 3.1b against oracle of 0.1b and baseline of 3.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
done97

end0.0ms

sample15.6s

Algorithm
intervals
Results
4.9s2608×body2560valid
4.9s2022×body10240exit
3.9s3411×body1280valid
764.0ms1110×body640valid
380.0ms10022×pre80true
111.0ms334×body320valid
77.0ms127×body160valid
42.0ms410×body80valid