Details

Time bar (total: 31.2s)

sample387.0ms

Algorithm
intervals
Results
160.0ms86×body2560valid
88.0ms110×body1280valid
76.0ms57×body10240exit
17.0ms33×body640valid
8.0ms313×pre80true
4.0ms13×body320valid
1.0ms10×body80valid
1.0ms4×body160valid

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01724
14024
210124
325824
476524
5400824
done500024

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.4b

localize33.0ms

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)

rewrite165.0ms

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:
83.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
14.0ms
(- (exp (* b eps)) 1.0)
24.0ms
(- (exp (* a eps)) 1.0)
34.0ms
(- (exp (* (+ a b) eps)) 1.0)

series218.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
38.0ms
(- (exp (* b eps)) 1.0)
37.0ms
(- (exp (* a eps)) 1.0)
69.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify1.7s

Counts
150 → 150
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02213064
15392630
225932205
done50012041

prune710.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 52.4b

localize87.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 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))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
40×add-exp-log
32×unswap-sqr
28×unpow-prod-down
23×*-un-lft-identity
22×prod-exp
21×add-cube-cbrt
20×associate-*r* associate-*l* add-cbrt-cube sqr-pow
14×cube-prod
12×pow-to-exp pow-exp
10×unpow2
9×prod-diff
6×cbrt-unprod add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u associate-*r/ div-exp log1p-expm1-u
3×flip3-- fma-neg flip--
2×cube-mult unpow3 pow-prod-down associate-/r/ *-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 → 169
Calls
4 calls:
55.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
17.0ms
(- (exp (* (+ a b) eps)) 1.0)
41.0ms
(* (pow a 2) (pow eps 2))
34.0ms
(* (pow a 3) (pow eps 3))

series1.3s

Counts
4 → 12
Calls
4 calls:
1.1s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
55.0ms
(- (exp (* (+ a b) eps)) 1.0)
35.0ms
(* (pow a 2) (pow eps 2))
94.0ms
(* (pow a 3) (pow eps 3))

simplify468.0ms

Counts
181 → 181
Iterations

Useful iterations: done (461.0ms)

IterNodesCost
03033711
18413435
done50012796

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite56.0ms

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:
53.0ms
(+ (/ 1 b) (/ 1 a))

series15.0ms

Counts
1 → 3
Calls
1 calls:
15.0ms
(+ (/ 1 b) (/ 1 a))

simplify2.3s

Counts
37 → 37
Iterations

Useful iterations: 3 (488.0ms)

IterNodesCost
042245
1110231
2460211
32128210
done5001210

prune176.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

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)))

rewrite329.0ms

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×expm1-log1p-u add-cbrt-cube log1p-expm1-u 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 → 167
Calls
4 calls:
231.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
20.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
35.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
23.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
131.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
117.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
110.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))

simplify1.4s

Counts
179 → 179
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01823562
14423100
219722905
done50002643

prune705.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes285.0ms

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

sample16.2s

Algorithm
intervals
Results
5.2s2608×body2560valid
4.8s3411×body1280valid
4.0s2022×body10240exit
897.0ms1110×body640valid
461.0ms10022×pre80true
120.0ms334×body320valid
43.0ms410×body80valid
30.0ms127×body160valid