Details

Time bar (total: 10.9s)

sample208.0ms

Algorithm
intervals
Results
71.0ms77×body2560valid
57.0ms120×body1280valid
45.0ms51×body10240exit
11.0ms31×body640valid
5.0ms307×pre80true
2.0ms11×body320valid
1.0ms13×body80valid
0.0ms4×body160valid

simplify94.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04013
110113
224513
369713
4346313
5500113

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.9b
(- (exp (* a eps)) 1.0)
4.1b
(- (exp (* b eps)) 1.0)
6.8b
(- (exp (* (+ a b) eps)) 1.0)

rewrite37.0ms

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:
24.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms
(- (exp (* a eps)) 1.0)
4.0ms
(- (exp (* b eps)) 1.0)
4.0ms
(- (exp (* (+ a b) eps)) 1.0)

series166.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
38.0ms
(- (exp (* a eps)) 1.0)
31.0ms
(- (exp (* b eps)) 1.0)
49.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify41.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0346733
11449673
25001673

prune335.0ms

Filtered
88 candidates to 66 candidates (75.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 48.4b

localize28.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* 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)))
6.8b
(- (exp (* (+ a b) eps)) 1.0)
13.2b
(* (pow a 2) (pow eps 2))
15.7b
(* (pow a 3) (pow eps 3))

rewrite73.0ms

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:
44.0ms
(/ (* 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)))
4.0ms
(- (exp (* (+ a b) eps)) 1.0)
8.0ms
(* (pow a 2) (pow eps 2))
11.0ms
(* (pow a 3) (pow eps 3))

series903.0ms

Counts
4 → 12
Calls
4 calls:
757.0ms
(/ (* 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)))
49.0ms
(- (exp (* (+ a b) eps)) 1.0)
31.0ms
(* (pow a 2) (pow eps 2))
66.0ms
(* (pow a 3) (pow eps 3))

simplify146.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (129.0ms)

IterNodesCost
08151795
146651494
250021458

prune630.0ms

Filtered
167 candidates to 91 candidates (54.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune9.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

3.9b
(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
6.8b
(- (exp (* (+ a b) eps)) 1.0)
12.2b
(* (pow eps 2) (pow b 2))
15.4b
(* (pow eps 3) (pow b 3))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
33×unswap-sqr
30×add-exp-log
28×unpow-prod-down
25×associate-*l*
23×associate-*r*
20×*-un-lft-identity sqr-pow
19×prod-exp
16×add-cube-cbrt
14×cube-prod
12×pow-to-exp pow-exp
10×add-cbrt-cube unpow2
6×pow1 add-log-exp
4×frac-times flip3-- flip--
3×flip3-+ pow-prod-down *-commutative cbrt-unprod flip-+
2×cube-mult unpow3 associate-*r/ associate-*l/ distribute-lft-out-- difference-of-squares
1×distribute-rgt-in sub-neg distribute-lft-in diff-log
Counts
4 → 154
Calls
4 calls:
129.0ms
(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
4.0ms
(- (exp (* (+ a b) eps)) 1.0)
8.0ms
(* (pow eps 2) (pow b 2))
11.0ms
(* (pow eps 3) (pow b 3))

series359.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
50.0ms
(- (exp (* (+ a b) eps)) 1.0)
31.0ms
(* (pow eps 2) (pow b 2))
66.0ms
(* (pow eps 3) (pow b 3))

simplify135.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
07241457
139051310
250031267

prune705.0ms

Filtered
166 candidates to 91 candidates (54.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
093
193

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.4s2525×body2560valid
1.7s1957×body10240exit
1.7s3405×body1280valid
311.0ms1108×body640valid
175.0ms9961×pre80true
71.0ms386×body320valid
24.0ms453×body80valid
15.0ms127×body160valid