Details

Time bar (total: 7.4s)

sample212.0ms

Algorithm
intervals
Results
92.0ms80×body2560valid
73.0ms118×body1280valid
8.0ms24×body640valid
6.0ms299×pre80true
4.0ms15×body320valid
3.0ms43×body80overflowed
1.0ms13×body80valid
1.0msbody160valid

simplify98.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04013
110113
224513
369713
4346313
5500113

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 60.6b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
2.5b
(- (exp (* b eps)) 1.0)
2.9b
(- (exp (* a eps)) 1.0)
4.0b
(- (exp (* (+ a b) eps)) 1.0)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log add-cbrt-cube
10×add-sqr-sqrt flip3-- *-un-lft-identity flip-- add-log-exp
associate-/r/
pow1 cbrt-undiv frac-times add-cube-cbrt associate-*r/ div-exp prod-exp cbrt-unprod
sub-neg diff-log distribute-lft-out-- difference-of-squares
associate-*l/ associate-/l/
frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 73
Calls
4 calls:
16.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
3.0ms
(- (exp (* b eps)) 1.0)
3.0ms
(- (exp (* a eps)) 1.0)
4.0ms
(- (exp (* (+ a b) eps)) 1.0)

series91.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
7.0ms
(- (exp (* b eps)) 1.0)
7.0ms
(- (exp (* a eps)) 1.0)
14.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify55.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0488957
12299794
25001789

prune121.0ms

Filtered
85 candidates to 63 candidates (25.9%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New82385
Fresh000
Picked101
Done000
Total83386

Merged error: 0.1b

Counts
86 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
distribute-lft-out
times-frac
div-inv
add-sqr-sqrt add-cube-cbrt add-log-exp
pow1 add-exp-log +-commutative flip3-+ frac-add sum-log add-cbrt-cube flip-+
Counts
1 → 19
Calls
1 calls:
11.0ms
(+ (/ 1 b) (/ 1 a))

series3.0ms

Counts
1 → 3
Calls
1 calls:
3.0ms
(+ (/ 1 b) (/ 1 a))

simplify66.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
0101104
134594
2115391
3275590
4500190

prune28.0ms

Filtered
22 candidates to 14 candidates (36.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New20222
Fresh202
Picked011
Done000
Total22325

Merged error: 0.1b

Counts
25 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

14.5b
(/ (+ b a) (* b a))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity
add-exp-log add-cbrt-cube
times-frac associate-/l*
add-sqr-sqrt add-cube-cbrt
cbrt-undiv div-exp associate-/l/ distribute-lft-out
pow1 frac-2neg flip3-+ prod-exp clear-num associate-/r* cbrt-unprod flip-+ div-inv add-log-exp
Counts
1 → 25
Calls
1 calls:
6.0ms
(/ (+ b a) (* b a))

series6.0ms

Counts
1 → 3
Calls
1 calls:
6.0ms
(/ (+ b a) (* b a))

simplify46.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0145134
1519113
22023113
35001113

prune29.0ms

Filtered
28 candidates to 19 candidates (32.1%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New27128
Fresh011
Picked011
Done011
Total27431

Merged error: 0.1b

Counts
31 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (sqrt (+ b a)) b)
0.2b
(/ (sqrt (+ b a)) a)
5.1b
(* (/ (sqrt (+ b a)) b) (/ (sqrt (+ b a)) a))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
93×add-sqr-sqrt
91×*-un-lft-identity
63×add-cube-cbrt
62×sqrt-prod
25×associate-*r* associate-*l*
19×add-exp-log add-cbrt-cube
14×distribute-lft-out associate-/l*
unswap-sqr
cbrt-undiv div-exp associate-/r*
pow1
sqrt-div prod-exp cbrt-unprod div-inv associate-/l/
add-log-exp
frac-2neg flip3-+ clear-num flip-+
frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
3 → 169
Calls
3 calls:
6.0ms
(/ (sqrt (+ b a)) b)
6.0ms
(/ (sqrt (+ b a)) a)
22.0ms
(* (/ (sqrt (+ b a)) b) (/ (sqrt (+ b a)) a))

series40.0ms

Counts
3 → 9
Calls
3 calls:
11.0ms
(/ (sqrt (+ b a)) b)
15.0ms
(/ (sqrt (+ b a)) a)
13.0ms
(* (/ (sqrt (+ b a)) b) (/ (sqrt (+ b a)) a))

simplify64.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05691407
125091292
250011263

prune113.0ms

Filtered
178 candidates to 112 candidates (37.1%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1771178
Fresh011
Picked101
Done022
Total1784182

Merged error: 0.1b

Counts
182 → 4

regimes145.0ms

Accuracy

1.5% (2.5b remaining)

Error of 4.1b against oracle of 1.6b and baseline of 4.2b

bsearch75.0ms

Steps
ItersRangePoint
9
-7.171407062873763e+179
-1.6144988170776345e+174
-7.848637757653449e+176

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1176

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.9s2545×body2560valid
2.0s3395×body1280valid
363.0ms1035×body640valid
203.0ms9526×pre80true
112.0ms1524×body80overflowed
77.0ms329×body320valid
44.0ms560×body80valid
21.0ms138×body160valid

Profiling

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