Details

Time bar (total: 11.7s)

sample111.0ms

Algorithm
intervals
Results
35.0ms77×body10240exit
21.0ms51×body1280valid
19.0ms348×body80valid
13.0ms51×body640valid
3.0ms15×body320valid
0.0ms3×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (34.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 28.5b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b
(exp (* (- 1.0 eps) x))
0.0b
(exp (* (+ 1.0 eps) x))
0.5b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite401.0ms

Algorithm
rewrite-expression-head
Rules
1798×associate-/l*
1679×add-sqr-sqrt
1627×*-un-lft-identity
1428×frac-sub
1346×times-frac
1134×associate-/l/
937×add-cube-cbrt
467×associate-/r*
290×difference-of-squares
175×distribute-lft-out
163×distribute-lft-out--
155×frac-2neg
153×clear-num
79×div-inv
42×flip3-+ flip-+
36×flip3-- flip--
27×exp-prod
14×add-log-exp
9×associate-*l*
7×add-exp-log sub-div
6×associate-*r* add-cbrt-cube
4×pow1 exp-to-pow
3×div-sub
2×diff-log div-exp *-commutative rem-exp-log unswap-sqr
1×cbrt-undiv sub-neg distribute-rgt-out-- sum-log associate--r-
Counts
4 → 1564
Calls
4 calls:
17.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
7.0ms
(exp (* (- 1.0 eps) x))
7.0ms
(exp (* (+ 1.0 eps) x))
209.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series258.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
19.0ms
(exp (* (- 1.0 eps) x))
17.0ms
(exp (* (+ 1.0 eps) x))
174.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify547.0ms

Algorithm
egg-herbie
Counts
1576 → 1576
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
0500163135

prune4.8s

Filtered
1576 candidates to 933 candidates (59.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New157241576
Fresh000
Picked101
Done000
Total157341577

Merged error: 0.6b

Counts
1577 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
0.2b
(* 0.5 (pow x 2))
5.4b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
26×*-un-lft-identity
20×associate-*r*
13×add-exp-log
12×unswap-sqr
11×associate-*l*
10×add-cube-cbrt
9×unpow-prod-down
8×add-log-exp
7×pow1 add-cbrt-cube
6×prod-exp distribute-lft-out--
5×difference-of-squares sqr-pow
4×cube-prod distribute-lft-out
3×unpow2
2×pow-to-exp diff-log pow-prod-down pow-exp associate--l+ *-commutative cbrt-unprod
1×+-commutative cube-mult sub-neg flip3-- unpow3 sum-log flip--
Counts
3 → 86
Calls
3 calls:
10.0ms
(* 0.33333333333333337 (pow x 3))
6.0ms
(* 0.5 (pow x 2))
23.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series98.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(* 0.33333333333333337 (pow x 3))
23.0ms
(* 0.5 (pow x 2))
37.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify47.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0309492
11252448
25001425

prune194.0ms

Filtered
95 candidates to 54 candidates (56.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New92395
Fresh033
Picked011
Done000
Total92799

Merged error: 0.6b

Counts
99 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

5.9b
(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
5.9b
(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
28.1b
(sqrt (* 0.5 (pow x 2)))
28.1b
(sqrt (* 0.5 (pow x 2)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
50×sqrt-prod
42×add-sqr-sqrt
22×*-un-lft-identity
16×associate-*r* unswap-sqr
14×add-cube-cbrt
12×pow1 rem-sqrt-square
10×unpow-prod-down
8×associate-*l*
6×sqrt-pow1 unpow2 sqr-pow
4×add-exp-log pow1/2 sqrt-div add-cbrt-cube distribute-lft-out add-log-exp
2×flip3-+ pow-prod-down *-commutative flip-+
Counts
4 → 104
Calls
4 calls:
13.0ms
(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
13.0ms
(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
7.0ms
(sqrt (* 0.5 (pow x 2)))
7.0ms
(sqrt (* 0.5 (pow x 2)))

series175.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
53.0ms
(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
33.0ms
(sqrt (* 0.5 (pow x 2)))
37.0ms
(sqrt (* 0.5 (pow x 2)))

simplify152.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0247596
1778538
24405534
35002534

prune372.0ms

Filtered
116 candidates to 80 candidates (69.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1151116
Fresh055
Picked101
Done011
Total1167123

Merged error: 0.6b

Counts
123 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
0.1b
(* 0.33333333333333337 (pow x 3))
10.6b
(+ (* (- (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)))
12.1b
(/ (+ (* (- (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0))) (+ (* (pow x 2) (+ (* 0.33333333333333337 x) 0.5)) 1.0))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
779×*-un-lft-identity
373×distribute-lft-out
364×associate-*l*
140×times-frac
126×swap-sqr
119×distribute-rgt-neg-in
61×add-sqr-sqrt
47×add-cube-cbrt
28×associate-/l*
24×associate-*r*
16×add-exp-log
10×add-cbrt-cube
8×pow1 unpow-prod-down cube-prod unswap-sqr
6×prod-exp add-log-exp
5×associate-/r*
4×associate-+r+ sqr-pow
3×+-commutative flip3-+ flip-+
2×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in unpow3 pow-prod-down pow-exp associate-/r/ *-commutative cbrt-unprod associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 293
Calls
4 calls:
7.0ms
(* 0.33333333333333337 (pow x 3))
7.0ms
(* 0.33333333333333337 (pow x 3))
87.0ms
(+ (* (- (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)))
110.0ms
(/ (+ (* (- (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0))) (+ (* (pow x 2) (+ (* 0.33333333333333337 x) 0.5)) 1.0))

series244.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* 0.33333333333333337 (pow x 3))
40.0ms
(* 0.33333333333333337 (pow x 3))
47.0ms
(+ (* (- (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)))
118.0ms
(/ (+ (* (- (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0))) (+ (* (pow x 2) (+ (* 0.33333333333333337 x) 0.5)) 1.0))

simplify114.0ms

Algorithm
egg-herbie
Counts
305 → 305
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04295205
120215036
250025001

prune416.0ms

Filtered
305 candidates to 86 candidates (28.2%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New3023305
Fresh235
Picked101
Done011
Total3057312

Merged error: 0.6b

Counts
312 → 7

regimes151.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.3b

bsearch151.0ms

Steps
ItersRangePoint
9
0.08433677106829839
715934.3120435103
1.9121598632801717

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04126
14126

end0.0ms

sample3.1s

Algorithm
intervals
Results
871.0ms1990×body10240exit
820.0ms1778×body1280valid
568.0ms9707×body80valid
358.0ms1274×body640valid
117.0ms630×body320valid
43.0ms379×body160valid