Details

Time bar (total: 8.5s)

sample81.0ms

Algorithm
intervals
Results
18.0ms169×body80valid
14.0ms295×body80nan
7.0ms29×body1280valid
5.0ms20×body1280nan
4.0ms21×body640valid
4.0ms19×body640nan
3.0ms18×body320valid
2.0ms19×body160valid
2.0ms10×body320nan
1.0ms6×body160nan

simplify97.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04114
110114
223414
352514
4101614
5170114
6362614
7500214

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b
(* (sqrt 2.0) t)
12.3b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.6b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
7×pow1
6×times-frac associate-*l* associate-/r* add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
24.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms
(* (sqrt 2.0) t)
19.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts
4 → 12
Calls
4 calls:
418.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
39.0ms
(* (sqrt 2.0) t)
213.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify63.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04461290
122061177
250021172

prune359.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize21.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (pow l 2) x)
5.0b
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
7.9b
(/ (pow t 2) x)
25.7b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 127
Calls
4 calls:
4.0ms
(/ (pow l 2) x)
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series372.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (pow l 2) x)
68.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
19.0ms
(/ (pow t 2) x)
266.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify45.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0377811
11351724
25001715

prune490.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
5.0b
(fma 2.0 (pow t 2) (fma 2.0 (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
7.9b
(/ (pow t 2) x)
25.7b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt times-frac
23×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
9×add-exp-log
8×associate-/l*
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×cbrt-prod div-exp associate-/r* sqrt-prod
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow1/3 pow-exp clear-num fma-udef div-inv
Counts
4 → 89
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(cbrt x)
75.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
160.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

simplify41.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0343834
11297719
25002708

prune428.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

localize30.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1))
5.0b
(fma 2.0 (pow t 2) (fma 2.0 (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
7.9b
(/ (pow t 2) x)
25.7b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
34×times-frac
29×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
18×div-exp prod-exp associate-/l*
13×add-cbrt-cube
6×cbrt-prod pow-to-exp 1-exp pow-exp sqr-pow
5×pow1
4×cbrt-undiv expm1-log1p-u associate-/r* log1p-expm1-u unpow2 add-log-exp
3×sqrt-prod cbrt-unprod
2×frac-2neg clear-num div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 127
Calls
4 calls:
16.0ms
(/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1))
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
4.0ms
(/ (pow t 2) x)
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

series488.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1))
85.0ms
(fma 2.0 (pow t 2) (fma 2.0 (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))) (* 4.0 (/ (pow t 2) x))))
21.0ms
(/ (pow t 2) x)
277.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05881297
123831171
250011149

prune554.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.8b

regimes493.0ms

Accuracy

77.2% (5.4b remaining)

Error of 9.4b against oracle of 4.1b and baseline of 27.7b

bsearch360.0ms

Steps
ItersRangePoint
2
4.258838753023189e+61
4.8864700944733366e+61
4.808016176792068e+61
7
-1.4478719089695824e-243
-3.729343639150035e-245
-9.1577416971198e-244
7
-5.388105193354488e-210
-3.2415088457474183e-211
-7.0895915203531395e-211
9
-2.884473285972568e+119
-1.203303521956221e+113
-3.093140357296897e+118

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05796
15796

end0.0ms

sample2.0s

Algorithm
intervals
Results
477.0ms10064×body80nan
258.0ms5025×body80valid
219.0ms905×body1280valid
193.0ms1028×body640valid
138.0ms601×body1280nan
114.0ms622×body640nan
91.0ms654×body320valid
48.0ms364×body320nan
38.0ms388×body160valid
18.0ms185×body160nan