Details

Time bar (total: 9.1s)

sample95.0ms

Algorithm
intervals
Results
19.0ms34×body640valid
17.0ms353×body80nan
8.0ms157×body80valid
7.0ms31×body1280nan
7.0ms28×body1280valid
5.0ms25×body640nan
4.0ms25×body320valid
1.0ms10×body320nan
1.0ms12×body160valid
1.0ms6×body160nan

simplify87.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (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)
13.4b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.4b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite76.0ms

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×sqrt-div
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 diff-log pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
26.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
10.0ms
(* (sqrt 2.0) t)
13.0ms
(- (* (/ (+ 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)))

series1.9s

Counts
4 → 12
Calls
4 calls:
426.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
44.0ms
(* (sqrt 2.0) t)
214.0ms
(- (* (/ (+ 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)))

simplify61.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04171207
120511099
250021094

prune301.0ms

Filtered
92 candidates to 65 candidates (70.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.3b

localize20.0ms

Local error

Found 4 expressions with local error:

3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.1b
(/ (pow l 2) x)
9.7b
(/ (pow t 2) x)
28.8b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite33.0ms

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×associate-*r/ add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r* add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×sqrt-prod
2×cbrt-undiv pow-to-exp associate-+r+ frac-2neg pow-exp clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 130
Calls
4 calls:
9.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
4.0ms
(/ (pow l 2) x)
4.0ms
(/ (pow t 2) x)
10.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series272.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms
(/ (pow l 2) x)
18.0ms
(/ (pow t 2) x)
167.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05261067
12113984
25001978

prune464.0ms

Filtered
142 candidates to 97 candidates (68.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))))
9.7b
(/ (pow t 2) x)
28.8b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt
77×times-frac
56×unpow-prod-down
46×add-cube-cbrt *-un-lft-identity
37×associate-*r*
35×add-exp-log
24×unswap-sqr
22×cbrt-prod
18×sqr-pow
12×div-exp prod-exp
11×add-cbrt-cube unpow2
10×associate-*l*
9×associate-*r/
8×pow-to-exp pow-exp associate-/l*
6×add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×associate-/r* sqrt-prod
2×cbrt-undiv associate-+r+ cbrt-unprod div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 clear-num sum-log *-commutative
Counts
4 → 175
Calls
4 calls:
30.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
9.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))))
4.0ms
(/ (pow t 2) x)
10.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))))))

series344.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
89.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))))
18.0ms
(/ (pow t 2) x)
188.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))))))

simplify105.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
08512019
142561786
250011699

prune682.0ms

Filtered
187 candidates to 123 candidates (65.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

localize27.0ms

Local error

Found 4 expressions with local error:

16.3b
(cbrt (pow (cbrt l) 4))
16.3b
(cbrt (pow (cbrt l) 4))
16.3b
(cbrt (pow (cbrt l) 4))
28.8b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (* (cbrt (pow (cbrt l) 4)) (cbrt (pow (cbrt l) 4))) (* (cbrt (pow (cbrt l) 4)) (/ (pow (cbrt l) 2) x)))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
18×unpow-prod-down
15×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log sqrt-div associate-*r/ add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod sqr-pow
2×flip3-+ frac-add flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 71
Calls
4 calls:
2.0ms
(cbrt (pow (cbrt l) 4))
2.0ms
(cbrt (pow (cbrt l) 4))
2.0ms
(cbrt (pow (cbrt l) 4))
12.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (* (cbrt (pow (cbrt l) 4)) (cbrt (pow (cbrt l) 4))) (* (cbrt (pow (cbrt l) 4)) (/ (pow (cbrt l) 2) x)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
291.0ms
(cbrt (pow (cbrt l) 4))
283.0ms
(cbrt (pow (cbrt l) 4))
292.0ms
(cbrt (pow (cbrt l) 4))
191.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (* (cbrt (pow (cbrt l) 4)) (cbrt (pow (cbrt l) 4))) (* (cbrt (pow (cbrt l) 4)) (/ (pow (cbrt l) 2) x)))))))

simplify50.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03501116
114161072
250011044

prune398.0ms

Filtered
83 candidates to 65 candidates (78.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.6b

regimes453.0ms

Accuracy

75.6% (5.9b remaining)

Error of 9.8b against oracle of 3.9b and baseline of 28.0b

bsearch459.0ms

Steps
ItersRangePoint
8
1.245043086949984e+133
8.355688030489222e+136
1.3295537074089366e+133
8
3.9920941018400604e-199
1.0341623309317825e-196
8.363027552225931e-198
9
4.057362571362824e-285
4.0450842402039645e-278
5.316863584577416e-279
8
-2.3663462124314626e+100
-5.129643794534772e+97
-8.085419595728973e+99

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
073108
178108
281108
381108

end0.0ms

sample2.1s

Algorithm
intervals
Results
501.0ms10273×body80nan
256.0ms5121×body80valid
213.0ms859×body1280valid
197.0ms996×body640valid
151.0ms622×body1280nan
112.0ms583×body640nan
91.0ms639×body320valid
44.0ms320×body320nan
37.0ms385×body160valid
20.0ms198×body160nan