Details

Time bar (total: 7.1s)

sample47.0ms

Algorithm
intervals
Results
20.0ms272×body80valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05518
111618
232918
393518
4287618
5500118

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
0.1b
(* (+ (* z 3.13060547623) 11.1667541262) z)
2.2b
(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
29.9b
(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
10×pow1
9×associate-*r* associate-*l*
5×flip3-+ flip-+
4×associate-*r/ associate-*l/ prod-exp cbrt-unprod add-log-exp
3×times-frac pow-prod-down associate-/r* *-commutative unswap-sqr
2×cbrt-undiv div-exp associate-/r/ associate-/l/
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num div-inv associate-/l*
Counts
4 → 87
Calls
4 calls:
13.0ms
(* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
7.0ms
(* (+ (* z 3.13060547623) 11.1667541262) z)
15.0ms
(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
26.0ms
(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

series719.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
64.0ms
(* (+ (* z 3.13060547623) 11.1667541262) z)
162.0ms
(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
430.0ms
(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

simplify77.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
05731240
128061065
250011065

prune452.0ms

Filtered
99 candidates to 72 candidates (72.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (- (+ (* 3.13060547623 y) (/ (* t y) (pow z 2))) (* 36.527041698806414 (/ y z))))
0.2b
(* 36.527041698806414 (/ y z))
3.6b
(- (+ (* 3.13060547623 y) (/ (* t y) (pow z 2))) (* 36.527041698806414 (/ y z)))
14.0b
(/ (* t y) (pow z 2))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
21×add-sqr-sqrt
18×*-un-lft-identity times-frac add-log-exp
16×add-cube-cbrt
14×add-cbrt-cube
13×associate-*r*
8×associate-/r*
7×div-exp
6×pow1 unpow-prod-down
5×prod-exp sum-log
4×diff-log
3×cbrt-undiv associate-+r+ associate-*r/ associate-*l* cbrt-unprod
2×pow-to-exp sub-neg flip3-+ pow-exp associate--l+ frac-sub flip-+ div-inv unpow2 unswap-sqr sqr-pow
1×+-commutative associate-+r- flip3-- frac-2neg pow-prod-down clear-num *-commutative flip-- distribute-lft-out associate-/l*
Counts
4 → 101
Calls
4 calls:
8.0ms
(+ x (- (+ (* 3.13060547623 y) (/ (* t y) (pow z 2))) (* 36.527041698806414 (/ y z))))
6.0ms
(* 36.527041698806414 (/ y z))
9.0ms
(- (+ (* 3.13060547623 y) (/ (* t y) (pow z 2))) (* 36.527041698806414 (/ y z)))
6.0ms
(/ (* t y) (pow z 2))

series201.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(+ x (- (+ (* 3.13060547623 y) (/ (* t y) (pow z 2))) (* 36.527041698806414 (/ y z))))
23.0ms
(* 36.527041698806414 (/ y z))
55.0ms
(- (+ (* 3.13060547623 y) (/ (* t y) (pow z 2))) (* 36.527041698806414 (/ y z)))
35.0ms
(/ (* t y) (pow z 2))

simplify68.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0550772
12589718
25001718

prune336.0ms

Filtered
113 candidates to 75 candidates (66.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 36.527041698806414 (/ y z))
3.6b
(- (+ (* 3.13060547623 y) (/ t (/ (pow z 2) y))) (* 36.527041698806414 (/ y z)))
6.4b
(/ t (/ (pow z 2) y))
9.1b
(/ (pow z 2) y)

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
214×times-frac
123×add-sqr-sqrt
118×add-cube-cbrt *-un-lft-identity
48×unpow-prod-down
31×associate-/r*
24×add-exp-log
16×add-cbrt-cube unpow2 sqr-pow
13×associate-*r*
11×div-exp associate-/l*
9×add-log-exp
7×div-inv
6×pow1
5×cbrt-undiv
3×associate-*r/ associate-*l*
2×pow-to-exp frac-2neg diff-log pow-exp prod-exp clear-num frac-sub cbrt-unprod unswap-sqr
1×sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log associate-/r/ *-commutative flip-- flip-+
Counts
4 → 229
Calls
4 calls:
6.0ms
(* 36.527041698806414 (/ y z))
21.0ms
(- (+ (* 3.13060547623 y) (/ t (/ (pow z 2) y))) (* 36.527041698806414 (/ y z)))
8.0ms
(/ t (/ (pow z 2) y))
5.0ms
(/ (pow z 2) y)

series122.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* 36.527041698806414 (/ y z))
59.0ms
(- (+ (* 3.13060547623 y) (/ t (/ (pow z 2) y))) (* 36.527041698806414 (/ y z)))
27.0ms
(/ t (/ (pow z 2) y))
19.0ms
(/ (pow z 2) y)

simplify106.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09371751
145351518
250021518

prune703.0ms

Filtered
241 candidates to 162 candidates (67.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

8.0b
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
8.0b
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
22.7b
(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
24.7b
(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
66×times-frac
47×add-cube-cbrt *-un-lft-identity
42×sqrt-prod
24×associate-*r* associate-*l*
18×add-exp-log add-cbrt-cube
10×sqrt-div
9×unswap-sqr
8×pow1
6×flip3-+ associate-/r* associate-/r/ flip-+
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 150
Calls
4 calls:
11.0ms
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
11.0ms
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
46.0ms
(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
32.0ms
(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

series937.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
64.0ms
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
445.0ms
(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
359.0ms
(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

simplify99.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06734328
128913955
250013822

prune730.0ms

Filtered
162 candidates to 112 candidates (69.1%)
Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

regimes674.0ms

Accuracy

96.3% (1.0b remaining)

Error of 1.6b against oracle of 0.6b and baseline of 27.8b

bsearch273.0ms

Steps
ItersRangePoint
7
4.0285976431093624e+55
6.98082773152965e+57
7.35027383630455e+56
9
-3.855877503099219e+16
-133078281566.82077
-3.79207529877254e+16

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08049
18049

end0.0ms

sample1.1s

Algorithm
intervals
Results
806.0ms8865×body80valid