Details

Time bar (total: 4.6s)

sample34.0ms

Algorithm
intervals
Results
10.0ms289×body80valid
3.0ms110×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
4.0b
(* (* x y) z)
11.2b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.9b
(sqrt (- (* z z) (* t a)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
9.0ms
(- (* z z) (* t a))
16.0ms
(* (* x y) z)
28.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
14.0ms
(sqrt (- (* z z) (* t a)))

series191.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
21.0ms
(* (* x y) z)
80.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
54.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0368630
11941560
25001551

prune266.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.0b
(- (* z z) (* t a))
2.5b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
27.9b
(sqrt (- (* z z) (* t a)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ associate-*l* prod-diff clear-num *-commutative
Counts
4 → 122
Calls
4 calls:
14.0ms
(/ z (sqrt (- (* z z) (* t a))))
8.0ms
(- (* z z) (* t a))
42.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
10.0ms
(sqrt (- (* z z) (* t a)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ z (sqrt (- (* z z) (* t a))))
30.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify69.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04531067
12239963
25001942

prune319.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.9b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
1.9b
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.2b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
27.9b
(sqrt (- (* z z) (* t a)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×expm1-log1p-u sqrt-div pow-prod-down log1p-expm1-u
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff div-inv
Counts
4 → 102
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
37.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
44.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
10.0ms
(sqrt (- (* z z) (* t a)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
51.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
81.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
56.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0425829
11848729
25001717

prune268.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.9b

localize13.0ms

Local error

Found 4 expressions with local error:

2.2b
(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
8.2b
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
28.8b
(cbrt (- (* z z) (* t a)))
28.8b
(cbrt (- (* z z) (* t a)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
34×add-exp-log associate-*r* add-cbrt-cube
33×add-cube-cbrt *-un-lft-identity
22×sqrt-prod
17×cbrt-prod
16×associate-*l*
13×prod-exp cbrt-unprod
11×pow1
8×cbrt-undiv div-exp unswap-sqr
6×cbrt-div
5×associate-*r/
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×flip3-- flip--
2×frac-times pow1/3 sqrt-div associate-*l/ associate-/r/ *-commutative div-inv
Counts
4 → 135
Calls
4 calls:
54.0ms
(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
55.0ms
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
5.0ms
(cbrt (- (* z z) (* t a)))
5.0ms
(cbrt (- (* z z) (* t a)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
133.0ms
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
79.0ms
(cbrt (- (* z z) (* t a)))
78.0ms
(cbrt (- (* z z) (* t a)))

simplify85.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07562247
133991947
250021937

prune496.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.9b

regimes444.0ms

Accuracy

83.3% (3.3b remaining)

Error of 6.4b against oracle of 3.1b and baseline of 22.8b

bsearch40.0ms

Steps
ItersRangePoint
0
1.281024336404866e+68
1.3038645461094304e+68
1.292444441257148e+68
9
-2.1605719851212306e+156
-8.864743291636389e+150
-1.1315032243066199e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02510
13110
23110

end0.0ms

sample893.0ms

Algorithm
intervals
Results
311.0ms8880×body80valid
95.0ms3095×body80nan