Details

Time bar (total: 3.8s)

sample27.0ms

Algorithm
intervals
Results
10.0ms271×body80valid
3.0ms98×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
3.8b
(* (* x y) z)
9.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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:
3.0ms
(- (* z z) (* t a))
7.0ms
(* (* x y) z)
12.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series203.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
83.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0368630
11941560
25001551

prune255.0ms

Filtered
98 candidates to 71 candidates (72.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
3.3b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite37.0ms

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:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
19.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
87.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04531067
12239963
25001942

prune318.0ms

Filtered
134 candidates to 91 candidates (67.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
2.0b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.3b
(* y (/ z (sqrt (- (* z z) (* t a)))))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite53.0ms

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:
3.0ms
(- (* z z) (* t a))
23.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
19.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
5.0ms
(sqrt (- (* z z) (* t a)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
87.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
60.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0425829
11848729
25001717

prune293.0ms

Filtered
114 candidates to 79 candidates (69.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (fma z z (- (* t a)))))
0.8b
(fma z z (- (* t a)))
3.3b
(* (* x y) (/ z (sqrt (fma z z (- (* t a))))))
26.3b
(sqrt (fma z z (- (* t a))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×sqrt-prod
22×associate-*r*
18×add-exp-log add-cbrt-cube
10×pow1
6×prod-exp associate-/r* cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ associate-*l* clear-num *-commutative fma-udef
Counts
4 → 110
Calls
4 calls:
3.0ms
(/ z (sqrt (fma z z (- (* t a)))))
0.0ms
(fma z z (- (* t a)))
13.0ms
(* (* x y) (/ z (sqrt (fma z z (- (* t a))))))
1.0ms
(sqrt (fma z z (- (* t a))))

series265.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ z (sqrt (fma z z (- (* t a)))))
40.0ms
(fma z z (- (* t a)))
93.0ms
(* (* x y) (/ z (sqrt (fma z z (- (* t a))))))
74.0ms
(sqrt (fma z z (- (* t a))))

simplify57.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0368965
11857862
25001843

prune304.0ms

Filtered
122 candidates to 84 candidates (68.9%)
Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.0b

regimes409.0ms

Accuracy

78.6% (4.1b remaining)

Error of 7.5b against oracle of 3.4b and baseline of 22.7b

bsearch77.0ms

Steps
ItersRangePoint
6
2.01645319072261e+30
2.864590415848179e+31
1.6894597162167635e+31
9
-8.13895866141384e+30
-1.7311009141305664e+23
-1.1453877187877288e+27

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03111
13611
24711
34711

end0.0ms

sample783.0ms

Algorithm
intervals
Results
330.0ms8888×body80valid
107.0ms2944×body80nan