Details

Time bar (total: 4.6s)

sample50.0ms

Algorithm
intervals
Results
27.0ms280×body80valid
7.0ms85×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
5.3b
(* (* x y) z)
9.1b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.4b
(sqrt (- (* z z) (* t a)))

rewrite26.0ms

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))
6.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series192.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
22.0ms
(* (* x y) z)
78.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0368630
11941560
25001551

prune275.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.4b
(- (* z z) (* t a))
3.5b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.4b
(sqrt (- (* z z) (* t a)))

rewrite35.0ms

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))
18.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ z (sqrt (- (* z z) (* t a))))
31.0ms
(- (* z z) (* t a))
79.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04531067
12239963
25001942

prune331.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
0.8b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.1b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.4b
(sqrt (- (* z z) (* t a)))

rewrite49.0ms

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))
18.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
21.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
51.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
78.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0425829
11848729
25001717

prune258.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
1.1b
(* x (* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
25.4b
(sqrt (- (* z z) (* t a)))
25.4b
(sqrt (- (* z z) (* t a)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
28×sqrt-div
27×add-exp-log add-cbrt-cube
16×add-sqr-sqrt associate-*r*
13×pow1
12×prod-exp cbrt-unprod
10×add-cube-cbrt *-un-lft-identity
8×flip3-- associate-/r/ flip--
6×associate-*l* sqrt-prod
5×associate-*r/
4×cbrt-undiv expm1-log1p-u frac-times times-frac div-exp pow-prod-down log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative unswap-sqr
1×div-inv
Counts
4 → 97
Calls
4 calls:
50.0ms
(* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
100.0ms
(* x (* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
81.0ms
(* x (* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
59.0ms
(sqrt (- (* z z) (* t a)))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04271197
11744935
25002908

prune312.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.7b

regimes384.0ms

Accuracy

85.8% (2.7b remaining)

Error of 5.8b against oracle of 3.1b and baseline of 22.3b

bsearch95.0ms

Steps
ItersRangePoint
8
2.961003054450564e+80
3.580192485387106e+83
3.43469549411493e+83
8
-2.9116578623443026e+156
-9.998794794503373e+152
-1.0932223177976295e+154

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02710
13310
23310

end0.0ms

sample1.4s

Algorithm
intervals
Results
815.0ms8884×body80valid
257.0ms2952×body80nan