Details

Time bar (total: 5.9s)

sample32.0ms

Algorithm
intervals
Results
12.0ms285×body80valid
4.0ms106×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: 25.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
5.0b
(* (* x y) z)
8.7b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.9b
(sqrt (- (* z z) (* t a)))

rewrite71.0ms

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:
10.0ms
(- (* z z) (* t a))
17.0ms
(* (* x y) z)
28.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
14.0ms
(sqrt (- (* z z) (* t a)))

series193.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
21.0ms
(* (* x y) z)
81.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
55.0ms
(sqrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0368630
11941560
25001551

prune401.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.4b
(- (* z z) (* t a))
2.6b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.9b
(sqrt (- (* z z) (* t a)))

rewrite80.0ms

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))
43.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
11.0ms
(sqrt (- (* z z) (* t a)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ z (sqrt (- (* z z) (* t a))))
29.0ms
(- (* z z) (* t a))
79.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04531068
12233963
25002942

prune556.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize18.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
25.9b
(sqrt (- (* z z) (* t a)))
25.9b
(sqrt (- (* z z) (* t a)))
25.9b
(sqrt (- (* z z) (* t a)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
29×add-cbrt-cube
23×prod-exp cbrt-unprod
18×sqrt-div
13×associate-*r*
12×pow1 cbrt-div
11×add-sqr-sqrt
9×flip3-- sqrt-prod flip--
8×cbrt-undiv add-cube-cbrt *-un-lft-identity div-exp associate-/r/
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down
2×associate-*l/
1×times-frac associate-*l* *-commutative div-inv
Counts
4 → 98
Calls
4 calls:
105.0ms
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
13.0ms
(sqrt (- (* z z) (* t a)))
11.0ms
(sqrt (- (* z z) (* t a)))
11.0ms
(sqrt (- (* z z) (* t a)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
53.0ms
(sqrt (- (* z z) (* t a)))
57.0ms
(sqrt (- (* z z) (* t a)))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify70.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05151389
126181113
250011011

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
0.6b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.3b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.9b
(sqrt (- (* z z) (* t a)))

rewrite105.0ms

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))
38.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
44.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
10.0ms
(sqrt (- (* z z) (* t a)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(- (* z z) (* t a))
54.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
79.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
54.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0425829
11848729
25001717

prune431.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

regimes530.0ms

Accuracy

83.3% (3.2b remaining)

Error of 6.4b against oracle of 3.2b and baseline of 22.3b

bsearch181.0ms

Steps
ItersRangePoint
9
1.2335872890547797e+33
3.105913159301736e+42
2.224496559279278e+42
7
-4.0218020058701393e+49
-1.3475539460780654e+48
-3.9772643399440944e+49

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04129
14429
25229
35229

end0.0ms

sample1.0s

Algorithm
intervals
Results
572.0ms8898×body80valid
113.0ms2973×body80nan