Details

Time bar (total: 4.3s)

sample29.0ms

Algorithm
intervals
Results
10.0ms275×body80valid
3.0ms96×body80nan

simplify12.0ms

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: 25.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
5.0b
(* (* x y) z)
10.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite30.0ms

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:
4.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
15.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
112.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify57.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0368630
11941560
25001551

prune283.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
3.1b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite33.0ms

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

series220.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ z (sqrt (- (* z z) (* t a))))
35.0ms
(- (* z z) (* t a))
81.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify64.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04531067
12239963
25001942

prune353.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
2.2b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.3b
(* y (/ z (sqrt (- (* z z) (* t a)))))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite34.0ms

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:
4.0ms
(- (* z z) (* t a))
10.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
12.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
85.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
53.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0425829
11848729
25001717

prune297.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
0.8b
(- (* z z) (* t a))
3.1b
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
258×times-frac
143×add-sqr-sqrt
142×add-cube-cbrt *-un-lft-identity
71×associate-*r*
66×sqrt-prod
60×add-exp-log
30×add-cbrt-cube
22×associate-/r*
21×div-exp prod-exp
11×pow1
9×cbrt-undiv cbrt-unprod div-inv
6×rec-exp 1-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down associate-/l*
2×flip3-- sqrt-div associate-/r/ flip--
1×sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ associate-*l* prod-diff clear-num un-div-inv *-commutative inv-pow
Counts
4 → 253
Calls
4 calls:
9.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(- (* z z) (* t a))
25.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms
(sqrt (- (* z z) (* t a)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
32.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify47.0ms

Algorithm
egg-herbie
Counts
265 → 265
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09872740
150012395

prune555.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

regimes392.0ms

Accuracy

82.3% (3.5b remaining)

Error of 6.9b against oracle of 3.4b and baseline of 23.0b

bsearch184.0ms

Steps
ItersRangePoint
10
3.0886519766275007e+106
5.320008399497423e+116
1.3932528023672181e+110
9
5.1450817042009143e-194
2.3248318113166536e-186
1.1968985287902123e-192
11
-1.9460222259464434e-224
-1.69044388403838e-245
-1.4763620082139605e-232
1
-3.2219348736708655e+167
-3.0290001935999287e+167
-3.077233863617663e+167

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04727
14827
25127
35127

end0.0ms

sample846.0ms

Algorithm
intervals
Results
358.0ms8852×body80valid
118.0ms3042×body80nan