Details

Time bar (total: 3.8s)

sample30.0ms

Algorithm
intervals
Results
11.0ms293×body80valid
3.0ms100×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: 25.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
4.5b
(* (* x y) z)
11.2b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.0b
(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:
3.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
14.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series201.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
27.0ms
(* (* x y) z)
84.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0368630
11941560
25001551

prune270.0ms

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))))
0.2b
(- (* z z) (* t a))
2.2b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.0b
(sqrt (- (* z z) (* t a)))

rewrite38.0ms

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

series223.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ z (sqrt (- (* z z) (* t a))))
36.0ms
(- (* z z) (* t a))
84.0ms
(* (* 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
04531067
12239963
25001942

prune339.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
0.3b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.6b
(* y (/ z (sqrt (- (* z z) (* t a)))))
26.0b
(sqrt (- (* z z) (* t a)))

rewrite48.0ms

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

series232.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
79.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
57.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0425829
11848729
25001717

prune293.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
0.2b
(- (* z z) (* t a))
2.2b
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
26.0b
(sqrt (- (* z z) (* t a)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
32×add-sqr-sqrt
30×add-cbrt-cube
27×prod-exp
25×associate-*r*
22×times-frac
21×*-un-lft-identity
19×pow1 add-cube-cbrt
15×cbrt-unprod
14×sqrt-prod
9×pow-prod-down
6×div-exp add-log-exp
5×unswap-sqr
4×expm1-log1p-u sqrt-div associate-*r/ associate-*l* log1p-expm1-u
3×cbrt-undiv rec-exp flip3-- 1-exp flip--
2×associate-/r/ un-div-inv *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff div-inv
Counts
4 → 118
Calls
4 calls:
20.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
30.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
5.0ms
(sqrt (- (* z z) (* t a)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
32.0ms
(- (* z z) (* t a))
86.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify64.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05011017
12458840
25002802

prune289.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.3b

regimes368.0ms

Accuracy

84.2% (3.0b remaining)

Error of 6.3b against oracle of 3.2b and baseline of 22.4b

bsearch59.0ms

Steps
ItersRangePoint
6
3.12575023105307e+49
2.1730398410930375e+50
1.340662233520948e+50
4
-1.7065839339117034e+154
-1.1362783514012957e+154
-1.3433926726132482e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02710
13310
23310

end0.0ms

sample785.0ms

Algorithm
intervals
Results
333.0ms8857×body80valid
100.0ms3025×body80nan