Details

Time bar (total: 4.4s)

sample36.0ms

Algorithm
intervals
Results
13.0ms286×body80valid
3.0ms109×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: 24.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.6b
(* (* x y) z)
9.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.2b
(sqrt (- (* z z) (* t a)))

rewrite70.0ms

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:
8.0ms
(- (* z z) (* t a))
19.0ms
(* (* x y) z)
29.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms
(sqrt (- (* z z) (* t a)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
27.0ms
(* (* x y) z)
87.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0368630
11941560
25001551

prune264.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
1.4b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.2b
(sqrt (- (* z z) (* t a)))

rewrite82.0ms

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:
16.0ms
(/ z (sqrt (- (* z z) (* t a))))
8.0ms
(- (* z z) (* t a))
41.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
13.0ms
(sqrt (- (* z z) (* t a)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ z (sqrt (- (* z z) (* t a))))
37.0ms
(- (* z z) (* t a))
90.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04531067
12239963
25001942

prune331.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
0.6b
(- (* z z) (* t a))
1.4b
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
24.2b
(sqrt (- (* z z) (* t a)))

rewrite108.0ms

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:
18.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
8.0ms
(- (* z z) (* t a))
54.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
13.0ms
(sqrt (- (* z z) (* t a)))

series244.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
34.0ms
(- (* z z) (* t a))
92.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify47.0ms

Algorithm
egg-herbie
Counts
265 → 265
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09872740
150012395

prune546.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.4b
(* (* x y) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
24.2b
(sqrt (- (* z z) (* t a)))
24.2b
(sqrt (- (* z z) (* t a)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
28×sqrt-div
25×add-exp-log add-cbrt-cube
15×associate-*r*
11×pow1 prod-exp cbrt-unprod
10×add-sqr-sqrt
9×flip3-- flip--
8×add-cube-cbrt *-un-lft-identity associate-/r/
6×sqrt-prod add-log-exp
4×cbrt-undiv expm1-log1p-u frac-times div-exp log1p-expm1-u
3×times-frac associate-*r/ pow-prod-down
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/
1×sub-neg fma-neg diff-log associate-*l* prod-diff *-commutative div-inv
Counts
4 → 91
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
112.0ms
(* (* x y) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
11.0ms
(sqrt (- (* z z) (* t a)))
11.0ms
(sqrt (- (* z z) (* t a)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
90.0ms
(* (* x y) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
59.0ms
(sqrt (- (* z z) (* t a)))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0451999
12016786
25002777

prune304.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

regimes294.0ms

Accuracy

86% (2.7b remaining)

Error of 6.3b against oracle of 3.6b and baseline of 23.2b

bsearch70.0ms

Steps
ItersRangePoint
8
5.629384986291813e+133
2.372085431100728e+138
8.769862591561265e+136
8
-1.1755015533027564e+157
-4.376466409121207e+153
-1.3250618426451895e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02811
12911
23511
33511

end0.0ms

sample904.0ms

Algorithm
intervals
Results
316.0ms8844×body80valid
96.0ms3040×body80nan